The QCD Quark Propagator in Coulomb Gauge and - Institut fÃ¼r Physik

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90 6.5. Nucleon electromagnetic form factors: results From these results one finds that R 0 u(Q 2 > 4M 2 N ) < 0.5 R0 u(0). Therefore perturbative effects are dominant in the u-quark mass function on Q 2 ∈ (4MN 2 , ∞). On the other hand, 0.8 < Ru(Q 0 2 < MN 2 ) and hence the u-quark mass function is principally nonperturbative on Q 2 ∈ [0, MN 2 ]. Together these observations suggest that, in our model and in QCD, a judicious estimate of the least-upper-bound on the domain of soft momenta is Λ = M N , and this is the value employed in figure6.9: the figure does not provide compelling evidence for equation(6.100) on the domain up to 6 GeV 2 . One can attempt to fit equation(6.100) to the calculated results or data, and [BJY03] Λ = Λ fit ≈ 0.3 GeV, provides fair agreement. However, this value is significantly smaller than the natural scales we have identified in the model and R 0 u (Λ2 fit ) = 0.98 R0 u (0). In figure 6.10 we extended the calculations for set B to higher momenta. The results hint that the relation (6.100) may be valid for Q 2 6 GeV 2 .
Chapter 7 Epilogue In this thesis we have treated the elementary two-point function of quarks in QCD within Coulomb gauge and implications for hadronic observables and models. We have presented results for the rainbow truncated gap equation in the chiral limit keeping only the instantaneous time-time component of the gluon propagator. Since in Coulomb gauge this quantity corresponds to the colour Coulomb potential, which is calculated in lattice gauge theory, our ansatz is based on these numbers. Regulating the appearing infrared divergence we extract a mass function, which gives a third of the desired constituent quark mass in the infrared. To improve upon this we introduce transverse components with retardation in the gluon propagator ansatz, which is inspired by recent calculations in the Hamiltonian picture. However, the mass function shows no considerable increase after this extension. An explanation for this can be traced in the fact that a sizeable contribution has to come from a dressing of the quark-gluon vertex. An infrared analysis for the quark-gluon vertex carried out in Landau gauge [AFLE06], which showed an infrared enhancement, can be analogously performed in Coulomb gauge. However, a computation of the quark-gluon vertex is tedious and even a one-loop calculation awaits completion [Lic]. Hence Coulomb gauge calculations involving the quark propagator are currently limited to qualitative studies only. We obtain solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axialvector diquarks. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson masses and radii of both mesons and diquarks remain finite and well-defined. This suggests that diquarks might be reasonable degrees of freedom in describing baryons, especially the nucleon. Taking this implication serious we subsequently treat the Faddeev equation of the nucleon in a diquark-quark approximation, which maintains Poincaré covariance, and use the results to calculate nucleon form factors in this framework. In contrast to the chapters 91
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The QCD Quark Propagator in Coulomb
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3 Zusammenfassung In der vorliegend
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Contents 1 Prologue 1 2 Chiral Symm
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Chapter 1 Prologue Quantum Chromo D
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Chapter 1. Prologue 3 an ultraviole
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Chapter 2 Chiral Symmetry Breaking
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Chapter 2. Chiral Symmetry Breaking
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Chapter 3 Remarks on QCD in Coulomb
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Chapter 3. Remarks on QCD in Coulom
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Chapter 4 The Quark Dyson-Schwinger
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Chapter 4. The Quark Dyson-Schwinge
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Page 99 and 100: Appendix A Units and Conventions In
Page 101 and 102: Appendix B Gauge potential, field s
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Page 105 and 106: Bibliography 99 [Alk88] Alkofer, Re
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Page 111 and 112: Bibliography 105 [Mar04] Maris, Pie
Page 113 and 114: Bibliography 107 [PS] Peskin, Micha
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The QCD Quark Propagator in Coulomb Gauge and - Institut fÃ¼r Physik

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