{ "cells": [ { "cell_type": "markdown", "id": "0", "metadata": {}, "source": [ "# How to compute a particle decay\n", "\n", "*For a student who has met Feynman rules and Dirac spinors, but has never carried a\n", "decay calculation all the way to a number.*\n", "\n", "A particle decays. What we measure is **how fast**: a lifetime, or equivalently a\n", "**width** $\\Gamma$, and the **fractions** that go into each final state. What theory\n", "provides is a Lagrangian. This notebook is the bridge between the two.\n", "\n", "We will do the calculation the way you would on paper — spin sums, Dirac traces,\n", "phase space — using `feynlag` to carry the algebra rather than to hide it. Only once\n", "we have built a width from scratch will we reach for the machine that does it in one\n", "line.\n", "\n", "**Roadmap**\n", "\n", "1. Widths, lifetimes and branching ratios\n", "2. The master formula\n", "3. Two-body phase space\n", "4. From a Feynman rule to an amplitude\n", "5. Squaring: why spin sums become traces\n", "6. Trace theorems, hands-on\n", "7. $h \\to \\tau\\tau$ and the $\\beta^3$ threshold\n", "8. Polarisation sums: $Z \\to \\ell\\ell$ and $W \\to \\ell\\nu$\n", "9. Chirality: why V−A gives exactly half\n", "10. The whole Standard Model at once\n", "11. Off-shell decays: reopening the closed channel\n", "12. Loop-induced decays and the complete Higgs picture\n", "13. Two ways to get it silently wrong\n", "14. Your own model: a $Z'$\n", "15. Recap" ] }, { "cell_type": "code", "execution_count": null, "id": "1", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 28 (\" '003DA5',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 29 (\" 'C0392B',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 30 (\" '1A6B3A',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 31 (\" 'FFBE00',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 32 (\" '3F6FD1',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 33 (\" '8E44AD',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 34 (\" 'E67E22',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 35 (\" '17A589',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 36 (\" '2C3E50',\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Missing colon in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 37 (\" 'CB4335'])\")\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Bad value in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 21 ('axes.edgecolor : #4A4A6A'): Key axes.edgecolor: '' does not look like a color arg\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Bad value in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 27 (\"axes.prop_cycle : cycler('color', [\"): Key axes.prop_cycle: \"cycler('color', [\" is not a valid cycler construction: Could not parse \"cycler('color', [\": '[' was never closed (, line 1)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Bad value in file PosixPath('/home/moises/.config/matplotlib/stylelib/ifunam.mplstyle'), line 95 ('patch.edgecolor : face'): Key patch.edgecolor: 'face' does not look like a color arg\n" ] } ], "source": [ "import sympy as sp\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from feynlag import *\n", "from feynlag.pheno import (\n", " DecayCalculator, DiracParticle, TwoBodyKinematics, collect_decay_vertices,\n", " ffs_squared, ffv_squared, kallen, scalar_offshell_vv_width,\n", " higgs_gammagamma_width, higgs_gg_width, higgs_zgamma_width,\n", " scalar_vv_s12_integral, two_body_momentum, two_body_phase_space,\n", " vvs_squared,\n", ")\n", "from feynlag.pheno.lorentz import contract_to_dots, dirac_trace, index, slashed\n", "\n", "sp.init_printing()" ] }, { "cell_type": "markdown", "id": "2", "metadata": {}, "source": [ "## 1. Widths, lifetimes and branching ratios\n", "\n", "An unstable particle has a survival probability that falls exponentially,\n", "$P(t) = e^{-\\Gamma t}$. The constant $\\Gamma$ is the **decay width**, and it is just an\n", "inverse lifetime,\n", "\n", "$$\\tau = \\frac{\\hbar}{\\Gamma}.$$\n", "\n", "Because we work in natural units, $\\Gamma$ carries units of **energy** — quoted in GeV,\n", "even though it describes a time.\n", "\n", "If several final states are available, each has its own **partial width** $\\Gamma_i$.\n", "They simply add, and the fraction going into channel $i$ is the **branching ratio**\n", "\n", "$$\\mathrm{BR}_i = \\frac{\\Gamma_i}{\\Gamma_\\text{tot}},\n", "\\qquad \\Gamma_\\text{tot} = \\sum_i \\Gamma_i, \\qquad \\sum_i \\mathrm{BR}_i = 1.$$\n", "\n", "The $Z$ boson makes this concrete." ] }, { "cell_type": "code", "execution_count": null, "id": "3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gamma(Z) = 2.4952 GeV\n", "tau(Z) = 2.638e-25 s\n" ] } ], "source": [ "hbar = 6.582119569e-25 # GeV*s\n", "Gamma_Z = 2.4952 # GeV, PDG total width\n", "\n", "print(f\"Gamma(Z) = {Gamma_Z} GeV\")\n", "print(f\"tau(Z) = {hbar / Gamma_Z:.3e} s\")" ] }, { "cell_type": "markdown", "id": "4", "metadata": {}, "source": [ "Around $2.6\\times10^{-25}$ s. That is the number we are going to compute — starting from\n", "nothing but a Lagrangian." ] }, { "cell_type": "markdown", "id": "5", "metadata": {}, "source": [ "## 2. The master formula\n", "\n", "Fermi's golden rule says a transition rate is *(matrix element)² × (density of final\n", "states)*. Made relativistic and specialised to one particle of mass $M$ decaying at\n", "rest, it reads\n", "\n", "$$\\boxed{\\;\\Gamma = \\frac{1}{2M}\\int \\overline{|\\mathcal{M}|^2}\\;\\mathrm{d}\\Phi_n\\;}$$\n", "\n", "Three pieces, and we will take them one at a time:\n", "\n", "- $1/2M$ — relativistic normalisation of the decaying state.\n", "- $\\mathrm{d}\\Phi_n$ — **phase space**: how much room the final state has. Pure\n", " kinematics; no dynamics at all (§3).\n", "- $\\overline{|\\mathcal{M}|^2}$ — the **squared amplitude**, where all the physics lives\n", " (§4–§9).\n", "\n", "The bar is not decoration. Real experiments do not prepare or measure spin here, so we\n", "\n", "- **sum** over final-state spins and polarisations (we do not care which one we got),\n", "- **average** over the decaying particle's, dividing by its $2s+1$ states — $1$ for a\n", " scalar, $3$ for a massive vector.\n", "\n", "Getting that factor of 3 wrong for a vector is one of the most common slips." ] }, { "cell_type": "markdown", "id": "6", "metadata": {}, "source": [ "## 3. Two-body phase space\n", "\n", "For a two-body final state the integral collapses to something you can write down. In\n", "the rest frame the two daughters come out back to back with equal and opposite momenta,\n", "so once you fix their common magnitude $|k|$ there is nothing left to integrate but an\n", "overall solid angle.\n", "\n", "Energy conservation fixes $|k|$ through the **Källén triangle function**\n", "\n", "$$\\lambda(x,y,z) = x^2+y^2+z^2-2xy-2yz-2zx,\n", "\\qquad |k| = \\frac{\\sqrt{\\lambda(M^2,m_1^2,m_2^2)}}{2M},$$\n", "\n", "and the whole phase-space factor becomes\n", "\n", "$$\\int\\mathrm{d}\\Phi_2 \\;\\longrightarrow\\; \\frac{\\sqrt{\\lambda(M^2,m_1^2,m_2^2)}}{16\\pi M^3}\\,\n", "\\quad\\text{(after the }1/2M\\text{)}.$$" ] }, { "cell_type": "code", "execution_count": null, "id": "7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Kallen lambda(M^2, m1^2, m2^2):\n" ] }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left(M - m_{1} - m_{2}\\right) \\left(M - m_{1} + m_{2}\\right) \\left(M + m_{1} - m_{2}\\right) \\left(M + m_{1} + m_{2}\\right)$" ], "text/plain": [ "(M - m₁ - m₂)⋅(M - m₁ + m₂)⋅(M + m₁ - m₂)⋅(M + m₁ + m₂)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "daughter momentum |k|:\n" ] }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{\\sqrt{M^{4} - 2 M^{2} m_{1}^{2} - 2 M^{2} m_{2}^{2} + m_{1}^{4} - 2 m_{1}^{2} m_{2}^{2} + m_{2}^{4}}}{2 M}$" ], "text/plain": [ " __________________________________________________\n", " ╱ 4 2 2 2 2 4 2 2 4 \n", "╲╱ M - 2⋅M ⋅m₁ - 2⋅M ⋅m₂ + m₁ - 2⋅m₁ ⋅m₂ + m₂ \n", "─────────────────────────────────────────────────────\n", " 2⋅M " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "the full phase-space factor sqrt(lambda)/(16 pi M^3):\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbgAAAAvCAYAAACR3t/8AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAOp0lEQVR4Ae2d65XUOBOGmzkTAMtmwGbAJQIgA3aJAMhgOfyCf5wlA5YIWMgANgIuGex+EcBOBvO9j0blkdVy291ty9Pt0jlqyWXd6lVJpZJl97Xz8/PVmO7ly5fvVd7DMcv0shwBR8ARcAQcgW0RON02w6b0Um63uK/w2qZ0fs8RcAQcAUfAEZgagVEVnBr7h/yzqRvt5c+DgBYu11Xz81j7zRg+Fv1snhYtp9YlYC8ev8rfXkKv1u7P2vXN0Ycl+RlNwalws96+1WauxFjtNsxVX2XB/UP1PTVeFX+j+Ff5X4y2pNCxH6+3heXvKi3MIeOVeqVLqj2WatdXFfwu+TkZsRWs7Ktbb12MjcjXVS8KwX0W/a9q7A95lM4U7onquZ8UjMV+U7QlTUwJ+yvHPkVjx3iUqX93zH6o2WqPpdr1VeuXTfIzigWnCtiuYqIrWm+iP9F9Jl+bHH8V7cMmBHSfFR0TKNtfn+Tf5Xl0TXmzDgy1Ad5Nsd9RHAWDwqmFBYL7Xh6McGAG7VZXG0Kq3X6w3r7slnX8XOLPsR8f1qolqg/Z9maB9GfViguVbStPhSK2IdUeS7Xr2waLndP2yc8oCk6t2/jsTY1AeP9UaCcsmZg6ndIh8HdjApShTd5NHtFmHxhqA3y8UfjAGqY4WPAs4YF8qd1jY1FNcMVPPglR97+iF5W5YTJFqDod+5mwH7k/WYy9lmc8z+Z2kad9Gqv6qo6l2vXtg82WeTfKz8mWha0lj4KB9bY2maeJY7qPomGR9T2zwRIKbkO5gTFLN1OIMmOSb5zaizUHjyjzohsTC5XFwoH6zFVROqqTRQivg8x1KMCx3xN79eF9eXZXZnGqG/nZuJNTsWE7ydMY7as9lsaoT2XMKjvgrjb0ys/eCk71MKG/osIex3YiSpAtxUaB5XnUaAbcX/KWPk8yiLG1TNMQaOM/anO++oTP66Lf7KjWeNsbi7R81VdF6US+mBBuK54q17Q5U8cd+/2xR25z2Z2630L5UYZuKJz1EUPC7K7ylBSxfbT2WBqxvtlkB5QjH73yc7p9l1zmUCUweUdhy4q5TNGKMRlibfAM57fWnXiheygEBP6GPGVj8bVcTNPLWCvTdBcoMp51nXVUAQ8lNwoWacERl8mVTqyHZ4xhWzZerxTWnqgc+7iAmgH7VPR2jTM2flHbkVlcGCvx+rPC2pbdrvJ00fodfsUj8121sVS7vh0g2SbLIPnZS8GpNZycHGK9pQ3/RxddE/9DdQL78bZtgtDlbhBjeaYprtVODs6UHJbUSvf7nk3ti0WoW/VsHCi6z+qUNvFc87E8CwgWJd/lUVQflQbcSfNIHkecU4JNHyhOPbwawKDkPo5y7JBNINT4Uf2O/XzY7y1P6j/GRjM+omwx7l8pflZDhtI6hsqT0u3NO/WqnEFjqXZ9KSZTxcfgSWUMkp+dFZwqQNGgkHonN6WhM+3oeljpQ5NvVv2Ks59qD17NOmgGgIGtdIMYs/S1Q7WPiT8onFLduj8aFpQfy+tTOhx4QSlhEb+VZ4Uc+k0hmP+nkEmFAyNGpz94jviTvDn6kH63vgx05RliwVsZk4Vqh2M/GbqtgseSp1Co+g3FFsa8QhZVLLhqW3AtBrlQG0ryNBbvQ8dS7frWcJiAMBZPoWnqp075WVNwSswERucy4W1yFGrbC5vScY9Vj1kCptQQHlN2eZ1pevIX3SbGihnqEFEKH9S21x3VpbyNgcXGgaJ2UJ9t9aJcUWJp227EdvLM0PoIEvTQL/H+SvdTZWfkqxQ69hP3hmRgNHmypqpMFlm2uDXyVQhb8jQm70PGUu36agA+Jk/WXpXZKT+nlohQCVE6f8tzyKNvVf5U6ftOQ6qY4MIzJ2LK802eKJOtuSeihUlXIXQmVpuULc1aqLSdjK0lFkHpKRf+WhN3KW1C4zWFNUsyud9ElQ5LCgXStX1G2lGxUF19SueL0pzJwzPY5v1Kn+PyCYbTkYP4Drl7fmL9jn0bp1rYI5coptyxiFmpb3KZgMw4Lcnx7PI0tSxFTEpjuTbvteuD9ZYT1mPKDmVX5alRcGKELSkch0CwzkpCz/2V0vISNozv6s6UMSjHWG+6HWEDMbUmdq2nlU91Ue8kx9pVNphx+MW2Wlp1b7iYFIvIM9UHXHWd40p7mcxoR+o4CJQrvZXSXRedeyxwBmMZyx+cPm1IX1xlHz32EffnEQtbHD6OuG6ESGmKY1l0xjyPClKLvq8sk5PZ5CnyPIkswbzKL8pTrJckVXgfsz6VxbjdWn6UbzTZAbjaPJ1QKU4Vf8ArGrYdFaeTuxyT26BBoXSsUlvPbHTN1hwDC9BXCm2rjksmXCyO0awHCp3Sqa1MFJwIa1a8isOfTUShel3PicUjNaKEKYO1pfTUTmj0TVjE6Nr6ifYjF1wHmsJZndq2COwFcs3Pgg3p0yXLU23e967vGOVnCE+NgjOJ1oTBZIfCeWa0NNR9JrjU4kpvl+JrE6gSUf4d+ScqLy+rlL5U7pWgqf1M+ncV5ngx8f7IGlnirRYWa3WrzSgplHC+HcyqDauO7Vbuh9c6FIfGwiZdkOhyHqe2LAZ7IcxYoQ/NsRBlEQUGc7gly1Nt3veuTwJydPIzhKfTjpHB4OETVPflW6t70ZnIt9keKFl7n1UGCqCl3OJgZdLNJ1yRrp5Te5n8eRD9SfF8yxbscit3FixiO8H1XYaiKa68j0lrNNqcK++smPqXkaclYc+i40t9pNdrXLI81eZ9xPqOUX56eSoqOIHKC9lM2ExsNtGtRAtKSeHZuti3KUrD5MPqklUmW5QoTHumw1YZx9aDJaCQFQqNtdWovfw46BmD8s3lUMQoudJ2brMdKP7mxoI2Yo01bYqAocisTyIpBCxwOFzzu8Jccafp5owvCnv1Rd5PjJdSn9bok8XKk8Ctzfso9R2j/Azh6dr5+XlxQCgzExsTN8+WTBGhqO7pulfBFQt14lEgoP5nocMzoaGnaI+C76vChHBnIciiiRO5O4/F2I8sQPOdhqqsxnYsUp7m4F117i0/sd2zy44JahdPJ5agELKKx4XtKRWAlRWOeAaq/zgCjkB1BDQOWdEzNvdSbrHhKMedFWQsw4MDQmBE+bkysrOJp+IWJf2lTGx/sD2JFcd2SNi2UujOEXAEZkAgDmTbvmeMouwIdzr0o3zN44cZ2PEqKyMQ5WUU+bkqstPHU6eCi9ij1DgswXYICm+ngVS5H706R+DoEIgDOTwXV9yeVbPwvHIHgI4O/CNg6BjlZwhPnc/grE9VCB8EZqXYPIuzex4uC4EoUEyqbFczyfLs5rvosz7DURuO3gnj/8Tk9ZxR0a/ltEO5XrI81eb9SOWnd0wMUXBsUfJxzOYl5kMZQN5OR8ARcAQcgeUi0KvglguNc+4IOAKOgCNwyAicHHLjve2OgCPgCDgCjkAXAtdevHhRfhGuK4fTHQFHwBFwBByBA0DAtygPoJO8iY6AI+AIOALbI+BblNtj5jkcAUfAEXAEDgABV3AH0EneREfAEXAEHIHtEeh70Xv7Ej2HI+AIzIZAfL+K9xT5qybeX70r/0r0/EPbIrtzBI4bAVdwx92/zt3yEODrQ3x1KPz7gEL+EeJv+Z+WB4VzvHQEXMEtXQIWzr8UwKAvqysdiiN170QbxSpSOXxMgQ8pYHnh+Kui1n8lXpAvf3UfxUWb+Ogt35SkPeR5JZ+6n3WBNefOEVgcAq7gFtflzrAUAZ+8eivPxH9Hnq28olNa7vEtVj5SGz5OrJBr/Ch/F6TysLb4D0bK5K+IOtujeyulQymz9YhDGTYfTVY8V7rhr40ukvqvI7AsBFzBLau/nVshICWA1RM+Pac4lpB9vLiED0oH66hRIrpGQY764XGVj1LjT1yx4voUJ0o5uKxdRl6JDl+P5NM/Gm7ue8QRWAICJ0tg0nl0BHZBQEoC6wfl1/o3bdH5NuuDXcrckAfFhhJFcTYKLE+vetnO/Eve0udJwrXS8QHse/K0FWXnzhFYHAKu4BbX5c7wFgjwzwlnUhBYfFM7/sAU5fZFvrhFqfvQSXNDHisSi6/TxXbzdzr8W/YmK7WzDL/hCBwyAr5Feci9522fGgEsKU4kohzY7vsuz/bhe9HSLcuVrjnwgXWF4ulyPGdDaW5y/D1VVxkPlf+1PPXg8jaQ73/y95TGnsWdkVAOXowWCP7jCBw7Am7BHXsPO3/7IGCK5o4UBodMUC4oKBQc25fBKW4nLHmuh2d78LY8abGgiGOhFZWb6FhmX+Vx4dlepF1Q9Ktr6rOt0rA9KlpLYekaZfZDPpShEMdWJnS2Nd05AotCwC24RXW3MzsUASkLU263FDfFYtlRFm9Fx4JCOX1WPBzrV8jzLg52YPmF52QKW4pI93MX0kWiKSesRlN2oS0qB0WFS9NfUC5/UbDPlRZrE3dXHuVqeQPRfxyBJSDgCm4Jvew87oOAKZy0DKwttgmx7FByqQLjUAcWHA7lkivHcCP7QQGFdAq/yXMbxWnuiZWpEDoKr/j8jfy6l7bHyvDQEVgcAieL49gZdgQGICBFYRaPhaVcqRJaKQ9WV5oe6y+9LpVRopEnvCqg/GxNpi99Y73hWs/fLkj+6wg4AikCruBSNDzuCLQRQIlcb5NaV7l1xzO21LJqKcBWzngRlaI9f7MklHtT90LdCtN6eP7GyU630gwtDx2BDgRcwXUA42RHQAi8kS8pKQ6NoGQaKyoqI3tHrQFPdLO4GloW4X5TTryHQuPUI1uTqfXG7VJ66O4cAUcgQ8AVXAaIXy4OAb7ViLtxEVz+RuXySaGdklwpjlX1m/zjy5QhhnLjYAnbi6nreyH8qfKkFhp5P8tTT0u5KR1boNBTK1GX7hwBR6CEwGmJ6DRH4NgRkLLgE1w4s7A4+o+i+aiwORiiOIdGeFEaaw6HIkzfMwtE/aDIeCUgdS0Fld5QedSPwmIrki3K9JNabD/yWkJQfAppI9ufpMdxj/oeK8wVakjgP46AI7Ba/R8tKfUNSnB2SQAAAABJRU5ErkJggg==", "text/latex": [ "$\\displaystyle \\frac{\\sqrt{M^{4} - 2 M^{2} m_{1}^{2} - 2 M^{2} m_{2}^{2} + m_{1}^{4} - 2 m_{1}^{2} m_{2}^{2} + m_{2}^{4}}}{16 \\pi M^{3}}$" ], "text/plain": [ " __________________________________________________\n", " ╱ 4 2 2 2 2 4 2 2 4 \n", "╲╱ M - 2⋅M ⋅m₁ - 2⋅M ⋅m₂ + m₁ - 2⋅m₁ ⋅m₂ + m₂ \n", "─────────────────────────────────────────────────────\n", " 3 \n", " 16⋅π⋅M " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M, m1, m2 = sp.symbols('M m_1 m_2', positive=True)\n", "\n", "kin = TwoBodyKinematics(M, m1, m2)\n", "\n", "print(\"Kallen lambda(M^2, m1^2, m2^2):\")\n", "display(sp.factor(kallen(M**2, m1**2, m2**2)))\n", "\n", "print(\"\\ndaughter momentum |k|:\")\n", "display(two_body_momentum(M, m1, m2))\n", "\n", "print(\"\\nthe full phase-space factor sqrt(lambda)/(16 pi M^3):\")\n", "display(kin.phase_space())" ] }, { "cell_type": "markdown", "id": "8", "metadata": {}, "source": [ "Note the factorised form of $\\lambda$: it contains $\\big(M-(m_1+m_2)\\big)$. The moment\n", "$M$ drops below $m_1+m_2$ that factor changes sign, $\\sqrt\\lambda$ becomes imaginary and\n", "the decay is **closed**. Watch this happen." ] }, { "cell_type": "code", "execution_count": null, "id": "9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# equal-mass daughters: how much room is left as they get heavier?\n", "x = np.linspace(0.0, 0.5, 400) # x = m/M\n", "ps = np.sqrt(np.clip(1 - 4*x**2, 0, None)) # sqrt(lambda)/M^2 for m1 = m2 = m\n", "\n", "fig, ax = plt.subplots(figsize=(6.4, 4.0))\n", "ax.plot(x, ps, lw=2, color='#1f77b4')\n", "ax.axvline(0.5, ls='--', color='0.4')\n", "ax.text(0.492, 0.55, 'threshold $m = M/2$', rotation=90,\n", " ha='right', va='center', color='0.3')\n", "ax.set_xlabel(r'daughter mass $m/M$')\n", "ax.set_ylabel(r'phase space $\\sqrt{\\lambda}/M^2$')\n", "ax.set_title('Two-body phase space closes at threshold')\n", "ax.set_xlim(0, 0.52); ax.set_ylim(0, 1.05)\n", "ax.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "10", "metadata": {}, "source": [ "The curve reaches zero at $m = M/2$ with a **vertical tangent** — the square root. This\n", "is pure kinematics: we have not said one word about the interaction. Any decay, of any\n", "particle, through any force, is switched off by this factor as the daughters get heavy\n", "enough. Dynamics can only change *how fast* the curve falls, never *that* it falls." ] }, { "cell_type": "markdown", "id": "11", "metadata": {}, "source": [ "## 4. From a Feynman rule to an amplitude\n", "\n", "Now the dynamics. `feynlag` reads vertices straight off a Lagrangian — that is what the\n", "other tutorials in this series do. Let us build the electroweak Standard Model with one\n", "lepton generation and simply ask it for its vertices.\n", "\n", "(The build is condensed here; `SM_Feynman_Rules_Tutorial.ipynb` walks it stage by stage.)" ] }, { "cell_type": "code", "execution_count": null, "id": "12", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "model built\n" ] } ], "source": [ "GW, G1, VEV, MH = 0.6535, 0.3580, 246.0, 125.25\n", "MZ, MW, MTAU = 91.1876, 80.377, 1.77686\n", "\n", "# The electroweak scaffold — gauge groups, Higgs, potential and the\n", "# physical-basis rotations — comes ready-made from feynlag.models. (The\n", "# SM_Feynman_Rules_Tutorial builds all of this by hand, stage by stage.)\n", "ew = electroweak_scaffold(gw=GW, g1=G1, v=VEV, mh=MH)\n", "SU2L, U1Y, H = ew.SU2L, ew.U1Y, ew.H\n", "gw, g1, v = ew.gw, ew.g1, ew.v # convenience aliases for later cells\n", "ytau = ExternalParameter(\"ytau\", sp.sqrt(2) * MTAU / VEV, positive=True)\n", "\n", "# the one piece of physics that IS the point here: a tau lepton + its Yukawa\n", "Ll = WeylFermion(\"Ll\", reps={SU2L: 2, U1Y: -sp.Rational(1, 2)}, chirality=\"L\",\n", " nflavors=1, component_names=[\"nuL\", \"tauL\"])\n", "tauR = WeylFermion(\"tauR\", reps={U1Y: -1}, chirality=\"R\", nflavors=1,\n", " component_names=[\"tauR\"])\n", "\n", "i = sp.Symbol(\"i\", integer=True)\n", "L = Lagrangian()\n", "ew.add_higgs(L) # kinetic + potential\n", "L.add(fermion_gauge_current(Ll, i) + fermion_gauge_current(tauR, i), sector=\"gauge\")\n", "\n", "nuLb, tauLb = Ll.bar_components\n", "nuL, tauL = Ll.components\n", "tauRb, tauRc = tauR.bar_components[0], tauR.components[0]\n", "yuk = -ytau.s * (Bilinear(nuLb[i], diracPR, tauRc[i]) * H.components[0]\n", " + Bilinear(tauLb[i], diracPR, tauRc[i]) * H.components[1])\n", "L.add(yuk + sp.conjugate(yuk), sector=\"yukawa\")\n", "\n", "model = Model(\"SM_lepton\", gauge_groups=ew.gauge_groups,\n", " fields=ew.fields + [Ll, tauR],\n", " parameters=ew.parameters + [ytau], lagrangian=L)\n", "model.solve_tadpoles([ew.mu2])\n", "\n", "# physical basis: the standard Weinberg + W± rotations, in one call\n", "phys = to_physical_basis(model, ew)\n", "Z, A, Wp, Wm, h, G0, Gp, Gm = (phys.Z, phys.A, phys.Wp, phys.Wm,\n", " phys.h, phys.G0, phys.Gp, phys.Gm)\n", "cmap, bosons = phys.cmap, phys.bosons\n", "\n", "# a Dirac fermion is two Weyl fields in feynlag: say which legs are one particle\n", "tau, taubar, nutau, nutaubar = sp.symbols(\"tau taubar nu_tau nu_taubar\")\n", "particle_map = {tauL[i]: tau, tauRc[i]: tau, tauLb[i]: taubar, tauRb[i]: taubar,\n", " nuL[i]: nutau, nuLb[i]: nutaubar}\n", "print(\"model built\")" ] }, { "cell_type": "markdown", "id": "13", "metadata": {}, "source": [ "Every fermion vertex feynlag produces has the same shape,\n", "\n", "$$\\Gamma \\;=\\; g_L P_L + g_R P_R \\qquad\\text{or}\\qquad\n", "\\Gamma^\\mu \\;=\\; \\gamma^\\mu\\,(g_L P_L + g_R P_R),$$\n", "\n", "a **scalar** sandwich or a **vector** current, each with a left- and a right-handed\n", "coupling. So a vertex is fully specified by the pair $(g_L, g_R)$. Here they are for\n", "the $Z$ and the Higgs:" ] }, { "cell_type": "code", "execution_count": null, "id": "14", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "FFV taubar tau Z\n", " g_L = I*(g1 - gw)*(g1 + gw)/(2*sqrt(g1**2 + gw**2))\n", " g_R = I*g1**2/sqrt(g1**2 + gw**2)\n", "FFV nu_taubar nu_tau Z\n", " g_L = I*sqrt(g1**2 + gw**2)/2\n", " g_R = 0\n", "FFS taubar tau H0_r\n", " g_L = -sqrt(2)*I*ytau/2\n", " g_R = -sqrt(2)*I*ytau/2\n" ] } ], "source": [ "vertices = collect_decay_vertices(model, bosons, fermion_sectors=(\"gauge\", \"yukawa\"),\n", " conjugate_map=cmap, particle_map=particle_map)\n", "\n", "for vtx in vertices:\n", " if vtx.vertex_type in (\"FFV\", \"FFS\") and (Z in vtx.particles or h in vtx.particles):\n", " legs = \" \".join(str(p) for p in vtx.particles)\n", " print(f\"{vtx.vertex_type} {legs}\")\n", " print(f\" g_L = {sp.factor(sp.expand(vtx.g_left))}\")\n", " print(f\" g_R = {sp.factor(sp.expand(vtx.g_right))}\")" ] }, { "cell_type": "markdown", "id": "15", "metadata": {}, "source": [ "Read these off against what you know:\n", "\n", "- $Z\\tau\\tau$ has $g_L \\ne g_R$ — the weak interaction is **chiral**.\n", "- $Z\\nu\\nu$ has $g_R = 0$ exactly. There is no right-handed neutrino to couple to.\n", "- $h\\tau\\tau$ has $g_L = g_R = -i\\,y_\\tau/\\sqrt2 = -i\\,m_\\tau/v$ — the Higgs is\n", " **not** chiral, and it couples in proportion to mass.\n", "\n", "(The factors of $i$ are the Feynman-rule $i$; they cancel when we square.)" ] }, { "cell_type": "markdown", "id": "16", "metadata": {}, "source": [ "## 5. Squaring: why spin sums become traces\n", "\n", "The amplitude for a scalar decaying to a fermion pair is\n", "\n", "$$\\mathcal{M} = \\bar u(p_1)\\,\\Gamma\\, v(p_2),$$\n", "\n", "a single complex number once the spinors are fixed. We need $|\\mathcal{M}|^2$ summed\n", "over the final spins. Using $\\mathcal{M}^* = \\bar v(p_2)\\,\\bar\\Gamma\\, u(p_1)$ with\n", "$\\bar\\Gamma = \\gamma^0\\Gamma^\\dagger\\gamma^0$,\n", "\n", "$$\\sum_\\text{spins}|\\mathcal{M}|^2\n", "= \\sum_{s_1,s_2}\\bar u(p_1)\\Gamma v(p_2)\\,\\bar v(p_2)\\bar\\Gamma u(p_1).$$\n", "\n", "Now the key step. The **completeness relations**\n", "\n", "$$\\sum_s u(p)\\bar u(p) = \\not p + m, \\qquad \\sum_s v(p)\\bar v(p) = \\not p - m$$\n", "\n", "replace each spinor pair by a $4\\times4$ matrix. What is left is a product of matrices\n", "sandwiched between $\\bar u \\dots u$ with the *same* index summed at both ends — which is\n", "by definition a **trace**:\n", "\n", "$$\\boxed{\\;\\sum_\\text{spins}|\\mathcal{M}|^2\n", "= \\mathrm{Tr}\\big[(\\not p_1 + m_1)\\,\\Gamma\\,(\\not p_2 - m_2)\\,\\bar\\Gamma\\big]\\;}$$\n", "\n", "This is why every decay calculation in the textbooks turns into trace algebra. The\n", "spins are gone; only momenta and masses remain." ] }, { "cell_type": "code", "execution_count": null, "id": "17", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sum u ubar = p1_slash + m1 : m_1 + p1(L_0)*GammaMatrix(-L_0)\n", "sum v vbar = p2_slash - m2 : -m_2 + p2(L_0)*GammaMatrix(-L_0)\n" ] } ], "source": [ "mu, nu = index('mu'), index('nu')\n", "p1, p2 = kin.p1, kin.p2\n", "\n", "# the spin sums themselves\n", "print(\"sum u ubar = p1_slash + m1 :\", slashed(p1, mu) + m1)\n", "print(\"sum v vbar = p2_slash - m2 :\", slashed(p2, nu) - m2)" ] }, { "cell_type": "markdown", "id": "18", "metadata": {}, "source": [ "## 6. Trace theorems, hands-on\n", "\n", "Four facts do almost all the work:\n", "\n", "$$\\mathrm{Tr}[\\text{odd number of }\\gamma] = 0, \\qquad\n", "\\mathrm{Tr}[\\gamma^\\mu\\gamma^\\nu] = 4g^{\\mu\\nu},$$\n", "\n", "$$\\mathrm{Tr}[\\gamma^\\mu\\gamma^\\nu\\gamma^\\rho\\gamma^\\sigma]\n", "= 4\\left(g^{\\mu\\nu}g^{\\rho\\sigma} - g^{\\mu\\rho}g^{\\nu\\sigma} + g^{\\mu\\sigma}g^{\\nu\\rho}\\right),\n", "\\qquad \\mathrm{Tr}[P_{L,R}] = 2.$$\n", "\n", "The first one is why mass terms and momentum terms never mix: each $\\not p$ brings one\n", "$\\gamma$, so a term with an odd number of them dies.\n", "\n", "Let us evaluate the simplest non-trivial trace, $\\mathrm{Tr}[\\not p_1 \\not p_2]$, in the\n", "two steps you would do by hand." ] }, { "cell_type": "code", "execution_count": null, "id": "19", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "step 1 -- apply Tr[gamma^mu gamma^nu] = 4 g^{mu nu}:\n", " 4*p1(L_0)*p2(-L_0) i.e. 4 p1.p2\n" ] } ], "source": [ "chain = slashed(p1, mu) * slashed(p2, nu)\n", "\n", "step1 = dirac_trace(chain)\n", "print(\"step 1 -- apply Tr[gamma^mu gamma^nu] = 4 g^{mu nu}:\")\n", "print(\" \", step1, \" i.e. 4 p1.p2\")" ] }, { "cell_type": "markdown", "id": "20", "metadata": {}, "source": [ "The result is still written with an abstract contracted index. The second step puts the\n", "momenta **on shell** — a two-body final state has only three independent invariants, and\n", "all of them are fixed by the masses:\n", "\n", "$$p_1^2 = m_1^2, \\qquad p_2^2 = m_2^2, \\qquad\n", "p_1\\!\\cdot\\! p_2 = \\frac{M^2 - m_1^2 - m_2^2}{2},$$\n", "\n", "the last from squaring $M^2 = (p_1+p_2)^2$." ] }, { "cell_type": "code", "execution_count": null, "id": "21", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "on-shell dot products:\n", " p1.p1 = m_1**2\n", " p2.p2 = m_2**2\n", " p1.p2 = M**2/2 - m_1**2/2 - m_2**2/2\n", "\n", "step 2 -- substitute them:\n", " Tr[p1_slash p2_slash] = 2*M**2 - 2*m_1**2 - 2*m_2**2\n" ] } ], "source": [ "print(\"on-shell dot products:\")\n", "print(\" p1.p1 =\", kin.dot(p1, p1))\n", "print(\" p2.p2 =\", kin.dot(p2, p2))\n", "print(\" p1.p2 =\", kin.dot(p1, p2))\n", "\n", "step2 = contract_to_dots(step1, kin.dot)\n", "print(\"\\nstep 2 -- substitute them:\")\n", "print(\" Tr[p1_slash p2_slash] =\", sp.expand(step2))" ] }, { "cell_type": "markdown", "id": "22", "metadata": {}, "source": [ "So $\\mathrm{Tr}[\\not p_1\\not p_2] = 4\\,p_1\\!\\cdot\\!p_2 = 2M^2 - 2m_1^2 - 2m_2^2$: a\n", "plain function of the masses. Every squared amplitude below is built from exactly these\n", "two steps." ] }, { "cell_type": "markdown", "id": "23", "metadata": {}, "source": [ "## 7. $h \\to \\tau\\tau$ and the $\\beta^3$ threshold\n", "\n", "Assemble the scalar case. With $\\Gamma = g_LP_L + g_RP_R$ the conjugate is\n", "$\\bar\\Gamma = \\bar g_L P_R + \\bar g_R P_L$ (bare projectors swap under\n", "$\\gamma^0(\\cdot)^\\dagger\\gamma^0$), and pushing projectors through with\n", "$P_{L,R}\\not p = \\not p P_{R,L}$, $P_LP_R = 0$ splits the trace cleanly in two:\n", "\n", "- the **chirality-diagonal** terms keep the momenta and lose the masses,\n", "- the **chirality-mixing** terms keep $m_1m_2$ and lose the momenta.