HW 11 problems/solutions

HW 11 problems/solutions - Homework solution set 11 Problem...

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Homework solution - set # 11 Problem XI.1 : Give explicitely the muonic part of the GWS Lagrangian for the muon. We can deﬁne : L μ = ± ν μ μ ! L R μ = μ R which is the SU (2) W doublet, singlet respectively. Lepton sector of the GWS model is then given as : L lepton = i ¯ L γ μ ( μ - igA a μ τ a 2 - ig 0 Y L B μ ) L + i ¯ μ ( μ - ig 0 Y R B μ ) R and the interaction part L ( int ) lepton = g ¯ L γ μ τ a 2 L A a μ - 1 2 g 0 ¯ L γ μ L B μ - g 0 ¯ R γ μ R B μ = = g ( ¯ L γ μ τ + 2 L A - μ + ¯ L γ μ τ - 2 L A + μ ) + L ( diag ) where τ ± = 1 2 ( τ 1 ± i τ 2 ) A ± μ = 1 2 ( A 1 μ ± iA 2 μ ) 1 2 τ + = 1 2 ± 0 1 0 0 ! 1 2 τ - = 1 2 ± 0 0 1 0 ! so that we can rewrite the leptonic part of the Lagrangian : 1

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±L ( int ) lepton = g 2 [ ( ¯ ν L , ¯ μ L ) γ μ ± 0 1 0 0 ν L μ L ! A - μ + + ( ¯ ν L , ¯ μ L ) γ μ ± 0 0 1 0 ν L μ L ! A
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HW 11 problems/solutions - Homework solution set 11 Problem...

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