Quantum Chromodynamics 3rd. Edition by Walter Greiner, Stefan Schramm, Eckart Stein, D.A. Bromley | 9783540485346 | 3540485341 | Holooly

Basic Electrical

Quantum Chromodynamics

43 SOLVED PROBLEMS

Question: 3.4

The Inclusive Weak Lepton–Nucleon Scattering The coupling of the charged vector bosons Wµ^± of the weak interaction to leptons is described by the interaction Lagrangean (4.23), Lint = +g/√2 Ψf(T-Wµ^+ + T+Wµ^−)γ^µΨf , (1) where Ψf = (νe e)L denotes the doublet of the left-handed electron–neutrino ...

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Since the neutrino is massless and the electron ma...

Question: 2.12

Positron–Pion Scattering Show that the cross section for e^+π^+ scattering is, in the one-photonexchange approximation, equal to that for e^−π^+ scattering. ...

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The graph for

\mathrm{e}^{+} \pi^{+}[/latex...

Question: 3.3

The Nucleonic Scattering Tensor with Weak Interaction Repeat the discussion leading from (3.6) to (3.18) assuming that parity is not conserved, i.e., that Γµ consists of Lorentz vectors and Lorentz axial vectors. Take into account that time-reversal invariance still holds. ...

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Have a look at Fig. 3.2. We are again discussing t...

Question: 2.11

Electron–Pion Scattering (II) Evaluate in detail the nonpolarized π^+e^− cross section. Start with the expressions given in (2.116) and (2.120) and use dσ = 1/4Eω|v| 1/2 ∑s,s′|Fss′|²d Lips(s; k′p′) . Determine dσ/dΩ in the rest system of the pion (p^µ = (M, 0)). ...

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We denote the four-momenta of the pion before and ...

Question: 2.10

Features of Dirac Matrices Start with the anticommutator {γ^µ, γ^ν} = 2g^µν 1 (1) and show that the following relations hold: (a) ab = −ba + 2a · b. (2) (b) (k − m0)(k + m0) = (k + m0)(k − m0) = 0 , for k² = m0². (3) (c) Λ + (k) = (k + m0), (4) which eliminates the negative energy parts of an ...

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(a)

\not a \not b+\not b \not a =a_{\mu} \g...

Question: 2.9

Elastic e^−π^+ Scattering (I) Determine the scattering amplitude and explain the formal steps necessary to evaluate the cross section. ...

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The graph for

\mathrm{e}^{-} \pi^{+}[/latex...

Question: 2.1

Consider the matrix element Mf i = ∫ d³x ∫ dt e^ipf·x (∂µ A^µ(x)+ A^µ(x)∂µ)e^−ipi·x . (1) Assume that the four-potential fulfills the conditions A^0(x,t) → 0 for t → ±∞ , (2a) |A(x,t)| → 0 for |x| → ∞ , (2b) and show that ...

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(a) A partial integration of the time integral yie...

Question: 8.1

The QCD Vacuum Energy Density Derive (8.31) from (8.30). ...

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The sums in (8.30) can be directly evaluated: [la...

Question: 7.4

Calculation of QCD Sum-Rule Graphs with Dimensional Regularization Calculate the first integral in (7.259) using the techniques of dimensional regularization introduced in Sect. 4.3. ...

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We first introduce the usual Feynman parameters: [...

Question: 5.13

Calculation of the Gluonic Contribution to FL(x, Q²) Calculate in the same way as done in the foregoing text the contribution to FL due to photon–gluon scattering via a quark loop. The corresponding diagrams are shown in the figure. A usefull trick is to express the product of two propagators ...

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The color factor for the diagrams coming from the ...

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