Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

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andλ(a, b, c) = a 2 + b 2 + c 2 − 2ab − 2ac − 2bc (187)satisfy energy and momentum conservation and the mass shell conditions for e + e − → ZHwith m e = 0. Compute16(p + q)(p − q) . (188)Problem 26. Compute the differential cross sectionfor unpolarized Higgs strahlung e + e − → ZH.NB: use the fact that ∑ ɛ µ ɛ ∗ ν is symmetric in µ ↔ ν.dσdΩ (θ e − H) (189)Problem 27. Compute the integrated cross section for Higgs strahlung e + e − → ZH.38
7 SolutionsSolution 1.∂ µ e −ipx = −ip µ e −ipx(a∂)(b∂)e −ipx = −(ap)(bp)e −ipx∂ 2 e −ipx = −i(p∂)e −ipx = −p 2 e −ipx(190a)(190b)(190c)Solution 2.∂ µ x µ = gµ ν ∂x µ /∂x ν = gµ ν δ µ ν = g µ µ = 4 (191a)( )∂ 2 e −x2 /2 = −∂ µ x µ e −x2 /2= −x µ ∂ µ e −x2 /2 − (∂ µ x µ ) e −x2 /2= x µ x µ e −x2 /2 − g µµ e −x2 /2 = (x 2 − 4)e −x2 /2(191b)Solution 3.( ) ( )[γ k , γ l] 0 σ = k 0 σl+ −σ k 0 −σ l + (k ←→ l) =0=( )−σ k σ l 00 −σ k σ l( ) (−[σ k , σ l ] + 00 −[σ k , σ l = −2δ] kl 1 0+ 0 1+ (k ←→ l))(192a)Solution 4.ū k (p) = u † k (p)γ 0 = u † k (⃗ 0)γ 0 γ 0¯v k (p) = ¯v k ( ⃗ 0)/p − m√p0 + m/p † + m√p0 + m γ 0 = ū k ( ⃗ /p + m0) √p0 + m(193a)(193b)Using the definition and multiplying with γ 0 from the right2∑k=1u k ( ⃗ 0)ū k ( ⃗ 0) = γ 0 + 1,22∑k=1v k ( ⃗ 0)¯v k ( ⃗ 0) = γ 0 − 12(194)39
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 and 38: 6 Standard Model(C, T) Y Q = T 3 +
Page 39: • Yukawa couplingspp, µp, µfZ 0
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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