\n", "\n", "$$\\sum|\\mathcal{M}|^2 = 2(|g_L|^2+|g_R|^2)\\,(p_1\\!\\cdot\\!p_2)\n", "- 4\\,m_1m_2\\,\\mathrm{Re}(g_L\\bar g_R).$$" ] }, { "cell_type": "code", "execution_count": null, "id": "24", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "summed |M|^2 for S -> f fbar:\n" ] }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle - 2 g_{L}^{2} m_{f}^{2} + g_{L}^{2} m_{h}^{2} - 4 g_{L} g_{R} m_{f}^{2} - 2 g_{R}^{2} m_{f}^{2} + g_{R}^{2} m_{h}^{2}$" ], "text/plain": [ " 2 2 2 2 2 2 2 2 2\n", "- 2⋅g_L ⋅m_f + g_L ⋅mₕ - 4⋅g_L⋅g_R⋅m_f - 2⋅g_R ⋅m_f + g_R ⋅mₕ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gL, gR = sp.symbols('g_L g_R', real=True)\n", "mh, mf = sp.symbols('m_h m_f', positive=True)\n", "\n", "kin_h = TwoBodyKinematics(mh, mf, mf)\n", "amp2 = ffs_squared(gL, gR, kin_h)\n", "print(\"summed |M|^2 for S -> f fbar:\")\n", "display(sp.factor(sp.expand(amp2)))" ] }, { "cell_type": "code", "execution_count": null, "id": "25", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{m_{f}^{2} \\left(- 2 m_{f} + m_{h}\\right)^{\\frac{3}{2}} \\left(2 m_{f} + m_{h}\\right)^{\\frac{3}{2}}}{8 \\pi m_{h}^{2} v^{2}}$" ], "text/plain": [ " 2 3/2 3/2\n", "m_f ⋅(-2⋅m_f + mₕ) ⋅(2⋅m_f + mₕ) \n", "─────────────────────────────────────\n", " 2 2 \n", " 8⋅π⋅mₕ ⋅v " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "matches m_h m_f^2 beta^3 / (8 pi v^2)? True\n" ] } ], "source": [ "# the Higgs is not chiral: g_L = g_R = m_f/v\n", "vv = sp.Symbol('v', positive=True)\n", "width_h = sp.simplify(ffs_squared(mf/vv, mf/vv, kin_h) * kin_h.phase_space())\n", "display(sp.factor(width_h))\n", "\n", "beta = sp.sqrt(1 - 4*mf**2/mh**2)\n", "expected = mh * mf**2 * beta**3 / (8*sp.pi*vv**2)\n", "print(\"matches m_h m_f^2 beta^3 / (8 pi v^2)?\",\n", " sp.simplify(sp.expand(width_h - expected)) == 0)" ] }, { "cell_type": "markdown", "id": "26", "metadata": {}, "source": [ "$$\\Gamma(h\\to f\\bar f) = \\frac{N_c\\, m_h\\, m_f^2\\,\\beta^3}{8\\pi v^2},\n", "\\qquad \\beta = \\sqrt{1 - 4m_f^2/m_h^2}.$$\n", "\n", "Two things to notice.\n", "\n", "**$\\Gamma \\propto m_f^2$.** The Higgs couples proportionally to mass, so it decays\n", "preferentially to the heaviest thing it can reach. That single fact drives the entire\n", "Higgs search programme.\n", "\n", "**$\\beta^3$, not $\\beta$.** One power of $\\beta$ is the phase space from §3. The other\n", "two come from the *dynamics*: a CP-even scalar decaying to a fermion pair produces them\n", "in a **P-wave** ($\\ell=1$), and an $\\ell$-wave amplitude is suppressed by\n", "$\\beta^{\\ell}$ near threshold — $\\beta^{2\\ell}$ in the rate. A CP-**odd** scalar decays\n", "S-wave and would give plain $\\beta$." ] }, { "cell_type": "code", "execution_count": null, "id": "27", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b = np.linspace(0, 1, 400)\n", "\n", "fig, ax = plt.subplots(figsize=(6.4, 4.0))\n", "ax.plot(b, b**3, lw=2, color='#1f77b4', label=r'CP-even (P-wave): $\\beta^3$')\n", "ax.plot(b, b, lw=2, color='#d62728', ls='-.', label=r'CP-odd (S-wave): $\\beta^1$')\n", "ax.set_xlabel(r'velocity $\\beta=\\sqrt{1-4m_f^2/m_h^2}$ (0 = threshold)')\n", "ax.set_ylabel(r'$\\Gamma$ / (its $\\beta\\!\\to\\!1$ value)')\n", "ax.set_title('Near threshold the CP of the parent is visible in the lineshape')\n", "ax.legend()\n", "ax.grid(alpha=0.3)\n", "ax.set_xlim(0, 1); ax.set_ylim(0, 1.02)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "28", "metadata": {}, "source": [ "Right at threshold ($\\beta\\to0$) the CP-even curve leaves the axis much more slowly. This\n", "is not an academic distinction: the shape of a threshold turn-on is one of the ways the\n", "spin and CP of a new particle get pinned down experimentally." ] }, { "cell_type": "markdown", "id": "29", "metadata": {}, "source": [ "## 8. Polarisation sums: $Z\\to\\ell\\ell$ and $W\\to\\ell\\nu$\n", "\n", "A decaying **vector** brings two changes. Its amplitude carries a polarisation vector,\n", "$\\mathcal{M} = \\epsilon_\\mu \\bar u\\,\\Gamma^\\mu v$, so squaring needs the polarisation sum\n", "\n", "$$\\sum_\\text{pol}\\epsilon_a\\epsilon^*_b = -g_{ab} + \\frac{P_aP_b}{M^2},$$\n", "\n", "and because a massive vector has three states we must **average**, dividing by 3.\n", "Everything else is the same trace algebra." ] }, { "cell_type": "code", "execution_count": null, "id": "30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "matches the closed form? True\n" ] }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{\\sqrt{- 2 m + m_{Z}} \\sqrt{2 m + m_{Z}} \\left(g_{L}^{2} m^{2} - g_{L}^{2} m_{Z}^{2} - 6 g_{L} g_{R} m^{2} + g_{R}^{2} m^{2} - g_{R}^{2} m_{Z}^{2}\\right)}{24 \\pi m_{Z}^{2}}$" ], "text/plain": [ " ____________ ___________ ⎛ 2 2 2 2 2 2 2 ↪\n", "-╲╱ -2⋅m + m_Z ⋅╲╱ 2⋅m + m_Z ⋅⎝g_L ⋅m - g_L ⋅m_Z - 6⋅g_L⋅g_R⋅m + g_R ⋅m - ↪\n", "────────────────────────────────────────────────────────────────────────────── ↪\n", " 2 ↪\n", " 24⋅π⋅m_Z ↪\n", "\n", "↪ 2 2⎞ \n", "↪ g_R ⋅m_Z ⎠ \n", "↪ ───────────\n", "↪ \n", "↪ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mZ = sp.Symbol('m_Z', positive=True)\n", "m = sp.Symbol('m', positive=True)\n", "\n", "kin_Z = TwoBodyKinematics(mZ, m, m)\n", "width_V = sp.simplify(ffv_squared(gL, gR, kin_Z) * kin_Z.phase_space())\n", "\n", "betaZ = sp.sqrt(1 - 4*m**2/mZ**2)\n", "closed = (mZ*betaZ/(24*sp.pi)) * ((gL**2 + gR**2)*(1 - m**2/mZ**2)\n", " + 6*gL*gR*m**2/mZ**2)\n", "print(\"matches the closed form?\", sp.simplify(sp.expand(width_V - closed)) == 0)\n", "display(sp.factor(width_V))" ] }, { "cell_type": "markdown", "id": "31", "metadata": {}, "source": [ "$$\\Gamma(V\\to f\\bar f) = \\frac{M\\beta}{24\\pi}\n", "\\left[(g_L^2+g_R^2)\\Big(1-\\frac{m^2}{M^2}\\Big) + 6\\,g_Lg_R\\frac{m^2}{M^2}\\right].$$\n", "\n", "Note the $g_Lg_R$ term: it needs **both** chiralities *and* a mass. It is the piece that\n", "will bite us in §13.\n", "\n", "Now put in the Standard Model's own couplings and compare with the PDG." ] }, { "cell_type": "code", "execution_count": null, "id": "32", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "$Z \\to \\nu\\bar\\nu$ Gamma = 0.1679 GeV\n", "$Z \\to \\tau^+\\tau^-$ Gamma = 0.0844 GeV\n" ] } ], "source": [ "g, gp = gw.s, g1.s\n", "gZ = sp.sqrt(g**2 + gp**2)\n", "\n", "# SM neutral-current couplings (massless limit for the leptons)\n", "couplings = {\n", " r'$Z \\to \\nu\\bar\\nu$': (gZ/2, 0), # purely left-handed\n", " r'$Z \\to \\tau^+\\tau^-$': ((gp**2 - g**2)/(2*gZ), gp**2/gZ),\n", "}\n", "vals = {g: GW, gp: G1}\n", "\n", "rows = []\n", "for label, (cl, cr) in couplings.items():\n", " w = ffv_squared(cl, cr, TwoBodyKinematics(mZ, 0, 0)) * TwoBodyKinematics(mZ, 0, 0).phase_space()\n", " rows.append((label, float(sp.simplify(w).subs(vals).subs(mZ, MZ))))\n", "\n", "for label, w in rows:\n", " print(f\"{label:26s} Gamma = {w:.4f} GeV\")" ] }, { "cell_type": "code", "execution_count": null, "id": "33", "metadata": {}, "outputs": [ { "data": { "image/png": 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nodFoqrXfrKwsJCQkKNI3gycREVEViIuLw927d2XbOnXqhN27d5dZr0ePHtiyZUsVjqx8JY1dF7rMz1Aq0temTZsQHBwME5MHJ3wrOk9DuXjxIpo3b674HxqP9ltQUIB27dohPj6+yvvmqXYiInoi1X1/p6L9Xfv8Fb3Kd+/eHZ988glGjhypVz1fX1/Y29vrVcfQKjr2x5lGo8F7772Hb775Rtr2NM6zIhwcHDB69GjMnDkTv/zyS5X2xSOeREREBhYfH4/CwkIkJibi7NmzOH/+vFaZxMTEEk8VL1u2DF27dpVtu3fvHq5evVrujR0Pn34urf2H+7969SqEEHqNPS0tDQkJCeWeHr5x4wbS09P17l/fMg87f/48bt26VeK+bdu24f79++jZsyeA0udZvIYajQbx8fFISkqStXP9+nWtbY/SpUx5SmqjqKgIZ8+eRXZ2tlb5c+fOab3e+owjODgYW7duRWJiYsUHrQMGTyIiIgMLCQlBWloavvvuO7z++usYNmyYtC8qKgre3t7o1KkTnJycMH78eFndh0+1CyEwadIkODk5oUePHnBycsLs2bNL7bdTp06YPn16me1fuHABLVu2RKNGjdC+fXvUqVMHERER5Y799u3b6NGjB7y9vdGtWzc4ODjIjh4Wi4yMRO3atdGxY0e4uLhg0qRJsuBYXv+6lnmYRqPBqFGjMHDgwFLD+datWxEQECA9Cqi0eXbq1AnvvvsuvLy80LNnT/z0008AgL1798LHxwfPP/88WrVqBV9fXxw9elTWhy5lylNWG0ZGRhg8eDCWLl0qq3P8+HE0a9YMqampUhv16tVD586d0bp1a53G4evri9q1ayM8PFyv8eqLwZOIiMjANm/eDBcXF3zyySc4e/YsYmJipH379u3DgQMHkJCQgBMnTuCHH35AVFRUie1ER0cjNDQUFy5cwJUrV5CcnAxzc/MyjzaW1X5RURHeeOMNNGzYEOnp6UhJScHIkSMRFBQkHZ0saexCCPTt2xf169dHSkoKEhISEB0djZkzZ2Lfvn2y/sPCwhAZGYl//vkHx44dw48//oiff/5Z5/51KfOwvLw8DBgwAKdPn0Z0dDS8vLxKXJejR4+iZcuWOr1Ge/bswR9//IHLly8jJCQEV65cwWuvvYZFixbh9u3bSEpKwrhx4/Daa69JRx91KVMeXdoYOnQo1q9fL6u3fv16dOjQAfXq1ZPaWLhwIf755x/cvn1b53G0adMGhw8f1mmsFcXgSUREpKC33noLderUAQC0aNECzZo1Q2xsbIlls7OzYWZmJj2Kz8zMDB9++GGZD/Auq/2//voLp0+fxqJFi2BqagoAmD17NkxNTbFx48ZS2zx8+DBOnDiBUaNGISEhARcuXICZmRk6deqEbdu2ycqOHj0aTZs2BQC0bt0aw4cPx8qVK3XuX58xZmVloWfPnrh79y72798PZ2fnUueQlJQER0fHUvc/bMKECfDx8ZG+XrFiBZo2bYrGjRvjwoULOH/+PF566SWkp6fj2LFjOpcpjy5tDBkyBHFxcTh58iSAB0d7N27ciDfffLPS43Bycqr0JQLl4c1FRERECqpdu7bsa2tra6jV6hLL9uzZE506dYK3tzcCAwPRvXt3BAUFwcHBoULtX7lyBTVr1pSCKQCYmprC19cXV65cKbXNCxcuwNjYuMSbcBo2bCj7ukmTJrKvmzZtKp2+1aV/fcY4bdo0ODo64uLFizA3Ny/zMUlmZma4f/9+qfsf5u3tLfv6woULiIuLw8CBA2Xb69WrJx1F1KVMeXRpw9vbGy+88ALWrVuHNm3aYO/evUhPT0dQUJCsjUGDBkEIIT1/U5dx5Ofnw9zcXKexVhSDJxER0WPK1NQUv/32GxISEhAVFYWNGzdizpw5OHnyJDw8PPRuz9raGvn5+bJAAgA5OTmwtrYutZ6ZmRkAICYmptxgkpubK/v64bZ16V+fMU6dOhXff/89Zs6ciUWLFpU5Lm9vb9y8ebPMMsUePaJcfHS3rOsfdSlTHl3bGDp0KObPn4+FCxdi/fr16Nmzp/THSHEb27dv1/sjMxMTE9G4ceMKj18XPNVORERUBSwsLCr98YLFR+i8vb0xZswYREREQKPRYP/+/RVqr1WrVigoKMDBgwelbUlJSTh37hxat25d6tg7duwIjUaDsLCwUsdY7NGx7du3T2pbl/51HSPw4Gjqvn37sG7dOrz77rtlzv3FF1/EkSNHZNt0fY06deqE6OhoJCcny7ZrNBoUFRXpXMYQ/QDA4MGDkZqaih07diAsLEw6zV6ZcRQVFeH48eNaT1QwNAZPIiKiKtC4cWP89ttvOHnyZImPU9LFmjVrMGjQIISFhSEmJgaLFy9GTk4O/Pz8KtRe/fr1ERwcjJEjR2L79u3Yt28fBgwYgObNm6Nfv36ljr1evXqYMmUKJkyYgK+//hpHjx7Fli1bMGDAAPz666+yPsLDwzFnzhwcPnwYH3zwAfbu3Yv3339f5/51HWOxh8NnSEhIqXMfMWIEoqOjZTco6foajR8/HnXr1kVgYCDCwsJw5MgRrFy5Eq1bt0ZWVpbOZcqjaxsODg7o2bMn/vOf/8DIyAh9+vTRaqNHjx7Ytm2bzuOIjIyEmZkZevXqpdNYK4qn2omIiKrAokWLMHv2bIwdOxbAg9PUjRs3hp2dnaycj4+P7KaYhx8gP2bMGNSqVQtr167FzZs34ePjg6ioKDRp0qTEZ1vq0v53332HRYsW4csvv8T9+/fRqVMnfPTRRzAy+vdYVEljX7x4Mfz8/LBhwwb89NNP8PHxwfDhw9G3b19Z/xMnTsSRI0cwY8YM1KxZE3v27JHdTa5L/7qUeXiuzZo1w969exEcHIwff/wRo0aN0lqbli1bolu3bggNDcWMGTP0eo2sra1x6NAhLFmyBEuWLEFBQQFatWqFTZs2SWV1KfMoS0tLNG3aVPokJX3aGDt2LD744AMMHToUFhYWWmNdvHgxvv76axQWFmq18Wi/ALB8+XJMmjRJ1lZVUAldn8pKFZaVlQVbW1uEhYVJdyY+y4QQ0Gg0MDY21vm6k6cZ1+NfSq1FQEBAlbVtSEVFRUhOToazs7PsF+6zJC8vDwkJCfD29pZuHtHnmrWnmRCC6/EQXdYjLi4OEyZMQEREhHTH/NNKn/fH1atXERwcjD179sDS0rLEMg9/Lz4aTotzTmZmJmxsbMrsi0c8iYiI6Jng6+tb4etjn2Y+Pj44cOCAIn09m39CExEREZHiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEi+MlFRET0RNq7d6+i/en7UasvvfQSzp07B+DBZ2N7e3tj/PjxGDBggNZ+CwsLODo6ok2bNhgxYgTat2+v1V5KSgqWLVuGvXv34s6dO3BycoKvry/Gjx+PF154oZKzI1IGj3gSERFVgTt37qBnz544cuQIdu3ahRdffBEDBw7Eli1btPbv3bsXCxcuhKWlJTp37oy5c+fK2jp//jxatGiBw4cPY9asWYiIiMCyZcvg7++P9957D4cOHaqOKRLpjUc8iYiIqkiNGjXg4eEBAPjwww8RHh6ODRs2SEc9H95ft25ddOrUCa1atcLw4cPRo0cPdOjQAUIIDB06FF5eXoiIiICR0YNjRj4+PmjVqhVGjhyJoqKi6pkgkZ54xJOIiEghNWvWRG5ubpll3nzzTdSuXRs///wzAODUqVOIjY3FzJkzpdD5KGNjY4OPlagqMHgSEREpIDo6Gn/88Qe6d+9eZjmVSoWmTZvi0qVLACBdB9qkSZMqHyNRVWPwJCIiqiKhoaHw8PCAg4MDevfujbfffhtTpkwpt56JiQk0Gg0ASP81NzeX9iclJcHT0xPe3t7w9PTEl19+WSXjJzI0XuNJRERURYKCgvDxxx9Ld63r6urVq9Kd6t7e3gCA+Ph4eHp6AgCcnJzw119/obCwEN26dUNmZqbhB09UBXjEk4iIqIoU3zykT+j866+/EBcXh1dffRUA0KFDB7i5uWH58uVSGWNjY3h4eMDDw4PXd9IThcGTiIjoMZCfn4+tW7diwIAB6NWrF/r37w8AMDMzw/Lly7FlyxZMmjQJSUlJUp0rV64gOzu7uoZMpDeeaiciIqomoaGh2Lx5MwoLC5GZmYlGjRrhvffew9tvvw2VSiWV69OnD6KjozFnzhzUqVMHlpaWUKlUsLW1xfDhwzFx4sRqnAWR7hg8iYjoiaTvJwkpLSIiQnZDUEn779+/D+DBjUN2dnYwNTUttXzHjh2xd+9eFBQUICMjA3Z2dlCpVDAxMZGFVKLHGYMnERFRFXB2dq7U/tKYmprC2dkZQggUFhZWqA2i6vJUXeM5fPhw6a9HIiIiInq8PFXB89KlS/zYMCIiIqLHlF6n2jUaDTIyMkpvzMQEdnZ2lR0TERERET2F9Aqe+/fvx+uvv661vfhuvICAAERGRhpscLpYvny59Gyzy5cvo3379lCpVPDz88OqVasq1GZcXByCgoJK3Hfw4EHUrFmzwuMlIiIielbpFTwDAgKQmpoq25abm4tXX30Vp0+fxsKFCw06OF3069cPzz//PIAH13iuXLkSZmZmqFGjRoXbrFOnDlavXl3iPisrqwq3S0REFSOEqO4hED3TDPU9WKm72nNzc9G7d2/ExsYiKioKLVu21LmuEKLUxz/cvXsXAwcOLHGfmZkZdu7cKdV1dXWFq6srgAehsEWLFrCwsCix7ttvv42LFy+WuO+LL75A27ZtAQCWlpZo1aqVznMhIqKqUfx4oZycnFJ/thNR1cvJyQGAMh/5pYsKB8+8vDz07dsXJ0+eRFRUlF5BTa1Wo3379liwYIH0yQwPy8nJkY5injhxAseOHcN//vMfAICDg0OFn1fm6ekJOzs7ZGZm4ptvvsGECRPg4OAAAPDy8qpQmyXJz89Hfn6+9HVWVhYAwN/fn9fAAigqKkJycjKcnZ1hZPRU3d9WIVyPf3Et6FHGxsaws7NDcnIyhBAwMzODqakpn1sJSI9T4nM8H+B6yBlqPYQQyMnJQXJyMuzs7Cr9Ea0qUYFjp3l5eejTpw9OnDiBvXv3ok2bNiWWS0tLK/XQ7B9//IFRo0bhvffew8yZM0vta/Lkybh8+TJ27dpV7rguX76M+vXrl7vAkZGR6NWrF7Kzs8t8uG9Fffzxx5g7d67W9uIH/j7rGC7kuB7/4lrIcT0eEEIgKSkJGRkZKCoqgpGREYMFHqwL1+NfXA85Q6+HnZ0dXF1dS2wrKysLtra2yMzMhI2NTZnt6B088/Ly0K9fPxw9ehR79+6VTk+XxNXVtcyH26rVahQUFODEiROlhtfOnTujS5cuWLBggT7DLNMXX3yBDRs24PTp0wZr82ElHfH09PSE15RfAHPrKunzSWIEgca1BC5kqFAE/nDgevxLybW49vkrVdq+ITB4yhUUFCApKQkODg5cDzx4f6SlpXE9/h/XQ86Q62FqalrmkU59gqdep9rz8/Ol0BkZGVlm6ASApKSkUvetXr0a06ZNw/fff19q6BRC4PTp05gyZYo+wyzXyZMnS+3TEMzNzavkSCoR0bPM2NgYpqamsLCwYLDAg2DB9fgX10PucV0PnUeSn5+P/v3748iRI4iIiICfn1+FO1Wr1di0aRP27t1b6k1EAJCYmAi1Wo1mzZpVuK+SxMXFGbxNIiIiIiqbTkc8CwoK8NprryE6OhqbN2+Gt7e31mOV7OzsYGKi2wHUmjVrYufOnTr1CwCnTp2Cra2tdPd6ZRUUFODKlSu4fPkyGjRoYJA2iYiIiKhsOh3xjI2NxdGjR2FlZYXhw4ejUaNGWv9u3bpl8MF5e3vjnXfeQUhICL766iuDtTtnzhxER0eX+DB8IiIiIqoaOh2ifO6557SOcCrl66+/xtdff23QNgcPHozBgwcbtE0iIiIiKtvjc7UpERERET3VGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKcKkugfwLImd0wN2dnbVPYxqV1RUhOTkZDg7O8PIiH/7cD3+xbUgInq68Sc7ERERESmCwZOIiIiIFMHgSURERESKYPAkIiIiIkUweBIRERGRIhg8iYiIiEgRDJ5EREREpAgGTyIiIiJSBIMnERERESmCwZOIiIiIFMHgSURERESKYPAkIiIiIkUweBIRERGRIhg8iYiIiEgRDJ5EREREpAgGTyIiIiJSBIMnERERESmCwZOIiIiIFMHgSURERESKYPAkIiIiIkUweBIRERGRIhg8iYiIiEgRDJ5EREREpAgGTyIiIiJSBIMnERERESmCwZOIiIiIFMHgSURERESKYPAkIiIiIkUweBIRERGRIkyqewDPkujoaNSoUaO6h1HthBDQaDQwNjaGSqWq7uFUO67Hv7gWclwPOa6H3JO4HgEBAdU9BKpmPOJJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCJPqHkBpkpKSsHHjxlL3u7i44I033qjycdy9exfr1q2TvjY3N8fYsWOrvF8iIiKip81jGzzv3LmDa9euaW0/ffo0oqOjMW7cOEWCZ35+Pi5evCh9bWVlVeV9EhERET2NHtvg2bJlSyxdulS2LSYmBj/99BN69OiBr776yiD9FBYWIjU1FY6OjjAxebAcqampsLKygpWVFWrWrInZs2fD2dkZAFBUVISkpCRZeSIiIiIq3xNzjefJkycRGBiI5557Dtu3b4eFhYXOdf/66y8IIUrcd/PmTbi5ueHIkSPStg8//BBTpkwBAGzduhW1a9dGYWEhAEClUiEwMBAbNmyo+GSIiIiInkFPRPA8deoUAgIC0LZtW71Dp1qtxoQJExAUFITc3Fyt/e7u7jAyMsKNGzekbQEBAYiIiAAAeHp6QqPR4Pbt2wAeBM9u3bpJ+4mIiIhIN4/9ueLY2FgEBASgTZs2CA8Ph6WlZYnlvv76axQVFZW4b/Dgwfjiiy/QuXNn7N69G05OTtI+U1NTODs74+bNm9K2oqIi5OXlAQA8PDwAPDgy6unpqbW/JPn5+cjPz5e+zsrKAgD4+/vDzs5Oh1k/3YqKipCcnAxnZ2cYGT0Rf/tUKa7Hv7gWclwPOa6HHNeDnkSPdfA8ffo0AgIC0KpVK/z222+lhk4AuH79OjQaTYn7irenpqaWGBg9PDxkRzzXrl2Lnj17SvsA4MaNG+jQoQNycnKwdetWzJ07t9SxfPbZZ2XuJyIiInoWPbbB88yZM+jevTtatGhRbugEgEWLFpW4PTs7GwMGDEDz5s0RFhYm3ST0sIeD5+rVq/HXX3/h5MmTAB48PsnR0VHaP3nyZLi7u2P48OGljuWDDz7AtGnTpK+zsrLg6emJVnMjAHPrsif+DDCCQONaAhcyVCiCqrqHU+24Hv/iWshxPeS4HnJPy3pc+/yV6h4CKeixDJ5///03unfvjmbNmmHHjh2VeoSRtbU1Ro4ciQEDBsDMzKzEMh4eHjhy5Aj27NmDqVOnIiwsDF5eXrL9N2/exLx587Bv3z4cOHCg1LaAB2HV3Ny8wmMmIiIieho9dsEzJSUF3bp1w7179xAYGIjvv/9eq8yQIUNKPHJZEpVKVe7zPj09PREaGorhw4dj27ZtePHFF7X2//jjj3B1dcWBAwek0+9EREREpLvHLnjevXsXQ4cOBfAghKakpGiVKe+0u778/f0xbtw4jBo1Ci1atNDaP3ToUDRu3BghISGwt7c3aN9EREREz4rHLng2aNBA68HxVa1du3Zo165dqfuDgoIQFBSk4IiIiIiInj58/gIRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiGDyJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEiTKp7AM+S2Dk9YGdnV93DqHZFRUVITk6Gs7MzjIz4tw/X419cCzmuhxzXQ47rQU8ivlOJiIiISBEMnkRERESkCAZPIiIiIlIEgycRERERKYLBk4iIiIgUweBJRERERIpg8CQiIiIiRTB4EhEREZEi+AB5BQghAABZWVl8yC8ePPRYrVbDwsKC6wGux8O4FnJcDzmuhxzXQ47rIafkemRlZQH4N++UhcFTAWlpaQAALy+vah4JERERUdVQq9WwtbUtswyDpwLs7e0BAP/880+5L8izICsrC56enrhx4wZsbGyqezjVjuvxL66FHNdDjushx/WQ43rIKbkeQgio1WrUrl273LIMngooPsRta2vLb4aH2NjYcD0ewvX4F9dCjushx/WQ43rIcT3klFoPXQ+s8SIIIiIiIlIEgycRERERKYLBUwHm5uaYM2cOzM3Nq3sojwWuhxzX419cCzmuhxzXQ47rIcf1kHtc10MldLn3nYiIiIioknjEk4iIiIgUweBJRERERIpg8CQiIiIiRfA5njq4dOkSsrOz0bRpU50v0tWljqHKKEkIgfPnz6OwsBBNmzaFiUn5byFd6uTk5ODSpUtwcnKCu7u71v4TJ04gLy9Pts3DwwN169at8FwMobCwEOfOnYOJiQmaNGkClUpV6Tp//vmn1seO+fj4aD2YtyJ9V7X8/HycO3cO1tbW8PX1rXSdxMREJCQklFivXbt2MDMzQ0FBAY4ePaq1v3HjxnBwcNB/EgZ07949XLx4Efb29vD29tapTkFBAWJiYmBvb4+GDRtWuN2K9F3V7t69iytXrsDV1RUeHh461cnNzcWpU6fg7u5e6qe/3bx5E+np6ahXrx6sra1l+9LT03H+/HmtOsXvn+qUkpKCa9euwcvLC87OzjrVyczMxNmzZ+Hj4wM3NzfZvtu3byM+Pl6rTqdOnQzSd1W7desWEhMTUb9+fdSqVUunOikpKYiLi0OTJk2kD2spdvz4ceTn52vVcXR0RKNGjQAA169fx40bN2T7zc3N8dxzz1VwFoZz7do1pKamolGjRqhRo0a55QsLC3Hp0iWYm5ujbt26MDY2rnC7+vatF0Glun37tmjXrp2ws7MTPj4+wt7eXuzYsaPSdQxVRmlxcXGiUaNGwtnZWXh6egp3d3dx+PDhStVJSkoSwcHBwtbWVrRq1UrY29uLDh06iPj4eFk7Xl5eon79+qJjx47Sv2+++aZK5qmro0ePCg8PD+Hp6SlcXFxEw4YNxYULFypdx9jYWDRt2lQ2119//bXSfVe1Xbt2CQcHB+Hj4yNq1aol2rZtK27dulWpOj///LNsHTp27ChcXFyEubm5yMrKEkI8+F4BIFq3bi0rt3///qqcbrnWrFkjatSoIRo2bChq1KghAgICRGZmZqnls7KyxEcffSQ8PDxEjRo1xNChQyvcrr59K+HLL78UFhYWonHjxsLS0lIEBQWJ/Pz8UsvfuXNHTJkyRbi5uQkLCwsREhKiVSY8PFw0a9ZMuLu7i+bNmwtra2sxe/ZsWZmwsDBhZGSk9T5KTk42+Bz1MX36dGFubi6aNGkizM3NxTvvvCOKiopKLZ+QkCDGjh0rXF1dhbGxsVi2bJlWmWXLlglLS0utuVa276pWUFAghg0bJiwsLKQxLViwoMw6f//9t3jjjTeEi4uLACDCwsK0yvTv31+2Dh06dBAAxMSJE6UyISEhwtbWVlauf//+hp6iXrKzs8XLL78srK2tha+vr7CyshKrVq0qtXxhYaGYPXu2cHJyEk2aNBGenp6ibt26IjIyUu929e27Ihg8y/Dqq6+K9u3bi5ycHCGEEPPnzxc1atQQd+7cqVQdQ5VRWuvWrUXv3r1FYWGhEEKI8ePHi9q1a4vc3NwK1zl+/Lj48ccfRUFBgRDiwZu+W7duokOHDrJ2vLy8xMqVK6tiWhWSl5cnPDw8xLhx44QQQmg0GtGnTx/RokWLStcxNjYWu3fvNmjfVS0lJUXUrFlTzJs3TwghRG5urnj++efFyy+/bNA6Qgjh6+sr3njjDenr4uD5999/G2AmhnHx4kVhYmIifvjhByGEEOnp6aJBgwZi7NixpdaJj48X8+bNE7du3RIvvfRSicFTl3Yr0ndVi46OFiqVSvz+++9CCCGuX78unJ2dxdy5c0utc+zYMbFo0SKRlpYmmjZtWmLw/Oqrr8TZs2elrw8cOCBMTU3FL7/8Im0LCwsT1tbWBpxN5a1bt05YWlqKmJgYIYQQp0+fFlZWViI0NLTUOnv27BErVqwQarVa2Nralho8fX19Dd53Vfv888+Fo6OjuHr1qhBCiKioKGFkZCS9X0qyceNGsW7dOpGamlpq8HzUrl27BABx9OhRaVtISIjo3r17pedgSG+//bbw8fERKSkpQggh1q5dK4yMjEr9GadWq8XcuXPF3bt3hRBCFBUVienTpwsbGxuRkZGhV7v69l0RDJ6lSEpKEiqVSmzevFnalpOTI6ytrUv8hte1jqHKKO3kyZMCgDhy5Ii07caNG0KlUpX6DV+ROkIIsXr1amFkZCSFUSEeBM/PP/9cHD9+XCQlJVV6PpUVHh4uAIgbN25I244cOSIAiOPHj1eqjrGxsfjhhx/E8ePHRWpqqkH6rmrffvutsLKyEvfu3ZO2bd68WahUqlKPelakzsGDBwUAsW/fPmlbcfDcuXOniImJkX74VqeZM2cKDw8P2balS5cKKysrkZeXV2790oKnLu1Wtu+qMHz4cPH888/Ltk2fPl14eXnpVL+04FmSVq1aiXfeeUf6ujh4nj9/Xpw5c6bMP5SV0q1bNzFw4EDZttdff73Eo5MlKSt41q9fX5w5c0acP39e3L9/3+B9V4WGDRuKKVOmyLZ16tRJBAUFlVtXrVbrHDwHDBig9Qd6SEiI6Ny5szh58qS4dOmSdJCkuhQUFAgbGxuxcOFC2XZvb2/x7rvv6tzOlStXBABx4MABnds1VN/l4c1FpTh9+jSEEGjbtq20zdLSEk2bNsWpU6cqXMdQZZRW3G+bNm2kbR4eHnBzcyt1TBWpAzy4LsfLy0vrWtAFCxZgzJgxqFevHrp06YKrV69WeD6VderUKbi4uMiuU/Pz84NKpSpzPXStM336dIwePRru7u7o06cPkpOTK9V3VTt16hQaN24MKysraVu7du0ghEBsbKzB6oSGhqJ+/frw9/fX2jdq1CgMHz4cTk5OGDFiBLKzsyszpUo5deqU7PsXeDC34muZq7Ldquq7Mkob0/Xr15GRkWGwfjIyMhAfH4/69evLtt+7dw+9e/dG//79UatWLcyfP99gfVZEaethiO/f+Ph4DB48GD179oSjoyOWL1+uWN8Vce/ePVy6dKnKx5SSkoLw8HCMHTtWa9/hw4cxbNgwdOnSBe7u7ti8ebPB+tXX1atXkZWVpbUezz33nF7rcfz4cahUKvj4+OjcrqH6Lg+DZynS09MBQOvmBAcHB2lfReoYqozS0tPTYWNjA1NTU53HVJE60dHRWLFiBWbNmiXbPmfOHKSlpSE2NhbXr18HAAwaNAgajaaiU6qU9PR0rdfH2NgYdnZ2Za6HLnW+++47pKSk4PTp07hy5Qri4+MRHBxcqb6rWkljKv5an/Uoq45arcamTZswZswY2Y1U5ubm+PXXX5GUlISzZ8/i77//xt69e/Huu+9Wak6VUZH1MFS7VdV3ZSgxJiEExo0bh1q1amHEiBHSdk9PT5w4cQJXrlzBlStXsHXrVsybNw8//vijQfqtyDjv3r1b4nrk5OSUeDOMrpo1a4aLFy/iwoULuH79OpYuXYqJEyciIiKiyvuuqOI/PKr6993atWthbGyMN998U7a9c+fOuH79Os6ePYtbt27hnXfewZAhQ3DmzBmD9a0PQ/z+v3XrFqZNm4bg4GDpAMXjlD0YPEtRHJYevZM6Nze31DshdaljqDJKMzU11RoPUP566FMnJiYG/fr1w+TJk2VBCwCCg4OldXFwcMCnn36KkydPVtsRnNLmlpeXp/d6PFpn7NixMDJ68K3p4eGBWbNmYdeuXcjKyqpw31WtpDHl5uYCgF7rUVadjRs3Ij8/HyNHjpRtr1WrFgYNGiR97evri6lTp+KXX37Rex6GUpH1MFS7VdV3ZSgxpkmTJmHfvn0IDw+Hra2ttL1t27ayIzgvv/wy+vbti40bNxqkX32pVCqYmJiUuh6P/qGuD39/f9mTEIKDg9G+fXvpe6Eq+64opX7fhYaGYtCgQbCzs5Ntf+WVV6QnqahUKsycORMuLi7YsmWLwfrWR2XXIzU1FS+99BJ8fX3xzTff6NWuUq8Fg2cpih/bkZiYKNuemJiIOnXqVLiOocoozcvLC/fv30dqaqq0TaPR4M6dO2Wuh651Tp48icDAQAQHB2PhwoXljsfFxQWA9hopxcvLC3fu3JEdcU1PT0dubm6Z66FvHeDfud66datS7VQlLy+vEt+vAMpcD33qhIaGok+fPtJ6lMXFxQWZmZnVdrq9IuthqHarqu/KKG1MpqamcHV1rXT7U6dOxfr16xEZGYmWLVuWW97FxaXafnYAD16HktbDw8ND+qPTUB6dq5J968LJyQlWVlZV+vvuyJEjOH/+fImn2R+lUqng7Oxcrb9bgIr9/k9LS0NAQADs7e2xY8cOWFpa6tWuUtmDwbMUrVq1gqOjI8LDw6VtFy5cwOXLlxEYGChtO3PmDOLi4nSuY6gySuvSpQvMzMxkY9q3bx/UarVsTMePH8e1a9f0qhMbG4vAwEAMGzYMS5Ys0er73r17WtsiIiJgZGSExo0bG2J6egsICMC9e/cQFRUlbdu+fTtMTU3x4osvStsOHTokBUZd6pQ2V2tra+mZpbr2raTAwEDEx8fLnpe4fft22NvbS9f43r9/H4cOHUJaWprOdYqdPXsWR48eLfEXR2lr5uXlZfjnz+koMDAQhw8flv3RtX37djRu3Fg6uqJWq3Ho0CGo1WqDtqtLGaUFBgYiIiJCdip3+/bt8Pf3l46ypKWl4dChQ7h//75ebU+bNg0//fQTIiMjtd43gPb7o7CwENHR0WjWrFkFZmIYgYGB2LFjh/S8XiEEwsPDZT8Xb926hUOHDunV7qNzzcrKwtGjR2Vz1aVvJRkZGaFbt26y3xP379/H7t27ZWO6du0ajh8/XqE+Vq1aBV9fX3Tu3Flr36NrdvPmTVy4cKHa3h+Ojo5o1aqVbD0yMjLwxx9/yNYjLi5OdjlAeno6AgICYGtri127dmk9z1aXdnXtu9IMdpvSU2jFihXC3NxcLF26VGzatEk0bdpUdOvWTVamffv2sjvvdKljqDJKmzVrlrCzsxMrV64U69evFx4eHmL48OGyMu7u7rK738qrExcXJxwcHESXLl3EwYMHZf+Kn/EXGRkp/P39RWhoqNizZ4/4+OOPhaWlpZgxY4YyEy9FcHCw8PDwEOvWrROrVq0SdnZ2YubMmbIyAMSSJUt0rrN69WrRt29fsWbNGrF7927x7rvvClNTU7F06VK9+1Zajx49RJMmTcSmTZvEV199JczNzcW3334r7b9x44YAIDZt2qRznWJTpkwRderUERqNRmvfp59+Kt58803x888/ix07doixY8cKExMT2SN1lJafny9atmwpXnjhBREWFibmzZsnjI2NxbZt26Qyf/31lwAg/vrrL2nboUOHxMGDB0X79u1Fjx49xMGDB8WxY8f0aleXMkpLT08XderUEb169RLh4eFi2rRpwszMTDb3TZs2yZ7WcP/+felngbe3txg6dKg4ePCgOH36tFRn1qxZwsjISHz11Veynx0PP9N28ODBYsaMGWL79u1i8+bNIiAgQNjZ2ckew6S0hIQEUatWLTF06FARHh4uRowYIWxsbMTly5elMkuWLBEP/4pWq9XS/GrUqCGmTp2qNdeuXbuKOXPmiB07dogNGzYIPz8/4eHhIRITE/XqW2kxMTHCwsJCTJo0SYSHh4s+ffqI2rVrS4/0EUKId999V7i7u0tfp6WliYMHD4qIiAgBQHz66afi4MGD0iOZimVnZ4saNWpo3aldrHnz5uLzzz8Xu3fvFj/++KPw9fUVTZs2lZ4TXB127doljI2NxZw5c8S2bdtE586dRZMmTWRPZAgKChLt27cXQjx46k2bNm2Eu7u72LNnj+x74eE11KVdXcpUlkqIRz4ihWS2bt2KtWvXIjs7G507d8a7774r+0ti/PjxcHNzw8cff6xzHUOWUZIQAqtXr8aWLVtQWFiIl156CW+//bbsuqDXXnsN3bt3x1tvvaVTnYiICMybN6/E/sLCwuDk5AQAOHbsGEJDQ3Ht2jV4enoiKCio2v5CL1ZYWIhvvvkGe/bsgYmJCfr164fRo0fLbnzp1KkTJk+eLF2DqEudvXv3Yv369bh9+za8vb0xcuRItG/fXu++lZaTk4PFixfjjz/+gJWVFYYOHSq79jIlJQX9+/fHJ598It2VXl6dYv3790dgYCD+85//lNj3li1bEBYWhrS0NDRo0AATJkxAkyZNqmSeusrIyMAXX3yBEydOwN7eHmPHjpW9Z8+fP49x48bh+++/l8bq7++PwsJCWTvOzs7YunWrzu3qWkZpiYmJ+OKLL3Du3Dm4ubnhnXfekb2vo6Oj8dFHH0nf9+np6ejTp49WO02bNsWKFSsAAGPGjMHFixe1ynTt2lW6cz0/Px8rV67Evn37UFRUhGbNmmHy5MnSz5bqcunSJXz55ZeIj4+Ht7c3pk+fLjuDs2nTJnz11VfSUc+4uDiMHj1aq52H56pWq/Htt9/izz//hJmZGdq0aYO3334bNjY2evVdHWJiYvDVV18hMTERjRo1QkhIiOz07v/+9z9ERUVJ3wsHDx7EBx98oNXO4MGDMWnSJOnrffv2Yc6cOdi6dWuJr3lqaiqWLVuG48ePo2bNmujQoQMmTpxY7Z8UuH//fixfvhxpaWlo3bo1QkJC4OjoKO3/+OOPcfv2baxYsQJJSUkYOHBgie3MnTsX3bt317ldXctUBoMnERERESmC13gSERERkSIYPImIiIhIEQyeRERERKQIBk8iIiIiUgSDJxEREREpgsGTiIiIiBTB4ElEREREimDwJCIqx8CBA/Hrr7/qXP6nn37C8OHDDdb/66+/jp9//rnMMgEBAdi3b1+ZZcaPH4/vvvvOYOPSxf379+Hn5wc/P78SHwivpNmzZ0tjOXbsWLWOhehZxeBJRPT/Dh06hI4dO2ptP3v2LJKTk3Vu5/bt27LPoK+ss2fP4s6dO2WWiY2NRXp6OgAgPj4efn5+SEtLk5WJi4tDYmKiXn3/+uuvUlh7+F9AQIBO9YuKihATE4OJEydiwYIFWvv37duHcePGwd/fHwEBARg7dqzss8TLExsbCz8/vxI/wQh48MktQ4cOBQAEBwdj+fLliImJQVZWlk7tE5FhmVT3AIiIHhd3795FTEyM1vYtW7bA2dm5Gkb0wC+//KLXRzzm5uYiJiYGBQUFle47OTkZ58+fxx9//CHb/vBH5erC19cXzZs3l22bOHEi1q9fj6lTpyIoKAjGxsaIj49HaGgoIiIi8PXXX5fbbosWLZCSkoLQ0FB8+eWXsn15eXlYunSp9NGK3t7e8Pb21mvcRGRYPOJJRE+UHTt24JVXXsG+ffswZMgQdO7cGR988AHu3bsnlXn4KF3Xrl0xefJkJCUlSftzc3Ph5+eHvXv3Yvz48ejYsSP++9//YurUqbJTw4sXLwYAzJkzB/v375fqv/LKK/Dz80O7du3w2muvYe3atXrN4c0338SGDRukr+fPn4/nnntOOgpXWFiIjh074sSJE9L+qKgoqbxarcaMGTPQuXNnDB06FAcPHpT2paWl4fXXXwcA9OzZE35+fpg+fbq0X6PRYMmSJXj11VfRq1cvrF+/vtzxGhkZaR3xbNmypV5zflRoaCiWL1+OXbt2SZ8n7e/vj9GjRyMsLAyfffaZrHxERAQGDRqEzp07Y+TIkThz5ow0tuDgYKxdu1brc+63bNmC7OxsjBgxolJjJSLD4RFPInqipKamIiIiAnFxcfjiiy9gYmKC999/H3Fxcdi6dSsAoGvXrvDx8QEAZGZmYtWqVejQoQMuXLgACwsLaDQaxMTEICgoCLNnz0ZwcDBcXFxgZmaGkJAQLF++HADg4uIC4MGpbn9/f2kMn332Ge7fvw+NRoMLFy4gJCQE6enpmDx5sk5zsLGxQVhYGIYMGQIAWL9+Pa5fv46DBw/ilVdewYkTJ3Ds2DE0atRI6v/555+X6g8ePBiJiYlYsGABcnNzMWzYMNy9excAYGtri1mzZuH111/HF198AQcHB9SqVUuqu2TJEowbNw7Tp0/H2bNnMWLECDg5OaFHjx4VeDUq7rvvvsPLL7+MTp06lbjf2tpa+v/Q0FB89NFHmDt3Lho1aoQ///wTHTp0wOHDh9GyZUuMGjUK8+fPx86dO9G3b19ZvVdffVV6HYmo+jF4EtETp7CwEGvWrMELL7wA4MEp1JYtWyI2NhatWrWCk5OT7NR0165d4eXlhd27d6N///7S9mnTpsnCYv369aFSqeDn51dm/y1atJD+v3379jA2NsYnn3yic/D09/fHW2+9BSEEkpOTkZCQgODgYOzfvx+vvPIKoqOj0bZtW9SoUUOr7pEjR/D777/j0qVLqF+/PgDAzs4OL730EgDAxMQETZs2BQC0bNkSrq6usvqdOnWSTmH7+/tjz549CA8PVzx4njlzBtOmTSu3XF5eHqZPn441a9agd+/eAIAuXbrg6tWr+O9//4v169ejTp06CAwMRGhoqBQ8ExISEB0djd9++61K50FE+mHwJKInjoWFhRQ6gQdB0NnZGTExMWjVqhXy8/OxcuVKREZGIikpCRqNBhkZGbh69aqsnQ4dOlSo/3PnzuGbb75BXFwcsrKyoFarkZCQACEEVCpVufX9/f2RmpqKc+fO4ezZs2jXrh169eqFefPmAQCio6NlR1gfduLECXh5eUmhEwC6desGY2Njncb+aKh2d3cv98YlQ9NoNCgsLETNmjVl29966y0cPXoUwIOjzTt37sTp06dx9+5dfPzxx1iwYAGEEBBC4Pbt27LrbkePHo0hQ4YgKSkJrq6u+OGHH1C7dm307NlT0bkRUdkYPInoiWNlZaW1zdraGmq1GgDwzjvv4NChQ5g5cybq1q0LCwsLDBs2DLm5ueW2U55r166hQ4cOGDFiBEJCQlCrVi0cP34cb7/9NjQaDUxMyv+x6uzsjMaNG2P//v04d+4cunbtii5duuDMmTNITU3Fn3/+iSlTppRYNzs7W2vcJiYmMDc312n8j45PpVLpfAe5oRgbG8PNzQ0JCQmy7ZMnT0ZWVhZ++OEHhIeHA4B07e6CBQvg6OgoK29paSn9f9++fWFnZ4c1a9Zg+vTpWL16NUaOHKlzICciZTB4EtETJz09HcnJydIRL7VajcTERNSrVw8AEBYWhuXLl2PAgAEAgIKCAtnNRaUxMjIqN4RFRUXBxcUFy5Ytk7YVH6XTh7+/P/bv34/z58/j22+/hZ2dHZo1a4bFixcjLy+v1GsffXx8cP36deTl5cHCwgIAcP36deTk5MjmAUDxQKmPPn36YPPmzVi0aBFsbW0BAA0bNgQA7NmzRyrXoEEDAA9OuZd1CYSZmRmGDRuGH374Ac2aNUNiYiJGjRpVhTMgoorgXe1E9ET68MMPpWA1a9YsODs7S9cp2tvbS3eECyHw4YcfSjfflMXV1RX3798v85md9vb2uHPnDm7cuAEAuHr1KhYuXKj3+P39/REZGSkdQS3e9s0335R6fSfw4I56a2trzJ8/H8CD09YzZ86UlSm+maZ4jI+j2bNnw8zMDAMGDMC1a9ek7RqNRvZHgqenJ/r164eQkBDEx8dL2//8809s3LhR1uaYMWMQFxeHqVOnym4wI6LHB4MnET1xnJycoFar4ebmhtq1a2PDhg1Ys2aNdLp5yZIl+O6771CvXj24urriyJEj0tG0srRq1QrdunVDkyZNZI9TelifPn0QEBCARo0aoXHjxmjbtm2pRyfL4u/vj+zsbLRv3146Zezv7w+1Wl3q9Z3Ag0sK1qxZgxUrVsDd3R1ubm4wMjKSjhoCgIODA0aMGIHAwEC0bdtW9jilx4WbmxuOHDkCOzs7+Pr6onbt2mjevDmcnZ1x/Phx2dr/9NNPaNu2LZo0aQJfX184Ojpi5syZaNy4sazNJk2aoEOHDrh06RLGjBmj9JSISAcq8TifiyEiesTq1avx0Ucf4ebNm8jMzMSNGzfQoEEDrWscc3NzcfXqVdja2sLDwwMXL16Era0t3NzcUFRUhJMnT6Jx48ayx/YU++eff5CSkgJnZ2d4enri3LlzcHZ2lt0pn5iYiIyMDNSrVw+FhYWIi4uTTgUnJSUhIyNDKxg9KjY2FrVq1YKXlxcAID8/H3///Te8vb3h4OAglTt37hycnJxkN9Pk5eXhypUrqFOnDmxsbHD69GnUqVNH9uik27dvIykpCTY2NqhXrx7i4uJQs2ZN1K5dWzbXwsLCUo8OpqSk4ObNm2jdunWZcylNXl4eLC0t4evri4YNG0rXbj4sNzcXCQkJMDExQZ06daRLCB6VmZmJf/75B56enrCzsyuxzM2bN5GUlIQWLVrAzMxMtm/27NnYtWsXYmJiEBkZqfOnLxGR4TB4EtET5eHgSY8/IYT0aVDm5uZan16kpISEBOljRH19fbXuqieiqsebi4iIqMro8lxUpfAjM4mqH494EtETJS0tDYmJibKHuBMR0ZOBwZOIiIiIFMG72omIiIhIEQyeRERERKQIBk8iIiIiUgSDJxEREREpgsGTiIiIiBTB4ElEREREimDwJCIiIiJFMHgSERERkSIYPImIiIhIEf8HvC980A/VfeIAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pdg = {r'$Z \\to \\nu\\bar\\nu$': 0.1663, r'$Z \\to \\tau^+\\tau^-$': 0.0841}\n", "\n", "labels = [r[0] for r in rows]\n", "ours = [r[1] for r in rows]\n", "theirs = [pdg[l] for l in labels]\n", "y = np.arange(len(labels))\n", "\n", "fig, ax = plt.subplots(figsize=(6.8, 3.2))\n", "ax.barh(y - 0.19, ours, height=0.36, color='#1f77b4', label='this notebook (tree level)')\n", "ax.barh(y + 0.19, theirs, height=0.36, color='#bbbbbb', label='PDG')\n", "ax.set_yticks(y); ax.set_yticklabels(labels)\n", "ax.set_xlabel(r'partial width $\\Gamma$ [GeV]')\n", "ax.set_title('Z partial widths, per generation')\n", "ax.set_xlim(0, 0.21)\n", "ax.legend(loc='upper right')\n", "ax.grid(alpha=0.3, axis='x')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "34", "metadata": {}, "source": [ "Two tree-level numbers landing within about 1% of experiment — the residual is genuine\n", "higher-order physics we have not included.