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PS10 - 253a/Schwartz Due Problem Set 10 1 Particle decays...

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253a/Schwartz Due November 16, 2010 Problem Set 10 1. Particle decays. Recall that the decay rate is given by the general formula d Γ = 1 2 E 1 |M| 2 d 3 p 2 (2 π ) 3 1 2 E 2 d 3 p n (2 π ) 3 1 2 E n (2 π ) 4 δ 4 ( p 1 p 2 p n ) (1) a) Evaluate the phase space integrals for 1 2 decays. Show that the total rate is: Γ( φ e + + e - ) = 1 4 x 2 16 πm φ |M| 2 , x = m e m φ (2) b) Evaluate Γ for a particle φ of mass m φ decaying to e + e - of mass m e if i. φ is a scalar , with interaction g S φψ ¯ ψ ii. φ is a a pseudoscalar , with interaction ig P φψ ¯ γ 5 ψ iii. φ is a vector , with interaction g V φ μ ψ ¯ γ μ ψ iv. φ is an axial vector , with interaction ig A φ μ ψ ¯ γ μ γ 5 ψ v. φ is an tensor , with interaction ig T φ μν ψ ¯ σ μν ψ c) The CDF collaboration may be seeing evidence of a new particle which decays only to leptons ( τ,μ and e ) whose mass is around 4 GeV. About 25% of the time it decays to τ + τ - . What spin and parity might this particle have? 2. The neutrino is a neutral particle like the electron. As we saw in the last problem set, its interactions violate parity: the left-handed neutrino couples to the W and Z bosons, while the right handed one does not.
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