Answer Happy

Massive Scalar Production in SU(N) Consider an SU(N) gauge theory with a massless fermion y in the fundamental represen- tation and a scalar 0 with mass m in the fundamental representation. Use the Feynman rules discussed in class, to show that the total cross section of the process for 40 + $0* as a function of the center of mass energy s is given by 9 1 1 olurit + dies“) – 10 (1 -->): ()_4m?) ( φφ*) 1927 N2 S (Hints: First show that the matrix element square is given by |M12 94 4N22 trace(92(P1 – P2)47(P1 – P2)) trace(TATB) trace(TATB), where TA, TB are generators of the fundamental representation of SU(N) and q1, 92, P1, P2 the momentum of the initial fermion, antifermion, scalar, and antiscalar, respectively. Then integrate over the phase space. The kinematics is easiest to evaluate in the center of mass frame.