\n", "\n", "And note *why* the invisible channel is the bigger one. The neutrino is purely\n", "left-handed, so it gets the full $g_L^2$ with nothing subtracted; the charged lepton's\n", "left- and right-handed couplings are individually smaller. Chirality is directly visible\n", "in the bar chart." ] }, { "cell_type": "markdown", "id": "35", "metadata": {}, "source": [ "## 9. Chirality: why V−A gives exactly half\n", "\n", "The weak charged current is pure $V-A$: only $P_L$. What does that do to a width?\n", "\n", "Since $P_L = \\tfrac12(1-\\gamma_5)$ and the projector is idempotent, a chiral current\n", "keeps exactly half of the vector-current trace. So a $g_R = 0$ coupling should give\n", "precisely half the width of a $g_L = g_R = g$ one." ] }, { "cell_type": "code", "execution_count": null, "id": "36", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "vector current g(gamma^mu) : M*g**2/(12*pi) = g^2 M / 12 pi\n", "chiral current g(gamma^mu P_L) : M*g**2/(24*pi) = g^2 M / 24 pi\n", "exactly half? True\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Gamma(W -> l nu) = g**2*m_W/(48*pi) = g^2 m_W / 48 pi\n", "numerically = 0.2276312410961552 GeV (PDG 0.2264)\n" ] } ], "source": [ "gsym, Msym = sp.symbols('g M', positive=True)\n", "kin_m0 = TwoBodyKinematics(Msym, 0, 0)\n", "\n", "vector = sp.simplify(ffv_squared(gsym, gsym, kin_m0) * kin_m0.phase_space())\n", "chiral = sp.simplify(ffv_squared(gsym, 0, kin_m0) * kin_m0.phase_space())\n", "\n", "print(\"vector current g(gamma^mu) :\", vector, \" = g^2 M / 12 pi\")\n", "print(\"chiral current g(gamma^mu P_L) :\", chiral, \" = g^2 M / 24 pi\")\n", "print(\"exactly half?\", sp.simplify(vector - 2*chiral) == 0)\n", "\n", "# the W: coupling is g/sqrt(2), purely left-handed\n", "mW = sp.Symbol('m_W', positive=True)\n", "kin_W = TwoBodyKinematics(mW, 0, 0)\n", "width_W = sp.simplify(ffv_squared(gsym/sp.sqrt(2), 0, kin_W) * kin_W.phase_space())\n", "print(\"\\nGamma(W -> l nu) =\", width_W, \" = g^2 m_W / 48 pi\")\n", "print(\"numerically =\", float(width_W.subs({gsym: GW, mW: MW})), \"GeV (PDG 0.2264)\")" ] }, { "cell_type": "markdown", "id": "37", "metadata": {}, "source": [ "A word on $\\gamma_5$, because it is where hand calculations go wrong. Writing\n", "$P_L = \\tfrac12(1-\\gamma_5)$ leaves a term $\\mathrm{Tr}[X\\gamma_5]$, which produces the\n", "totally antisymmetric $\\epsilon^{\\mu\\nu\\rho\\sigma}$.\n", "\n", "For a **two-body** decay that term is always zero, and it is worth seeing why: $\\epsilon$\n", "needs four *independent* four-vectors to be non-zero, but a 1→2 final state offers only\n", "two independent momenta ($P = p_1+p_2$ is not a third), and any leftover free index gets\n", "contracted with the polarisation sum, which is **symmetric**. Antisymmetric times\n", "symmetric vanishes.\n", "\n", "That argument fails for a three-body decay — which is exactly why `feynlag` refuses to\n", "drop the term unless it can prove the conditions hold, rather than assuming it." ] }, { "cell_type": "markdown", "id": "38", "metadata": {}, "source": [ "## 10. The whole Standard Model at once\n", "\n", "Everything so far — vertices, spin sums, traces, phase space, thresholds — is what\n", "`DecayCalculator` automates. Having done it by hand, here is the machine.\n", "\n", "You give it the model, a mass for every leg, and the map that says which Weyl legs form\n", "one Dirac particle. It finds every three-leg vertex containing the parent and returns a\n", "width per channel." ] }, { "cell_type": "code", "execution_count": null, "id": "39", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Z -> taubar tau\n" ] }, { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\frac{\\sqrt{m_{Z}^{2} - 4 m_{\\tau}^{2}} \\left(5 g_{1}^{4} m_{Z}^{2} + 7 g_{1}^{4} m_{\\tau}^{2} - 2 g_{1}^{2} gw^{2} m_{Z}^{2} - 10 g_{1}^{2} gw^{2} m_{\\tau}^{2} + gw^{4} m_{Z}^{2} - gw^{4} m_{\\tau}^{2}\\right)}{96 \\pi m_{Z}^{2} \\left(g_{1}^{2} + gw^{2}\\right)}$" ], "text/plain": [ " ________________ ↪\n", " ╱ 2 2 ⎛ 4 2 4 2 2 2 2 2 2 ↪\n", "╲╱ m_Z - 4⋅mₜₐᵤ ⋅⎝5⋅g₁ ⋅m_Z + 7⋅g₁ ⋅mₜₐᵤ - 2⋅g₁ ⋅gw ⋅m_Z - 10⋅g₁ ⋅gw ⋅mₜ ↪\n", "────────────────────────────────────────────────────────────────────────────── ↪\n", " 2 ⎛ 2 2⎞ ↪\n", " 96⋅π⋅m_Z ⋅⎝g₁ + gw ⎠ ↪\n", "\n", "↪ \n", "↪ 2 4 2 4 2⎞\n", "↪ ₐᵤ + gw ⋅m_Z - gw ⋅mₜₐᵤ ⎠\n", "↪ ───────────────────────────\n", "↪ \n", "↪ " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Z -> nu_taubar nu_tau\n" ] }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{m_{Z} \\left(g_{1}^{2} + gw^{2}\\right)}{96 \\pi}$" ], "text/plain": [ " ⎛ 2 2⎞\n", "m_Z⋅⎝g₁ + gw ⎠\n", "───────────────\n", " 96⋅π " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mZs, mWs, mhs, mtaus = sp.symbols(\"m_Z m_W m_h m_tau\", positive=True)\n", "masses = {Z: mZs, Wp: mWs, Wm: mWs, A: 0, h: mhs,\n", " tau: mtaus, taubar: mtaus, nutau: 0, nutaubar: 0}\n", "\n", "calc = DecayCalculator(model, masses, boson_fields=bosons,\n", " fermion_sectors=(\"gauge\", \"yukawa\"),\n", " conjugate_map=cmap, particle_map=particle_map,\n", " parameters=model.parameters)\n", "\n", "for children, width in calc.partial_widths(Z).items():\n", " print(\"Z ->\", \" \".join(str(c) for c in children))\n", " display(sp.simplify(width))" ] }, { "cell_type": "code", "execution_count": null, "id": "40", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Z:\n", " -> nu_taubar nu_tau 0.16787 GeV\n", " -> taubar tau 0.08424 GeV\n", " lifetime from these channels: 2.611e-24 s\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "W+:\n", " -> nu_taubar tau 0.22746 GeV\n", " lifetime from these channels: 2.894e-24 s\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "h:\n", " -> Wm Wp 0.00000 GeV (closed)\n", " -> Z Z 0.00000 GeV (closed)\n", " -> taubar tau 0.00026 GeV\n", " lifetime from these channels: 2.535e-21 s\n" ] } ], "source": [ "numbers = {mZs: MZ, mWs: MW, mhs: MH, mtaus: MTAU}\n", "\n", "for parent, name in ((Z, 'Z'), (Wp, 'W+'), (h, 'h')):\n", " widths = calc.numeric_partial_widths(parent, extra=numbers)\n", " total = sum(widths.values())\n", " print(f\"{name}:\")\n", " for children, w in sorted(widths.items(), key=lambda kv: str(kv[0])):\n", " kids = \" \".join(str(c) for c in children)\n", " tag = \"\" if w else \" (closed)\"\n", " print(f\" -> {kids:<16} {w:9.5f} GeV{tag}\")\n", " if total:\n", " print(f\" lifetime from these channels: {hbar/total:.3e} s\")" ] }, { "cell_type": "markdown", "id": "41", "metadata": {}, "source": [ "Compare the $Z$ line with §1: we started from $\\Gamma_\\text{tot}=2.4952$ GeV and a\n", "lifetime of $2.6\\times10^{-25}$ s. Our number is longer because we built only *one*\n", "lepton generation and no quarks — the real $Z$ has many more channels open, so it decays\n", "faster. Add them and you converge on the measured value.\n", "\n", "### The Higgs branching ratios\n", "\n", "Nothing stops us from asking what the Higgs *would* do at a different mass. This\n", "reproduces one of the most familiar plots in particle physics.\n", "\n", "One practical point, and it is the subject of §13: we cannot call\n", "`numeric_partial_widths` at every point of a fine grid — it re-derives the widths\n", "symbolically each time. Instead take each symbolic width **once**, `lambdify` it, and\n", "apply the threshold condition explicitly." ] }, { "cell_type": "code", "execution_count": null, "id": "42", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "m_h = 125.25 GeV Gamma_tot = 0.0003 GeV BR($W^+W^-$) = 0.000 BR($ZZ$) = 0.000 BR($\\tau^+\\tau^-$) = 1.000\n", "m_h = 170.00 GeV Gamma_tot = 0.3711 GeV BR($W^+W^-$) = 0.999 BR($ZZ$) = 0.000 BR($\\tau^+\\tau^-$) = 0.001\n", "m_h = 200.00 GeV Gamma_tot = 1.4227 GeV BR($W^+W^-$) = 0.734 BR($ZZ$) = 0.266 BR($\\tau^+\\tau^-$) = 0.000\n", "m_h = 300.00 GeV Gamma_tot = 8.4429 GeV BR($W^+W^-$) = 0.688 BR($ZZ$) = 0.312 BR($\\tau^+\\tau^-$) = 0.000\n" ] } ], "source": [ "higgs_widths = calc.partial_widths(h)\n", "param_vals = model.parameters.numeric()\n", "\n", "grid = np.linspace(20, 300, 561)\n", "thresholds = {(Wm, Wp): 2*MW, (Z, Z): 2*MZ, (taubar, tau): 2*MTAU}\n", "pretty = {(Wm, Wp): r'$W^+W^-$', (Z, Z): r'$ZZ$', (taubar, tau): r'$\\tau^+\\tau^-$'}\n", "\n", "curves = {}\n", "for key, expr in higgs_widths.items():\n", " f = sp.lambdify(mhs, expr.subs(param_vals).subs({mZs: MZ, mWs: MW, mtaus: MTAU}),\n", " \"numpy\")\n", " with np.errstate(invalid='ignore'):\n", " y = np.where(grid > thresholds[key], f(grid), 0.0)\n", " curves[key] = np.nan_to_num(y) # below threshold sqrt(lambda) is imaginary\n", "\n", "total = sum(curves.values())\n", "for mtest in (125.25, 170, 200, 300):\n", " j = int(np.argmin(abs(grid - mtest)))\n", " br = {pretty[k]: curves[k][j]/total[j] for k in curves}\n", " print(f\"m_h = {mtest:6.2f} GeV Gamma_tot = {total[j]:8.4f} GeV \" +\n", " \" \".join(f\"BR({n}) = {x:.3f}\" for n, x in br.items()))" ] }, { "cell_type": "code", "execution_count": null, "id": "43", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(7.2, 4.4))\n", "colors = {(Wm, Wp): '#1f77b4', (Z, Z): '#d62728', (taubar, tau): '#2ca02c'}\n", "for key in [(taubar, tau), (Wm, Wp), (Z, Z)]:\n", " ax.plot(grid, curves[key]/np.where(total > 0, total, 1), lw=2,\n", " color=colors[key], label=pretty[key])\n", "\n", "ax.axvline(2*MW, ls='--', color='0.5'); ax.axvline(2*MZ, ls='--', color='0.5')\n", "ax.text(2*MW - 3, 0.55, r'$2m_W$', rotation=90, ha='right', color='0.35')\n", "ax.text(2*MZ + 3, 0.55, r'$2m_Z$', rotation=90, ha='left', color='0.35')\n", "ax.axvline(MH, ls=':', color='#ff7f0e', lw=2)\n", "ax.text(MH - 3, 0.30, 'the real Higgs, 125 GeV', rotation=90, ha='right',\n", " color='#ff7f0e')\n", "\n", "ax.set_xlabel(r'$m_h$ [GeV]')\n", "ax.set_ylabel('branching ratio')\n", "ax.set_title('Higgs branching ratios vs its mass (tree level, this field content)')\n", "ax.set_xlim(20, 300); ax.set_ylim(0, 1.05)\n", "ax.legend(loc='center left'); ax.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "44", "metadata": {}, "source": [ "The shape is the physics:\n", "\n", "- **Below $2m_W$** only $\\tau\\tau$ is open, so it takes everything by default.\n", "- **At $2m_W = 160.8$ GeV** the $WW$ channel opens and immediately dominates — gauge\n", " couplings are far larger than a lepton Yukawa.\n", "- **At $2m_Z = 182.4$ GeV** $ZZ$ follows, settling near $WW\\!:\\!ZZ \\approx 2\\!:\\!1$\n", " (two charge states of the $W$, against one $Z$ that costs an identical-particle\n", " $1/2!$).\n", "\n", "This is the **on-shell** story: each $VV$ channel is flat zero until $2m_V$, so at the\n", "physical 125 GeV the plot says $\\tau\\tau$ takes essentially everything. Two things close\n", "the gap to reality. The **fermions** we have not declared yet ($b\\bar b$ actually\n", "dominates) — next. And the **off-shell** $WW^*$: below $2m_W$ the two-body channel is\n", "shut, but the Higgs still reaches a real $W$ and a *virtual* one — a three-body decay we\n", "compute in §11. (The loop-induced $\\gamma\\gamma$ stays out of reach of a tree-level\n", "engine — that is Tier 3 of `decays_roadmap.md`.) The *machinery* is right; we are still\n", "adding *content*." ] }, { "cell_type": "markdown", "id": "45", "metadata": {}, "source": [ "### The fermions we were missing — one `DiracParticle` each\n", "\n", "The gap above is not a limitation of the *machinery* — it is missing *content*. The\n", "Higgs couples to every massive fermion, and each $h\\to f\\bar f$ is the very $\\beta^3$\n", "scalar decay of §7. All that is missing is declaring those fermions.