feynlag.pheno.offshell.scalar_vv_squared¶

feynlag.pheno.offshell.scalar_vv_squared(m_V, kin)[source]¶

The reduced |M|² for S → V(p₁) [V^*→ f(p₂) f̄'(p₃)].

Returns the spin-summed squared amplitude stripped of the coupling factor g_{SVV}² g_V² / |q²−m_V²+i m_V Γ_V|² (reinstated by offshell_scalar_vv_width()), as a symbolic function of the Dalitz invariants s₁₂, s₂₃ (s₂₃ = q²). Massless fermions, left-handed V f f̄' current (the parity-violating ε term drops against the symmetric propagator/polarisation structure — see the roadmap §16.2).

Assembly (all contracted by the covariant engine):

P^{μμ'}_{V}(p₁) · (g_{μα})(g_{μ'α'}) · N_{αβ}(q) N_{α'β'}(q) · ½ Tr[p̸₂ γ^β p̸₃ γ^{β'}]

where P_V is the on-shell-V polarisation sum, N the propagator numerator, and the ½ is the left-handed projector (its ε piece dropped).