feynlag.pheno.kinematics.ThreeBodyKinematics¶

class feynlag.pheno.kinematics.ThreeBodyKinematics(M, m1, m2, m3, names=('p1', 'p2', 'p3'))[source]¶

Dalitz kinematics of parent(M) → 1(p₁) + 2(p₂) + 3(p₃).

Parametrised by the two Dalitz invariants s₁₂ = (p₁+p₂)² and s₂₃ = (p₂+p₃)² (the third, s₁₃, is fixed by s₁₂+s₁₃+s₂₃ = M²+m₁²+m₂²+m₃²). s₂₃ doubles as the invariant mass² of the (2,3) subsystem — the off-shell q² of a resonance decaying to particles 2 and 3.

The width follows the PDG form Γ = 1/((2π)³ 32 M³) ∬ |M|² ds₁₂ ds₂₃ over the physical Dalitz region.

Parameters:

M (Expr)
m1 (Expr)
m2 (Expr)
m3 (Expr)
names (tuple)

__init__(M, m1, m2, m3, names=('p1', 'p2', 'p3'))¶

Parameters:

M (Expr)
m1 (Expr)
m2 (Expr)
m3 (Expr)
names (tuple)

Return type:

None

Methods

`__init__`(M, m1, m2, m3[, names])
`dot`(head_a, head_b)	`p_a·p_b` as a function of the Dalitz invariants `s₁₂, s₂₃`.
`phase_space_constant`()	The `1/((2π)³ 32 M³)` prefactor of the Dalitz integral.
`s12_bounds`(s23_val)	`(s₁₂⁻, s₁₂⁺)` at a fixed numeric `s₂₃` (PDG Eq.
`s23_range`()	The outer `s₂₃` bounds: `[(m₂+m₃)², (M−m₁)²]`.

Attributes

`names`
`p1`
`p2`
`p3`
`s12`
`s23`
`M`
`m1`
`m2`
`m3`