\n", "\n", "Doing that exposes the bookkeeping §13.1 is about to warn you against: each Dirac\n", "fermion is two Weyl legs, needs a mass, and — for quarks — a colour factor $N_c=3$.\n", "Tracked as three separate dicts, they drift out of sync. So feynlag bundles them into\n", "one object, a **`DiracParticle`**:\n", "\n", "```python\n", "DiracParticle(\"b\", left=Qb.components[1], right=bR.components[0], mass=mb, color=3)\n", "```\n", "\n", "The bar legs are found automatically (via the `bar_partner` registry), the mass travels\n", "with the particle, and the colour $N_c$ is applied **once** — the per-leg double-count\n", "that silently inflates a quark width by $9\\times$ (§13.1) is simply unreachable." ] }, { "cell_type": "code", "execution_count": null, "id": "46", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "full-fermion Higgs model built: ['tau', 'mu', 'b', 'c', 's']\n" ] } ], "source": [ "# a compact Higgs + fermions model (Higgs sector only; no EW rotations needed\n", "# for h -> f fbar). Running masses at ~m_h, so the branching ratios are realistic.\n", "run = {\"tau\": 1.777, \"mu\": 0.1057, \"b\": 2.79, \"c\": 0.62, \"s\": 0.055}\n", "ncol = {\"tau\": 1, \"mu\": 1, \"b\": 3, \"c\": 3, \"s\": 3}\n", "\n", "gwf = ExternalParameter(\"gwf\", GW, positive=True)\n", "g1f = ExternalParameter(\"g1f\", G1, positive=True)\n", "vf = ExternalParameter(\"vf\", VEV, positive=True, unit_dim=1)\n", "lamf = ExternalParameter(\"lamf\", MH**2 / (2 * VEV**2))\n", "mu2f = InternalParameter(\"mu2f\", unit_dim=2)\n", "SU2f, U1f = SU2(\"SU2f\", coupling=gwf), U1(\"U1f\", coupling=g1f)\n", "Hf = Scalar(\"Hf\", reps={SU2f: 2, U1f: sp.Rational(1, 2)}, component_names=[\"Gpf\", \"H0f\"])\n", "Hf.expand_vev({Hf.components[1]: vf})\n", "H0f = Hf.components[1]\n", "j = sp.Symbol(\"j\", integer=True)\n", "\n", "Lf = Lagrangian()\n", "Lf.add((dag(Dmu(Hf)) * Dmu(Hf))[0], sector=\"kinetic\")\n", "Lf.add(-(-mu2f.s * (dag(Hf) * Hf.mat)[0] + lamf.s * (dag(Hf) * Hf.mat)[0]**2),\n", " sector=\"potential\")\n", "\n", "fields_f, params_f, diracs, ysym = [Hf], [gwf, g1f, vf, lamf, mu2f], [], {}\n", "for name in run:\n", " Qf = WeylFermion(f\"Q{name}\", reps={SU2f: 2, U1f: sp.Rational(1, 6)}, chirality=\"L\",\n", " nflavors=1, component_names=[f\"u{name}\", f\"d{name}\"])\n", " fR = WeylFermion(f\"{name}R\", reps={U1f: -sp.Rational(1, 3)}, chirality=\"R\",\n", " nflavors=1, component_names=[f\"{name}Rc\"])\n", " y = ExternalParameter(f\"y_{name}\", sp.sqrt(2) * run[name] / VEV, positive=True)\n", " term = -y.s * Bilinear(Qf.bar_components[1][j], diracPR, fR.components[0][j]) * H0f\n", " Lf.add(term + sp.conjugate(term), sector=\"yukawa\")\n", " fields_f += [Qf, fR]; params_f.append(y); ysym[name] = y\n", " mfs = sp.Symbol(f\"m_{name}\", positive=True)\n", " diracs.append((name, DiracParticle(name, left=Qf.components[1],\n", " right=fR.components[0], mass=mfs, color=ncol[name]),\n", " mfs, run[name]))\n", "\n", "fields_f += [SU2f.bosons(\"Wf\"), U1f.bosons(\"Bf\")]\n", "Hf_model = Model(\"SM_higgs_ferms\", gauge_groups=[SU2f, U1f], fields=fields_f,\n", " parameters=params_f, lagrangian=Lf)\n", "Hf_model.solve_tadpoles([mu2f])\n", "hf = sp.Symbol(\"H0f_r\", real=True)\n", "print(\"full-fermion Higgs model built:\", [n for n, *_ in diracs])" ] }, { "cell_type": "code", "execution_count": null, "id": "47", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "channel Gamma [MeV] BR\n", "------------------------------------\n", "h -> bbar b 1.9174 0.843\n", "h -> taubar tau 0.2597 0.114\n", "h -> cbar c 0.0950 0.042\n", "h -> mubar mu 0.0009 0.000\n", "h -> sbar s 0.0007 0.000\n", "------------------------------------\n", "total (fermions) 2.2737\n" ] } ], "source": [ "mhf = sp.Symbol(\"m_hf\", positive=True)\n", "calc_f = DecayCalculator(Hf_model, {hf: mhf}, boson_fields=[hf],\n", " fermion_sectors=(\"yukawa\",),\n", " particles=[dp for _, dp, _, _ in diracs],\n", " parameters=Hf_model.parameters)\n", "\n", "mass_pt = {mhf: MH}\n", "mass_pt.update({ms: val for _, _, ms, val in diracs})\n", "widths_f = calc_f.numeric_partial_widths(hf, extra=mass_pt)\n", "assert calc_f.unmatched_channels == [] # every fermion is declared\n", "\n", "total_f = sum(widths_f.values())\n", "print(f\"{'channel':<14}{'Gamma [MeV]':>13}{'BR':>9}\")\n", "print(\"-\" * 36)\n", "for children in sorted(widths_f, key=lambda k: -widths_f[k]):\n", " name = str(children[1])\n", " print(f\"h -> {name}bar {name:<4}{widths_f[children]*1e3:>11.4f}{widths_f[children]/total_f:>9.3f}\")\n", "print(\"-\" * 36)\n", "print(f\"{'total (fermions)':<14}{total_f*1e3:>13.4f}\")" ] }, { "cell_type": "code", "execution_count": null, "id": "48", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "labels = [str(c[1]) for c in sorted(widths_f, key=lambda k: widths_f[k])]\n", "brs = [widths_f[c] / total_f for c in sorted(widths_f, key=lambda k: widths_f[k])]\n", "tex = {\"b\": r\"$b\\bar b$\", \"tau\": r\"$\\tau^+\\tau^-$\", \"c\": r\"$c\\bar c$\",\n", " \"mu\": r\"$\\mu^+\\mu^-$\", \"s\": r\"$s\\bar s$\"}\n", "\n", "fig, ax = plt.subplots(figsize=(6.8, 3.6))\n", "ax.barh(range(len(labels)), brs, color=\"#1f77b4\")\n", "ax.set_yticks(range(len(labels)))\n", "ax.set_yticklabels([tex[l] for l in labels])\n", "ax.set_xlabel(\"branching ratio (tree-level fermions only)\")\n", "ax.set_title(r\"Higgs fermionic branching ratios at $m_h=125$ GeV\")\n", "for k, b in enumerate(brs):\n", " ax.text(b + 0.005, k, f\"{b:.1%}\", va=\"center\", color=\"0.3\")\n", "ax.set_xlim(0, 1.0); ax.grid(alpha=0.3, axis=\"x\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "49", "metadata": {}, "source": [ "Now $b\\bar b$ dominates — about 84% of the tree-level fermionic width — exactly as the\n", "canonical Higgs plot shows, with $\\tau\\tau$ a distant second. The two facts from §7 are\n", "both visible: the width tracks $m_f^2$ (so the heavy $b$ wins), and quarks carry the\n", "extra $N_c=3$.\n", "\n", "Every *tree-level fermionic* channel is now here, declared cleanly — and\n", "`calc_f.unmatched_channels` came back empty, our guarantee that no fermion was silently\n", "dropped. What is still missing from the plot is the **off-shell $WW^*/ZZ^*$** — which,\n", "it turns out, is *not* beyond a tree-level engine at all. That is §11." ] }, { "cell_type": "markdown", "id": "50", "metadata": {}, "source": [ "## 11. Off-shell decays: reopening the closed channel\n", "\n", "Look again at where the Higgs plot said $WW$ is *closed*: below $2m_W = 160.8$ GeV the\n", "two-body width is exactly zero, because $\\sqrt{\\lambda(m_h^2,m_W^2,m_W^2)}$ is imaginary\n", "(§12.2 makes a lesson of this). Yet the measured Higgs, at 125 GeV, decays to $WW^*$\n", "about a fifth of the time. How?\n", "\n", "Because the Higgs does not need *two* on-shell $W$'s. It reaches **one** on-shell $W$ and\n", "**one off-shell** $W^*$ that immediately materialises as a fermion pair:\n", "\n", "$$h \\;\\to\\; W\\,(W^* \\to f\\bar f').$$\n", "\n", "That is a **three-body** decay, $1\\to3$, and it is where the machinery takes its one real\n", "architectural step. A $1\\to2$ amplitude squares a *single* vertex. Here the amplitude is\n", "*vertex × propagator × vertex* — the $hWW$ coupling, the internal $W^*$ **propagator**\n", "\n", "$$\\frac{-i\\,(g_{\\mu\\nu} - q_\\mu q_\\nu/m_W^2)}{q^2 - m_W^2 + i\\,m_W\\Gamma_W},$$\n", "\n", "and the $W^*ff'$ current. The propagator's momentum $q=p_f+p_{\\bar f'}$ flows *into* the\n", "trace algebra — but $q = p_2+p_3$ is just a sum of the two fermion momenta, so the same\n", "covariant engine from §6 contracts it with nothing new to learn.\n", "\n", "One tidy detail: below threshold $q^2$ can never reach $m_W^2$ (its largest value is\n", "$(m_h-m_W)^2 \\approx 2000 \\ll m_W^2 \\approx 6500$), so the propagator never hits its\n", "pole and the width $\\Gamma_W$ in the denominator barely matters. The decay is genuinely\n", "*off-shell*, never *resonant*." ] }, { "cell_type": "code", "execution_count": null, "id": "51", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gamma(h -> WW*) = 0.8031 MeV (Keung-Marciano ~0.80)\n", "Gamma(h -> ZZ*) = 0.0888 MeV (Keung-Marciano ~0.089)\n" ] } ], "source": [ "# the W and Z total widths that feed the Breit-Wigner (themselves decay outputs)\n", "GammaW, GammaZ = 2.085, 2.4952\n", "gZ = np.sqrt(GW**2 + G1**2)\n", "sw2 = G1**2 / (GW**2 + G1**2)\n", "\n", "# h -> WW*: hWW = g m_W; 9 fermion channels (3 lepton + 2 quark gen x 3 colour),\n", "# each with the V-A coupling g/sqrt(2); factor 2 for which W is on-shell\n", "gWW = scalar_offshell_vv_width(MH, MW, GammaW, GW * MW,\n", " [(GW / np.sqrt(2), 0.0, 9)], identical=False)\n", "\n", "# h -> ZZ*: hZZ = g_Z m_Z; real chiral Z->ff couplings; identical Z (no factor 2)\n", "zchan = [(gZ * (T3 - Q * sw2), gZ * (-Q * sw2), Nc * cnt)\n", " for T3, Q, Nc, cnt in [(0.5, 0, 1, 3), (-0.5, -1, 1, 3),\n", " (0.5, 2/3, 3, 2), (-0.5, -1/3, 3, 3)]]\n", "gZZ = scalar_offshell_vv_width(MH, MZ, GammaZ, gZ * MZ, zchan, identical=True)\n", "\n", "print(f\"Gamma(h -> WW*) = {gWW*1e3:7.4f} MeV (Keung-Marciano ~0.80)\")\n", "print(f\"Gamma(h -> ZZ*) = {gZZ*1e3:7.4f} MeV (Keung-Marciano ~0.089)\")" ] }, { "cell_type": "markdown", "id": "52", "metadata": {}, "source": [ "Both land on the textbook Keung–Marciano values — the covariant $|M|^2$ integrated over\n", "the three-body Dalitz region, cross-checked against the closed form.\n", "\n", "It is worth *seeing* why the on-shell picture missed this. Plot the differential width\n", "$\\mathrm{d}\\Gamma/\\mathrm{d}q^2$ against the invariant mass $\\sqrt{q^2}$ of the $W^*$ —\n", "the mass the virtual $W$ actually carries." ] }, { "cell_type": "code", "execution_count": null, "id": "53", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mSs, mVs, s23 = sp.symbols(\"m_S m_V s23\", positive=True)\n", "inner = scalar_vv_s12_integral(mSs, mVs) # the analytic inner Dalitz integral\n", "inner_f = sp.lambdify((s23, mSs, mVs), inner, \"numpy\")\n", "\n", "q = np.linspace(0.5, MH - MW, 300) # sqrt(q^2), the W* invariant mass\n", "with np.errstate(invalid=\"ignore\"):\n", " dG = inner_f(q**2, MH, MW) / ((q**2 - MW**2)**2 + MW**2 * GammaW**2)\n", "dG = np.nan_to_num(dG)\n", "\n", "fig, ax = plt.subplots(figsize=(6.8, 3.8))\n", "ax.plot(q, dG / dG.max(), lw=2, color=\"#1f77b4\")\n", "ax.axvline(MW, ls=\"--\", color=\"#d62728\")\n", "ax.text(MW - 2, 0.5, r\"the $m_W$ pole\", rotation=90, ha=\"right\", color=\"#d62728\")\n", "ax.axvspan(MH - MW, MW, alpha=0.08, color=\"0.5\")\n", "ax.text((MH - MW + MW) / 2, 0.82, \"kinematically\\nforbidden\", ha=\"center\",\n", " va=\"center\", color=\"0.4\", fontsize=9)\n", "ax.set_xlabel(r\"$W^*$ invariant mass $\\sqrt{q^2}$ [GeV]\")\n", "ax.set_ylabel(r\"$\\mathrm{d}\\Gamma/\\mathrm{d}q^2$ (normalised)\")\n", "ax.set_title(r\"$h\\to W\\,W^*$: the virtual $W$ never reaches its mass shell\")\n", "ax.set_xlim(0, MW + 5); ax.set_ylim(0, 1.05); ax.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "54", "metadata": {}, "source": [ "The whole distribution sits **below** the $m_W$ pole — the virtual $W$ tops out around\n", "$m_h - m_W \\approx 45$ GeV, far short of 80. An on-shell $1\\to2$ calculation only ever\n", "samples $q^2 = m_W^2$ exactly; it sees *none* of this tail, which is why it reported the\n", "channel as flat zero. The off-shell width is the area under this curve.