feynlag.pheno.amplitudes.ffs_squared¶

feynlag.pheno.amplitudes.ffs_squared(g_left, g_right, kin)[source]¶

S(P) → f(p₁) f̄(p₂) for Γ = g_L P_L + g_R P_R.

Σ_spins |M|² = Tr[(p̸₁+m₁) Γ (p̸₂−m₂) Γ̄] with Γ̄ = ḡ_L P_R + ḡ_R P_L (dirac_conjugate(): bare projectors swap).

Pushing projectors right with P_{L,R} p̸ = p̸ P_{R,L}:

chirality-diagonal (|g_L|², |g_R|²) — the two mass insertions are killed by P_L P_R = 0, leaving ½Tr[p̸₁p̸₂] = 2(p₁·p₂);
chirality-mixing (g_L ḡ_R + c.c.) — the momentum terms die instead and m₁(−m₂)Tr[P_L] = −2m₁m₂ survives.

So Σ|M|² = 2(|g_L|²+|g_R|²)(p₁·p₂) − 4 m₁m₂ Re(g_L ḡ_R), and a scalar parent needs no spin average.