Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

4.5 Bhabha ScatteringProblem 18. Draw all Feynman diagrams for e + e − → e + e − (“Bhabha scattering”)• do we need to add or subtract the diagrams?• more general: what’s the relative phase of the diagrams?TT † = (T t − T s )(T t − T s ) † = T t T t † − T t T s † − T s T t † + T s T s†(138)• relative signs of the diagrams from permuting the endpoints of the fermion lines• equivalently: relative signs from the number of closed fermion lines in squareddiagramsT t T t † = (−1) 2 × , T t T s † = (−1) 1 × (139a)T s T t † = (−1) 1 × , T s T s † = (−1) 2 × (139b)4.6 FORM• declaration of variables as above• expressions• T s T † s just like in e + e − → µ + µ −T s = e 2 1 s [¯v(p 2)γ ρ u(p 1 )] [ū(q 1 )γ ρ v(q 2 )] (140)T t = e 2 1 t [¯v(p 2)γ ρ v(q 2 )] [ū(q 1 )γ ρ u(p 1 )] (141)4: local [SS*] =5: (g_(1, p2) - me*g_(1)) * g_(1, rho1)6: * (g_(1, p1) + me*g_(1)) * g_(1, rho2)7: * (g_(2, q1) + me*g_(2)) * g_(2, rho1)8: * (g_(2, q2) - me*g_(2)) * g_(2, rho2);• T t T † t similar9: local [TT*] =10: (g_(1, q1) + me*g_(1)) * g_(1, rho1)11: * (g_(1, p1) + me*g_(1)) * g_(1, rho2)12: * (g_(2, p2) - me*g_(2)) * g_(2, rho1)13: * (g_(2, q2) - me*g_(2)) * g_(2, rho2);28