\n", "\n", "Now add $WW^*$ and $ZZ^*$ to the fermion channels of §10 and read off the **complete\n", "tree-level Higgs branching ratios**." ] }, { "cell_type": "code", "execution_count": null, "id": "55", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " h -> b BR = 60.6%\n", " h -> WW* BR = 25.4%\n", " h -> tau BR = 8.2%\n", " h -> c BR = 3.0%\n", " h -> ZZ* BR = 2.8%\n", " h -> mu BR = 0.0%\n", " h -> s BR = 0.0%\n" ] } ], "source": [ "# combine: the fermion widths (widths_f, keyed by (fbar, f)) + the two off-shell ones\n", "combined = {\"WW*\": gWW, \"ZZ*\": gZZ}\n", "tex = {\"WW*\": r\"$WW^*$\", \"ZZ*\": r\"$ZZ^*$\", \"b\": r\"$b\\bar b$\", \"tau\": r\"$\\tau^+\\tau^-$\",\n", " \"c\": r\"$c\\bar c$\", \"mu\": r\"$\\mu^+\\mu^-$\", \"s\": r\"$s\\bar s$\"}\n", "for children, w in widths_f.items():\n", " combined[str(children[1])] = w\n", "grand = sum(combined.values())\n", "\n", "order = sorted(combined, key=lambda k: combined[k])\n", "brs = [combined[k] / grand for k in order]\n", "\n", "fig, ax = plt.subplots(figsize=(6.8, 4.0))\n", "colors = [\"#ff7f0e\" if k in (\"WW*\", \"ZZ*\") else \"#1f77b4\" for k in order]\n", "ax.barh(range(len(order)), brs, color=colors)\n", "ax.set_yticks(range(len(order)))\n", "ax.set_yticklabels([tex[k] for k in order])\n", "ax.set_xlabel(\"branching ratio (tree-level: $f\\\\bar f$ + off-shell $VV^*$)\")\n", "ax.set_title(r\"Complete tree-level Higgs branching ratios at $m_h=125$ GeV\")\n", "for k, br in enumerate(brs):\n", " ax.text(br + 0.005, k, f\"{br:.1%}\", va=\"center\", color=\"0.3\")\n", "ax.set_xlim(0, 0.72); ax.grid(alpha=0.3, axis=\"x\")\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "for k in sorted(combined, key=lambda k: -combined[k]):\n", " print(f\" h -> {k:<5} BR = {combined[k]/grand:.1%}\")" ] }, { "cell_type": "markdown", "id": "56", "metadata": {}, "source": [ "This is the **canonical Higgs picture**: $b\\bar b$ dominant (~60%), $WW^*$ second\n", "(~25%), then $\\tau\\tau$, $c\\bar c$, $ZZ^*$. Compare with the measured Higgs — $b\\bar b$\n", "58%, $WW^*$ 21%, $gg$ 8%, $\\tau\\tau$ 6%, $c\\bar c$ 3%, $ZZ^*$ 3% — and the only real\n", "absentee is the loop-induced $gg$ (and $\\gamma\\gamma$), which a tree-level engine cannot\n", "reach — the loop-induced $gg$ and $\\gamma\\gamma$. Those are next (§12), and then the\n", "whole picture is here.\n", "\n", "And notice what §13.2 is about to call a *trap* — a closed two-body channel with an\n", "imaginary $\\sqrt\\lambda$ — was really a *signpost*: the channel is not gone, it has\n", "gone **off-shell**.\n", "\n", "*Further reading*: the closed-form $R(x)$ this section reproduces is the original\n", "Keung & Marciano calculation (Phys. Rev. D 30, 248, 1984) in the notation of Djouadi's\n", "review (Phys. Rept. 457, 2008, arXiv:hep-ph/0503172) — see `docs/manual/decays_roadmap.md`\n", "§16.5 for the full citations." ] }, { "cell_type": "markdown", "id": "57", "metadata": {}, "source": [ "## 12. Loop-induced decays and the complete Higgs picture\n", "\n", "Two channels are still missing from the plot above, and they are missing for a *reason\n", "of principle*, not of content. The Higgs is electrically neutral and colourless, so it\n", "has no tree-level coupling to photons or gluons at all. Yet $h\\to gg$ is ~8% of the\n", "width and $h\\to\\gamma\\gamma$ was the *discovery* channel. They happen through a **loop**:\n", "a virtual top-quark triangle (both), plus a virtual $W$ loop (for $\\gamma\\gamma$ and\n", "$Z\\gamma$).\n", "\n", "A tree-level engine — everything this notebook has built — **cannot reach these from the\n", "Lagrangian**. So here we do something different, and say so plainly: we *import* the\n", "standard closed-form one-loop results. The loop is summarised by two form factors,\n", "$A_{1/2}(\\tau)$ for a spin-½ particle in the loop and $A_1(\\tau)$ for the $W$, with\n", "$\\tau = m_h^2/4m^2$. They are textbook functions; `feynlag.pheno.loop` provides them,\n", "and the widths follow:\n", "\n", "$$\\Gamma(h\\to\\gamma\\gamma) = \\frac{\\alpha^2 m_h^3}{256\\pi^3 v^2}\n", "\\Big|A_1(\\tau_W) + \\textstyle\\sum_f N_c Q_f^2\\,A_{1/2}(\\tau_f)\\Big|^2, \\qquad\n", "\\Gamma(h\\to gg) = \\frac{\\alpha_s^2 m_h^3}{72\\pi^3 v^2}\n", "\\Big|\\tfrac34 A_{1/2}(\\tau_t)\\Big|^2.$$\n", "\n", "This is a deliberate, documented exception to the *derive-it-from-the-Lagrangian* spirit\n", "of the rest of the library — the honest one-loop computation is a project the size of\n", "the whole engine, while the answer is a known closed form. (See\n", "`docs/manual/decays_roadmap.md` §16.3 and its references.)" ] }, { "cell_type": "code", "execution_count": null, "id": "58", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h -> gg Gamma = 0.3228 MeV (PDG ~0.34, with NLO QCD)\n", "h -> gamma gamma Gamma = 9.1955 keV (PDG ~9.3)\n", "h -> Z gamma Gamma = 5.8535 keV (PDG ~6.3)\n" ] } ], "source": [ "MT, ALPHA, ALPHA_S = 172.76, 1/137.036, 0.1126\n", "\n", "# h -> gamma gamma: W loop + top loop\n", "Ggaga = higgs_gammagamma_width(MH, MT, MW, VEV, ALPHA)\n", "# h -> gg: top loop, with the NLO-QCD K-factor (~1.64) that reaches the measured 8%\n", "Ggg = higgs_gg_width(MH, MT, VEV, ALPHA_S, qcd=True)\n", "# h -> Z gamma: W + top, a two-scale loop function\n", "GZga = higgs_zgamma_width(MH, MT, MW, MZ, VEV, ALPHA, sw2)\n", "\n", "print(f\"h -> gg Gamma = {Ggg*1e3:8.4f} MeV (PDG ~0.34, with NLO QCD)\")\n", "print(f\"h -> gamma gamma Gamma = {Ggaga*1e6:8.4f} keV (PDG ~9.3)\")\n", "print(f\"h -> Z gamma Gamma = {GZga*1e6:8.4f} keV (PDG ~6.3)\")" ] }, { "cell_type": "markdown", "id": "59", "metadata": {}, "source": [ "All three land on their measured values — the diphoton width to a few percent, the gluon\n", "width once the (also imported) NLO-QCD correction is applied.\n", "\n", "One physics detail worth pausing on: in $h\\to\\gamma\\gamma$ the $W$ loop and the top loop\n", "carry **opposite signs** ($A_1 \\approx -8.3$, the top's $N_cQ^2A_{1/2}\\approx +1.8$), so\n", "they interfere *destructively*. The photon rate is what is *left* after a big cancellation\n", "— which is exactly why it is such a sensitive probe of new charged particles: anything\n", "extra in the loop shifts that delicate balance.\n", "\n", "Now add these to the fermion and off-shell channels and read off the **complete**\n", "tree+loop Higgs branching ratios at 125 GeV." ] }, { "cell_type": "code", "execution_count": null, "id": "60", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " h -> b BR = 54.73%\n", " h -> WW* BR = 22.92%\n", " h -> gg BR = 9.21%\n", " h -> tau BR = 7.41%\n", " h -> c BR = 2.71%\n", " h -> ZZ* BR = 2.53%\n", " h -> gammagamma BR = 0.26%\n", " h -> Zgamma BR = 0.17%\n", " h -> mu BR = 0.03%\n", " h -> s BR = 0.02%\n" ] } ], "source": [ "full = dict(combined) # bb, tau, c, mu, s, WW*, ZZ* from section 11\n", "full.update({\"gg\": Ggg, \"gammagamma\": Ggaga, \"Zgamma\": GZga})\n", "tex_full = dict(tex, gg=r\"$gg$\", gammagamma=r\"$\\gamma\\gamma$\", Zgamma=r\"$Z\\gamma$\")\n", "gtot = sum(full.values())\n", "\n", "order2 = sorted(full, key=lambda k: full[k])\n", "brs2 = [full[k]/gtot for k in order2]\n", "loopset = {\"gg\", \"gammagamma\", \"Zgamma\"}\n", "\n", "fig, ax = plt.subplots(figsize=(7.0, 4.4))\n", "cols = [\"#2ca02c\" if k in loopset else \"#ff7f0e\" if k in (\"WW*\", \"ZZ*\")\n", " else \"#1f77b4\" for k in order2]\n", "ax.barh(range(len(order2)), brs2, color=cols)\n", "ax.set_yticks(range(len(order2))); ax.set_yticklabels([tex_full[k] for k in order2])\n", "ax.set_xlabel(\"branching ratio (tree + off-shell + loop)\")\n", "ax.set_title(r\"Complete Higgs branching ratios at $m_h = 125$ GeV\")\n", "for k, br in enumerate(brs2):\n", " if br > 5e-4:\n", " ax.text(br + 0.004, k, f\"{br:.1%}\", va=\"center\", color=\"0.3\", fontsize=9)\n", "from matplotlib.patches import Patch\n", "ax.legend(handles=[Patch(color=\"#1f77b4\", label=\"tree $f\\\\bar f$\"),\n", " Patch(color=\"#ff7f0e\", label=\"off-shell $VV^*$\"),\n", " Patch(color=\"#2ca02c\", label=\"loop-induced\")],\n", " loc=\"lower right\", fontsize=9)\n", "ax.set_xlim(0, 0.65); ax.grid(alpha=0.3, axis=\"x\")\n", "plt.tight_layout(); plt.show()\n", "\n", "for k in sorted(full, key=lambda k: -full[k]):\n", " print(f\" h -> {k:<11} BR = {full[k]/gtot:.2%}\")" ] }, { "cell_type": "markdown", "id": "61", "metadata": {}, "source": [ "That is the canonical Higgs plot — $b\\bar b$, $WW^*$, $gg$, $\\tau\\tau$, $c\\bar c$,\n", "$ZZ^*$, $\\gamma\\gamma$, $Z\\gamma$, in the measured order — and this notebook built every\n", "bar of it from a Lagrangian (the tree and off-shell pieces) plus the standard one-loop\n", "form factors (the three loop bars).\n", "\n", "### The same plot, across the Higgs mass — and where new physics would show\n", "\n", "The 125 GeV column is one slice. Sweep the Higgs mass and every channel traces a curve:\n", "the fermion widths grow slowly, the off-shell $VV^*$ climb steeply toward their on-shell\n", "thresholds, the loop channels rise with $m_h^3$. This is the plot in every Higgs review." ] }, { "cell_type": "code", "execution_count": null, "id": "62", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "def total_widths(mh):\n", " \"All channels as a function of m_h (GeV). Reuses the machinery from above.\"\n", " out = {}\n", " # tree f fbar: Gamma = N_c y_f^2 m_h beta^3/(16 pi), y_f = sqrt2 m_f/v\n", " for name, mf, nc in [(\"b\", 2.79, 3), (\"tau\", 1.777, 1), (\"c\", 0.62, 3),\n", " (\"mu\", 0.1057, 1), (\"s\", 0.055, 3)]:\n", " if mh > 2*mf:\n", " y = np.sqrt(2)*mf/VEV; beta = np.sqrt(1 - 4*mf**2/mh**2)\n", " out[name] = nc*y**2*mh*beta**3/(16*np.pi)\n", " else:\n", " out[name] = 0.0\n", " # off-shell WW*/ZZ* (reuse the Tier-2 helper; fast, cached inner integral)\n", " out[\"WW*\"] = scalar_offshell_vv_width(mh, MW, GammaW, GW*MW,\n", " [(GW/np.sqrt(2), 0.0, 9)], identical=False) if mh > MW else 0.0\n", " zchan = [(gZ*(T3-Q*sw2), gZ*(-Q*sw2), Nc*cnt) for T3, Q, Nc, cnt in\n", " [(0.5,0,1,3),(-0.5,-1,1,3),(0.5,2/3,3,2),(-0.5,-1/3,3,3)]]\n", " out[\"ZZ*\"] = scalar_offshell_vv_width(mh, MZ, GammaZ, gZ*MZ, zchan,\n", " identical=True) if mh > MZ else 0.0\n", " # loop channels\n", " out[\"gg\"] = higgs_gg_width(mh, MT, VEV, ALPHA_S, qcd=True)\n", " out[\"gammagamma\"] = higgs_gammagamma_width(mh, MT, MW, VEV, ALPHA)\n", " out[\"Zgamma\"] = higgs_zgamma_width(mh, MT, MW, MZ, VEV, ALPHA, sw2) if mh > MZ else 0.0\n", " return out\n", "\n", "grid = np.linspace(100, 160, 61)\n", "scan = [total_widths(m) for m in grid]\n", "chans = [\"b\", \"WW*\", \"gg\", \"tau\", \"ZZ*\", \"gammagamma\"]\n", "labels = {\"b\": r\"$b\\bar b$\", \"WW*\": r\"$WW^*$\", \"gg\": r\"$gg$\", \"tau\": r\"$\\tau\\tau$\",\n", " \"ZZ*\": r\"$ZZ^*$\", \"gammagamma\": r\"$\\gamma\\gamma$\"}\n", "tots = np.array([sum(s.values()) for s in scan])\n", "\n", "fig, ax = plt.subplots(figsize=(7.2, 4.6))\n", "for ch in chans:\n", " br = np.array([s[ch] for s in scan]) / tots\n", " ax.plot(grid, br, lw=2, label=labels[ch])\n", "ax.axvline(125.25, ls=\":\", color=\"0.4\"); ax.text(125.8, 0.62, \"125 GeV\", color=\"0.4\")\n", "ax.set_yscale(\"log\"); ax.set_ylim(1e-4, 1.0)\n", "ax.set_xlabel(r\"$m_h$ [GeV]\"); ax.set_ylabel(\"branching ratio\")\n", "ax.set_title(\"Complete Higgs branching ratios vs mass (the SM baseline)\")\n", "ax.legend(ncol=2, fontsize=9, loc=\"lower right\"); ax.grid(alpha=0.3, which=\"both\")\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "63", "metadata": {}, "source": [ "This is where the physics *ends* and the physics *begins*. These curves are the Standard\n", "Model's prediction — the baseline that every LHC Higgs measurement is compared against.\n", "New physics announces itself as a **deviation** from them:\n", "\n", "- a new charged particle in the loop (a fourth-generation quark, a charged Higgs, a\n", " stop) shifts $\\gamma\\gamma$ and $Z\\gamma$ — the channels that are already delicate\n", " cancellations;\n", "- a modified coupling ($\\kappa_b$, $\\kappa_t$, $\\kappa_V$ in the usual language)\n", " rescales one curve relative to the others;\n", "- an entirely new decay — $h\\to\\text{invisible}$, $h\\to aa$ — adds a slice to the\n", " denominator and pulls *every* visible branching ratio down.\n", "\n", "And computing any of those is not a different skill. It is this notebook again — declare\n", "the new fields, extract the vertices, square them, sum the channels — with new content in\n", "the model. The 1→2, 1→3 and loop machinery is exactly what an SM-extension study\n", "re-runs. That is the point of building it from a Lagrangian." ] }, { "cell_type": "markdown", "id": "64", "metadata": {}, "source": [ "## 13. Two ways to get it silently wrong\n", "\n", "Both of these produce a plausible-looking number rather than an error. That makes them\n", "worth more of your attention than anything else in this notebook.\n", "\n", "### 13.1 Forgetting that a Dirac fermion is two Weyl fields\n", "\n", "`feynlag` has no `DiracFermion`; an electron is a left-handed and a right-handed Weyl\n", "field. So the $Z$'s left- and right-handed currents arrive as **separate vertices**, and\n", "unless you say they are the same particle, you get two half-channels instead of one\n", "channel — each missing the other's $g_Lg_R$ interference.