Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

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– . . . two different reductions in the same FORM program require advancedtricks . . .• running the program:ohl@thopad2:~fdfp$ form bhabha.frmFORM by J.Vermaseren,version 3.3(Mar 28 2009) Run at: Thu Jul 7 18:37:42 2011[SS*] =+ me^2 * ( - 64*u - 64*t )+ me^4 * ( 192 )+ 8*u^2 + 8*t^2;[TT*] =+ me^2 * ( - 64*u )+ me^4 * ( 64 )+ 16*u^2 + 16*t*u + 8*t^2;[ST*] =+ me^2 * ( 64*u )+ me^4 * ( - 96 )- 8*u^2;[TS*] =+ me^2 * ( 64*u )+ me^4 * ( - 96 )- 8*u^2;0.00 sec out of 0.00 sec• NB: |T s | 2 (t, u) = |T t | 2 (s, u)• final result very symmetrical∑spinsProblem 19. Compute the differential cross section( )tTT ∗ = 8e 4 2 + u 2+ s2 + u 2+ 2u2 + O(m 2s 2 t 2 ste) (144)for Bhabha scattering in the region s, −t, −u ≫ m 2 e.dσ(cos θ) (145)dΩ30
5 QCD5.1 <strong>Feynman</strong> Rules∵ full account requires another full set of lectures∴ just a few SU(N) formulae– generators T a and totally anti symmetric structure constants f abc :(summations for c = 1, 2, . . . , (N 2 c − 1) implied).– normalization and contractions[T a , T b ] = if abc T c (146)tr (T a T b ) = 1 2 δ ab• physical degrees of freedom: quarks and gluons:(147a)T a T a = C F · 1 = N2 C − 1 · 12N C(147b)f acd f bcd = C F · δ ab(147c)k, µ, app ′ = igγ µ T a (148)• triple gluon couplings1gf a1 a 2 a 3g µ1 µ 2(k 1 µ 3− k 2 µ 3)23=+gf a1 a 2 a 3g µ2 µ 3(k 2 µ 1− k 3 µ 1)+gf a1 a 2 a 3g µ3 µ 1(k 3 µ 2− k 1 µ 2)(• quartic gluon couplings21−ig 2 f a1 a 2 bf a3 a 4 b×(g µ1 µ 3g µ4 µ 2− g µ1 µ 4g µ2 µ 3)=−ig 2 f a1 a 3 bf a4 a 2 b×(g µ1 µ 4g µ2 µ 3− g µ1 µ 2g µ3 µ 4)(3 4−ig 2 f a1 a 4 bf a2 a 3 b×(g µ1 µ 2g µ3 µ 4− g µ1 µ 3g µ4 µ 2)• Faddeev-Popov ghosts appear only in loop diagrams31
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: • the interference terms are more
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 and 40: • Yukawa couplingspp, µp, µfZ 0
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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