Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

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6.2 <strong>Feynman</strong> Rules• vector and axial vector couplingsg V = T 3 − 2Q sin 2 θ wg A = T 3(174a)(174b)• e. g. for electrons• neutral currentsfpfpZ 0fγfg V = − 1 − 4 sin2 θ w2k, µ= − ik, µ, g A = − 1 2g ( )gf2 cos θ V γ µ − g f Aγ µ γ 5w(175)(176)p ′ = − ieQ f γ µ (177)• charged currents (V ff ′ is the CKM matrix)pfk, µW −f ′ = − i √ g V ff ′τ + 1 − γ 5γ µ2 2p ′(178)• triple gauge couplingsk 1 , µ 1W −k Z 02 , µ 2 =W − k 3 , µ 3k 1 , µ 1W − γk 2 , µ 2 =W − k 3 , µ 3ie cot θ w g µ1 µ 2(k 1 µ 3− k 2 µ 3)+ie cot θ w g µ2 µ 3(k 2 µ 1− k 3 µ 1)+ie cot θ w g µ3 µ 1(k 3 µ 2− k 1 µ 2)ieg µ1 µ 2(k 1 µ 3− k 2 µ 3)+ieg µ2 µ 3(k 2 µ 1− k 3 µ 1)+ieg µ3 µ 1(k 3 µ 2− k 1 µ 2)(179)(180)36
• Yukawa couplingspp, µp, µfZ 0W ±kH= − i gm f(181)f2M Wp ′kHZ 0=p ′ , µ ′kHW ±i gM Zcos θ wg µµ ′ (182)p ′ , µ ′ = igM W g µµ ′ (183)• a lot more vertices: quartic couplings, Higgs selfcouplings, etc.6.3 Higgs StrahlungProblem 24. Compute the scattering amplitude for Higgs strahlung e + e − → ZHe + (p + )H(k)(184)e − (p − )Z 0 Z 0Z 0 (q)ignoring all terms of O(m e /M Z ), O(m e /M H ) and O(m e / √ s). You may assume that √ s ≫M 2 Z and ignore the width of the Z.Problem 25. Show that the four momentap − = (E; 0, 0, E)p + = (E; 0, 0, −E)k = (E H ; p sin θ cos φ, p sin θ sin φ, p cos θ)q = (E Z ; −p sin θ cos φ, −p sin θ sin φ, −p cos θ)(185a)(185b)(185c)(185d)withp =√λ(s, M2H, M 2 Z )2 √ s(186a)E H = s + M2 H − M2 Z2 √ sE Z = s + M2 Z − M2 H2 √ s(186b)(186c)37
Page 1 and 2: Feynman Diagrams For PedestriansTho
Page 3 and 4: 1 Introduction1.1 Scattering Amplit
Page 5 and 6: • a Lorentz transformation Λ mus
Page 7 and 8: 2.1 Klein-Gordon Equation(i∂ 0 )
Page 9 and 10: ∴ the formalism is consistent, if
Page 11 and 12: • we can verify the anti commutat
Page 13 and 14: • from which we can construct sol
Page 15 and 16: • invariant overlap from conserve
Page 17 and 18: k = (k 0 ; |⃗k| sin θ cos φ, |
Page 19 and 20: • that can be solved recursively
Page 21 and 22: ∵ intermediate states violate ene
Page 23 and 24: • the following Feynman rules pro
Page 25 and 26: • momentum conservation:s + t + u
Page 27 and 28: 4.2 Trace Techniques• consider a
Page 29 and 30: • traces9: trace4, 1;10: trace4,
Page 31 and 32: • the interference terms are more
Page 33 and 34: 5 QCD5.1 Feynman Rules∵ full acco
Page 35 and 36: with the “hadronic tensor”H µ
Page 37: 6 Standard Model(C, T) Y Q = T 3 +
Page 41 and 42: 7 SolutionsSolution 1.∂ µ e −i
Page 43 and 44: Solution 6.ū k (p)γ µ u l (p) =
Page 45 and 46: Solution 14.L µν = tr [(/p + m)γ
Page 47 and 48: []iT 1 = ū(q 1 )(igT a /ɛ ∗ i(k
Page 49 and 50: • the Higgs mass shell follows fr

Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

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