\n", "\n", "This is exactly what a `DiracParticle` bundles away — declared as one object, the two\n", "legs *cannot* be separated. But the lower-level `particle_map` lets you make the mistake,\n", "and it is worth seeing its size once, on the $Z'$ model we are about to build." ] }, { "cell_type": "code", "execution_count": null, "id": "65", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Z' model built\n" ] } ], "source": [ "gX = ExternalParameter(\"gX\", 0.3, positive=True)\n", "vx = ExternalParameter(\"vx\", 3000.0, positive=True, unit_dim=1)\n", "lamx = ExternalParameter(\"lamx\", 0.1)\n", "mux = InternalParameter(\"mux\", unit_dim=2)\n", "\n", "U1X = U1(\"U1X\", coupling=gX)\n", "S = Scalar(\"S\", reps={U1X: 1}, component_names=[\"S0\"])\n", "S.expand_vev({S.components[0]: vx})\n", "chiL = WeylFermion(\"chiL\", reps={U1X: sp.Rational(1, 2)}, chirality=\"L\",\n", " nflavors=1, component_names=[\"chiL\"])\n", "chiR = WeylFermion(\"chiR\", reps={U1X: sp.Rational(1, 2)}, chirality=\"R\",\n", " nflavors=1, component_names=[\"chiR\"])\n", "\n", "SdS = (dag(S) * S.mat)[0]\n", "DS = Dmu(S)\n", "Lx = Lagrangian()\n", "Lx.add((dag(DS) * DS)[0], sector=\"kinetic\")\n", "Lx.add(-(-mux.s * SdS + lamx.s * SdS**2), sector=\"potential\")\n", "Lx.add(fermion_gauge_current(chiL, i) + fermion_gauge_current(chiR, i), sector=\"gauge\")\n", "\n", "zp_model = Model(\"Zprime\", gauge_groups=[U1X], fields=[S, chiL, chiR, U1X.bosons(\"X\")],\n", " parameters=[gX, vx, lamx, mux], lagrangian=Lx)\n", "zp_model.solve_tadpoles([mux])\n", "\n", "Zp = U1X.bosons().components[0]\n", "Sr = sp.Symbol(\"S0_r\", real=True)\n", "chi, chibar = sp.symbols(\"chi chibar\")\n", "mZp, mchi, mS = sp.symbols(\"m_Zp m_chi m_S\", positive=True)\n", "chi_map = {chiL.components[0][i]: chi, chiR.components[0][i]: chi,\n", " chiL.bar_components[0][i]: chibar, chiR.bar_components[0][i]: chibar}\n", "print(\"Z' model built\")" ] }, { "cell_type": "code", "execution_count": null, "id": "66", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "with particle_map (1 channel):\n" ] }, { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\frac{gX^{2} \\sqrt{m_{Zp}^{2} - 4 m_{\\chi}^{2}} \\left(m_{Zp}^{2} + 2 m_{\\chi}^{2}\\right)}{48 \\pi m_{Zp}^{2}}$" ], "text/plain": [ " _______________ \n", " 2 ╱ 2 2 ⎛ 2 2⎞\n", "gX ⋅╲╱ m_Zp - 4⋅mᵪ ⋅⎝m_Zp + 2⋅mᵪ ⎠\n", "──────────────────────────────────────\n", " 2 \n", " 48⋅π⋅m_Zp " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "without (2 channels):\n" ] }, { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\frac{gX^{2} \\sqrt{m_{Zp}^{2} - 4 m_{\\chi}^{2}} \\left(m_{Zp}^{2} - m_{\\chi}^{2}\\right)}{48 \\pi m_{Zp}^{2}}$" ], "text/plain": [ " _______________ \n", " 2 ╱ 2 2 ⎛ 2 2⎞\n", "gX ⋅╲╱ m_Zp - 4⋅mᵪ ⋅⎝m_Zp - mᵪ ⎠\n", "────────────────────────────────────\n", " 2 \n", " 48⋅π⋅m_Zp " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "ratio wrong/right:\n" ] }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{m_{Zp}^{2} - m_{\\chi}^{2}}{m_{Zp}^{2} + 2 m_{\\chi}^{2}}$" ], "text/plain": [ " 2 2 \n", " m_Zp - mᵪ \n", "─────────────\n", " 2 2\n", "m_Zp + 2⋅mᵪ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# RIGHT: the two Weyl legs declared as one Dirac particle\n", "right = DecayCalculator(zp_model, {Zp: mZp, Sr: mS, chi: mchi, chibar: mchi},\n", " boson_fields=[Zp, Sr], fermion_sectors=(\"gauge\",),\n", " particle_map=chi_map)\n", "w_right = sum(right.partial_widths(Zp).values())\n", "\n", "# WRONG: particle_map omitted, so the L and R currents stay separate\n", "raw_masses = {Zp: mZp, Sr: mS,\n", " chiL.components[0][i]: mchi, chiR.components[0][i]: mchi,\n", " chiL.bar_components[0][i]: mchi, chiR.bar_components[0][i]: mchi}\n", "wrong = DecayCalculator(zp_model, raw_masses, boson_fields=[Zp, Sr],\n", " fermion_sectors=(\"gauge\",))\n", "w_wrong = sum(wrong.partial_widths(Zp).values())\n", "\n", "print(\"with particle_map (1 channel):\"); display(sp.simplify(w_right))\n", "print(\"without (2 channels):\"); display(sp.simplify(w_wrong))\n", "print(\"ratio wrong/right:\"); display(sp.simplify(w_wrong/w_right))" ] }, { "cell_type": "markdown", "id": "67", "metadata": {}, "source": [ "$$\\frac{\\Gamma_\\text{wrong}}{\\Gamma_\\text{right}}\n", "= \\frac{M^2-m_\\chi^2}{M^2+2m_\\chi^2}\\;\\xrightarrow[\\;m_\\chi\\to0\\;]{}\\;1.$$\n", "\n", "Look at that limit. For light fermions the mistake is **invisible** — the two answers\n", "agree exactly. It only appears once the daughter mass matters, because what got lost is\n", "precisely the $g_Lg_R\\,m^2/M^2$ interference term from §8. A bug that hides in the\n", "massless limit and emerges for heavy final states is the worst kind, which is why this\n", "notebook spends a section on it.\n", "\n", "### 13.2 Closed channels and imaginary widths\n", "\n", "With symbolic masses, `M >= m1 + m2` is simply undecidable, so a channel is kept. That\n", "is the right call — you may substitute masses later that open it. But if you then plug\n", "in numbers that leave it closed, $\\lambda < 0$ and $\\sqrt\\lambda$ is **imaginary**. A\n", "complex width silently poisons the total and every branching ratio." ] }, { "cell_type": "code", "execution_count": null, "id": "68", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h -> WW at m_h = 125 GeV, substituted naively: 0.7213819361810636j\n", " ... imaginary, because 2 m_W = 160.8 > 125.25\n", "\n", "via numeric_partial_widths: 0.0 (exactly zero)\n", "branching ratios then sum to 1.0\n" ] } ], "source": [ "naive = calc.numeric(calc.partial_widths(h)[(Wm, Wp)], extra=numbers)\n", "print(\"h -> WW at m_h = 125 GeV, substituted naively:\", naive)\n", "print(\" ... imaginary, because 2 m_W = 160.8 > 125.25\\n\")\n", "\n", "safe = calc.numeric_partial_widths(h, extra=numbers)\n", "print(\"via numeric_partial_widths:\", safe[(Wm, Wp)], \" (exactly zero)\")\n", "print(\"branching ratios then sum to\",\n", " sum(calc.numeric_branching_ratios(h, extra=numbers).values()))" ] }, { "cell_type": "markdown", "id": "69", "metadata": {}, "source": [ "So: `partial_widths` for symbolic work, and **`numeric_partial_widths` /\n", "`numeric_branching_ratios` whenever numbers go in** — they re-test the threshold after\n", "substitution and return an honest zero. This is also why the Higgs-mass scan in §10\n", "carried an explicit `np.where(grid > threshold, ...)` mask." ] }, { "cell_type": "markdown", "id": "70", "metadata": {}, "source": [ "## 14. Your own model: a $Z'$\n", "\n", "The point of doing this with a Lagrangian-level tool is that nothing above was specific\n", "to the Standard Model. We already built the model in §13: a new $U(1)_X$, broken by a\n", "singlet scalar getting a VEV, with a vector-like fermion $\\chi$ charged under it. Ask it\n", "for the width." ] }, { "cell_type": "code", "execution_count": null, "id": "71", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\frac{gX^{2} \\sqrt{m_{Zp}^{2} - 4 m_{\\chi}^{2}} \\left(m_{Zp}^{2} + 2 m_{\\chi}^{2}\\right)}{48 \\pi m_{Zp}^{2}}$" ], "text/plain": [ " _______________ \n", " 2 ╱ 2 2 ⎛ 2 2⎞\n", "gX ⋅╲╱ m_Zp - 4⋅mᵪ ⋅⎝m_Zp + 2⋅mᵪ ⎠\n", "──────────────────────────────────────\n", " 2 \n", " 48⋅π⋅m_Zp " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "m_chi -> 0 : gX**2*m_Zp/(48*pi) = g_X^2 m_Z' / 48 pi\n" ] } ], "source": [ "width_Zp = sp.simplify(sum(right.partial_widths(Zp).values()))\n", "display(width_Zp)\n", "\n", "# massless limit\n", "print(\"m_chi -> 0 :\", sp.simplify(width_Zp.subs(mchi, 0)), \" = g_X^2 m_Z' / 48 pi\")" ] }, { "cell_type": "markdown", "id": "72", "metadata": {}, "source": [ "$$\\Gamma(Z'\\to\\chi\\bar\\chi)\n", "= \\frac{g_X^2\\,\\sqrt{m_{Z'}^2-4m_\\chi^2}\\;\\big(m_{Z'}^2+2m_\\chi^2\\big)}{48\\pi\\,m_{Z'}^2}.$$\n", "\n", "Compare its threshold behaviour with the Higgs of §7. The fermion pair from a **vector**\n", "comes out in an S-wave, so the width turns on as $\\beta^1$, not $\\beta^3$ — and there is\n", "an extra $(1 + 2m_\\chi^2/m_{Z'}^2)$ enhancement from the longitudinal polarisation." ] }, { "cell_type": "code", "execution_count": null, "id": "73", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f_zp = sp.lambdify(mchi, width_Zp.subs({gX.s: 0.3, mZp: 1.0}), \"numpy\")\n", "r = np.linspace(0, 0.5, 400) # r = m_chi / m_Z'\n", "with np.errstate(invalid='ignore'):\n", " y = np.where(r < 0.5, f_zp(r), 0.0)\n", "y = np.nan_to_num(y)\n", "\n", "fig, ax = plt.subplots(figsize=(6.6, 4.0))\n", "ax.plot(r, y/y[0], lw=2, color='#9467bd', label=r\"$Z'\\to\\chi\\bar\\chi$ (S-wave, $\\beta^1$)\")\n", "beta_r = np.sqrt(np.clip(1 - 4*r**2, 0, None))\n", "ax.plot(r, beta_r**3, lw=2, ls='-.', color='#1f77b4',\n", " label=r'a scalar parent would give $\\beta^3$')\n", "ax.axvline(0.5, ls='--', color='0.5')\n", "ax.text(0.492, 0.5, r'threshold $m_\\chi = m_{Z^\\prime}/2$', rotation=90,\n", " ha='right', va='center', color='0.35')\n", "ax.set_xlabel(r\"$m_\\chi / m_{Z'}$\")\n", "ax.set_ylabel(r'$\\Gamma$ / $\\Gamma(m_\\chi\\!=\\!0)$')\n", "ax.set_title(\"A new gauge boson decaying to a new fermion\")\n", "ax.set_xlim(0, 0.52); ax.set_ylim(0, 1.15)\n", "ax.legend(); ax.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "74", "metadata": {}, "source": [ "The vector curve stays high almost until threshold and then drops steeply, while the\n", "scalar's $\\beta^3$ bends away early. Same phase space, different dynamics — exactly the\n", "distinction §7 promised." ] }, { "cell_type": "markdown", "id": "75", "metadata": {}, "source": [ "## 15. Recap\n", "\n", "You went from \"what is a width?\" to branching ratios for a model you invented. The\n", "through-line:\n", "\n", "- A width is an **inverse lifetime**; branching ratios are its shares.\n", "- $\\Gamma = \\frac{1}{2M}\\int\\overline{|\\mathcal M|^2}\\,\\mathrm{d}\\Phi$ splits into\n", " **kinematics** (phase space, which closes at threshold for any theory) and\n", " **dynamics** (the squared amplitude).\n", "- Spin sums turn $|\\mathcal M|^2$ into a **Dirac trace** — the reason trace theorems\n", " are the workhorse of this subject.\n", "- Threshold behaviour encodes **quantum numbers**: $\\beta^3$ for a CP-even scalar,\n", " $\\beta^1$ for a vector.\n", "- The chiral structure is visible in the answer: $Z\\to\\nu\\bar\\nu$ beats\n", " $Z\\to\\tau^+\\tau^-$ because the neutrino is purely left-handed.\n", "- A **closed** two-body channel is not the end: it can go **off-shell** ($1\\to3$\n", " through a Breit–Wigner propagator), which is how $h\\to WW^*$ dominates at 125 GeV.\n", "- Some channels have **no tree diagram at all** ($h\\to gg,\\gamma\\gamma$): they are\n", " loop-induced, imported as effective vertices — and their delicate cancellations make\n", " them the sharpest probes of new physics.\n", "\n", "**API cheat-sheet**\n", "\n", "| Call | Gives you |\n", "|---|---|\n", "| `kallen(x, y, z)` | the triangle function $\\lambda$ |\n", "| `TwoBodyKinematics(M, m1, m2)` | momenta, on-shell dot products, `phase_space()`, `beta` |\n", "| `slashed(p, mu)` | $\\not p$ for the trace engine |\n", "| `dirac_trace(chain)` | the trace, still with abstract indices |\n", "| `contract_to_dots(expr, kin.dot)` | the same, reduced to masses |\n", "| `ffs_squared(gL, gR, kin)` | $\\overline{\\|\\mathcal M\\|^2}$ for $S\\to f\\bar f$ |\n", "| `ffv_squared(gL, gR, kin)` | ... for $V\\to f\\bar f$ (already averaged over 3 pols) |\n", "| `vvs_squared(c, kin)` | ... for $S\\to VV$ |\n", "| `collect_decay_vertices(...)` | every three-leg vertex, with `g_left`/`g_right` |\n", "| `DecayCalculator(...).partial_widths(p)` | symbolic widths per channel |\n", "| `.numeric_partial_widths(p, extra=...)` | the same as floats, **closed channels zeroed** |\n", "| `.branching_ratios(p)` / `.numeric_branching_ratios(p, ...)` | the shares |\n", "| `scalar_offshell_vv_width(...)` | off-shell $\\Gamma(S\\to V V^*\\to V f\\bar f')$ |\n", "| `higgs_gg_width` / `higgs_gammagamma_width` / `higgs_zgamma_width` | loop-induced widths (imported form factors) |\n", "\n", "**Two rules worth remembering**\n", "\n", "1. Pass a `particle_map` whenever a Dirac fermion appears — the error hides in the\n", " massless limit.\n", "2. Use the `numeric_*` methods the moment numbers go in.\n", "\n", "**Where to go next**\n", "\n", "- `docs/manual/decays.md` — the algorithms chapter: how the covariant trace engine\n", " works, why the $\\gamma_5$ term is provably droppable for 1→2, and what happens at the\n", " guard when it is not.\n", "- `tests/test_pheno.py` — every width above is pinned there twice: against the closed\n", " form, and against an independent explicit-$4\\times4$-matrix evaluation.\n", "- `examples/sm_decays.py` — the same Standard Model as a plain script.\n", "- Implemented: **1→2** (SSS, FFS, FFV, VVS), **1→3 off-shell** $VV^*$, and the\n", " **loop-induced** $gg$/$\\gamma\\gamma$/$Z\\gamma$ (effective one-loop form factors). The\n", " full canonical Higgs branching-ratio plot — every visible channel — is now reproduced.\n", " The FFFF / $t\\to bW^*$ three-body topologies and a genuine one-loop engine are the\n", " remaining frontier (`docs/manual/decays_roadmap.md`)." ] } ], "metadata": { "kernelspec": { "display_name": "Python (lagrangian)", "language": "python", "name": "lagrangian" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }