Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

• the Higgs mass shell follows fromE 2 H − p 2 = s2 + M 4 H + M4 Z +2sM2 H − 2sM2 Z − 2M2 H M2 Z4s− s2 + M 4 H + M4 Z −2sM2 H − 2sM2 Z − 2M2 H M2 Z4s= M 2 H , (235)and the Z mass shell analogously: E 2 Z − p2 = M 2 Z .• finally4p ∓ q = 4E(E Z ± p cos θ) = s + M 2 Z − M 2 H ±√λ(s, M 2 H , M2 Z) cos θ , (236)i. e.16(p + q)(p − q) = (s + M 2 Z − M 2 H) 2 − λ(s, M 2 H, M 2 Z) cos 2 θ= 4sM 2 Z + λ(s, M 2 H, M 2 Z) sin 2 θ (237)Solution 26.∑|T| 2 =spinsg4 M 2 Z 14 cos 4 θ w (s − M tr (/p +/ɛ ∗ (q)(g e 2Z )2 V − g e Aγ 5 )/p − (g e V + g e Aγ 5 )/ɛ(q))= g4 M 2 Z 14 cos 4 θ w (s − M 2 (ge 2 Z )2 V + g e 2 A ) tr (/p + /ɛ ∗ (q)/p − /ɛ(q))= g4 M 2 Z (ge 2 V + g e 2 A ) 14 cos 4 θ w (s − M 2 Lµν (p + , p − , 0)ɛ ∗ µ(q)ɛ ν (q) (238)Z )2polarization sum∑pol.ɛ µ (q)ɛ ∗ ν(q) = −g µν + q µq νM 2 Z(239)∑spins, pol.|T| 2 = g4 M 2 Z (ge 2 V + g e 2 A ) 1 (pµcos 4 θ+p νw (s − M 2 Z )2 − + p µ −p ν + − p + p − g µν) ×(−g µν + q )µq νM 2 Z= g4 (g e 2 V + g e 2 A ) p + p − M 2 Z + 2(p +q)(p − q)cos 4 θ w (s − M 2 Z )2= g4 (g e 2 V + g e 2 A ) 8sM 2 Z + λ(s, M2 H , M2 Z ) sin2 θ(240)8 cos 4 θ w (s − M 2 Z )247