Atures and Flaws of a Contact Interaction Approximation to QCD 

Author  ChenChen 
Tutor  WanShaoLong 
School  University of Science and Technology of China 
Course  Theoretical Physics 
Keywords  QCD DysonSchwinger equation confinement DCSB hadrons baryonsstrangeness spectrum form factors 
CLC  O572.243 
Type  PhD thesis 
Year  2013 
Downloads  17 
Quotes  0 
Quantum Chromodynamics(QCD) is the most interesting part of the Standard Model and Nature’s only example of an essentially nonperturbative fundamental theory. It has two features:confinement and dynamical chiral symmetry broken(DCSB). These two features are not apparent in QCD’s Lagrangian, yet they play a dominant role in hadron physics. DysonSchwinger equation is the only continuum, nonperturbative approach on studying hadron physics. Herein we use a symmetrypreserving vector x vector contactinteraction model to calculate some properties of hadrons, especially for those with strangeness.In Chapter3we calculated the spectrum of mesons and baryons with strangeness. We described the first DSEbased calculation of the spectrum of strange and nonstrange hadrons that simultaneously correlates the dressedquarkcore masses of mesons and baryons groundand excitedstates within a single symmetrypreserving framework. It is the first time in the world people use DSEs to calculate the properties of hadrons with stangerness. Our results are typically bigger than the experimental results. This is a marked success since our DCSBcorrected kernel omits the resonant contributions; i.e., effects that may phenomenological be associated with meson cloud. Indeed, since meson cloud contributions typically induce a material reduction in hadron dressedquarkcore masses, any approach that omits such effects, whether deliberately or inadvertently, should be viewed with caution unless it overestimates masses by a similar magnitude. Meanwhile, We also got some information of the structure of hadrons. For example, we found that the diquark content of baryons is largely independent of strangeness, the baryon structure is flavourblind within our framework, something one should also expect in QCD; Another noteworthy result concerns the first radial excitation of each groundstate; viz., they posses negligible probability for J=0diquark content. Thus, the redial excitations are constituted almost entirely from axialvector diquark correlations. This possibility was first noted in connection with the Roper resonance.In Chapter4we calculated the elastic and semileptonic transition form factors of Pion and Kaon. We compared our form factors with those obtained using the same truncation but an interaction that preserves the oneloop renormalisation group behaviour of QCD. The comparison showed that in connection with experimental observ ables revealed by probes withQ2(?)M2, where M≈0.4GeV is an infrared value of the dressedquark mass, results obtained using a symmetrypreserving regularisation of the contactinteraction are not realistically distinguishable from those produced by more sophisticated kernels. The picture is different if one includes the domain Q2> M2, whereupon a consistent treatment of the contact interaction yields harder form factors than those obtained with oneloop QCD renormalisationgroupimproved kernels. This owes to the necessary presence in pseudoscalar meson BetheSalpeter amplitudes of terms that may be described as pseudovector in character. In this context, an inconsistent treatment of the contact interaction is possible; namely, through deliberate omission of the pseudoscalar mesons’pseudovector components. Results obtained thereby are just as soft as those produced by a fullyconsistent treatment of a momentumdependent kernel that behaves as1/k2in the ultraviolet. From a modern perspective, however, the omission might be used judiciously in order to build efficacious models for hadron physics phenomena that cannot readily be studied using more elaborate means, so long as neither agreement nor disagreement with experiment is interpreted as a challenge to QCD. In stepping toward these conclusions, we were able to make a number of other observations. For example, it was necessary to detail the properties of the inhomogeneous vector and scalar vertices, a process which led us to a novel Ward identity for the scalar vertex. In addition, we found that the charge distribution of a dresseduquark in the K+is very similar to that of the dresseduquark in the π+, whereas the charge distribution of the dressedsquark in the K+is noticeably harder than that of its uquark partner. This explains the positive slope of the K0form factor at Q2=0. Finally, whilst the Q2=0value of the subleading transition form factor,f_, is a gauge of flavour symmetry breaking, it is also sensitive to the difference between the explicit currentquark mass and the interactiongenerated dynamical mass.In Chapter5We explained and illustrated that the Ash form factor connected with the γ*N→Δ transition should fall faster than the neutron’s magnetic form factor, which is a dipole in QCD. In addition, we showed that the quadrupole ratios associated with this transition are a sensitive measure of quark orbital angular momentum within the nucleon and Δ. In Faddeev equation studies of baryons, this is commonly associated with the presence of strong diquark correlations. Finally, direct calculation revealed that predictions for the asymptotic behaviour of these quadrupole ratios, which follow from considerations associated with helicity conservation, are valid.