# HW10 - PHY5667 Problem Set#10(due Tue Nov 2(1 Consider a...

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PHY5667 Problem Set #10 (due Tue Nov 2) (1) Consider a theory of a neutral scalar φ (mass m φ ) and a Dirac fermion ψ (mass m ψ ) with the interaction L int = - λφ ψψ , where λ is a real constant. Assume m φ > 2 m ψ . (i) Obtain the Feynman rule for the φ - ψ a - ψ b vertex, where a, b = 1 , · · · , 4 label Dirac- spinor components. Indicate charge and momentum arrows wherever necessary. (ii) Compute the amplitude M fi for the decay process φ ψ + ψ , where the initial φ is at rest and the final ψ and ψ have 4-momenta ( E, ~ k ) and ( E 0 , ~ k 0 ) and spins s and s 0 , respectively. (iii) Compute the “total” decay rate (i.e. the final spins s and s 0 being summed over) for φ ψ + ψ . (2) Consider a theory of a charged vector A μ (mass m A ) and two Dirac fermions ψ 1 and ψ 2 (mass m 1 and m 2 , respectively) with the interaction L int = - gA μ ψ 1 γ μ ψ 2 - g * A μ ψ 2 γ μ ψ 1 , where g is a complex constant. Assume m 1 > m A + m 2 . (i) Obtain the Feynman rules for the A μ -( ψ 1 ) a -( ψ 2 ) b and A μ -( ψ 2 ) a -( ψ 1 ) b vertices, where a, b = 1 ,

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