Atures and Flaws of a Contact Interaction Approximation to QCD
|School||University of Science and Technology of China|
|Keywords||QCD Dyson-Schwinger equation confinement DCSB hadrons baryonsstrangeness spectrum form factors|
Quantum Chromodynamics(QCD) is the most interesting part of the Standard Model and Nature’s only example of an essentially nonperturbative fundamental the-ory. 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. Dyson-Schwinger equation is the only continuum, nonperturbative approach on studying hadron physics. Herein we use a symmetry-preserving vector x vector contact-interaction 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 DSE-based calculation of the spectrum of strange and nonstrange hadrons that simultaneously correlates the dressed-quark-core masses of mesons and baryons ground-and excited-states within a single symmetry-preserving 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 DCSB-corrected 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 dressed-quark-core masses, any approach that omits such effects, whether deliberately or in-advertently, 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 flavour-blind within our framework, something one should also expect in QCD; Another noteworthy result concerns the first radial exci-tation of each ground-state; viz., they posses negligible probability for J=0diquark content. Thus, the redial excitations are constituted almost entirely from axial-vector 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 one-loop renormalisation group be-haviour of QCD. The comparison showed that in connection with experimental observ- ables revealed by probes with|Q2|(?)M2, where M≈0.4GeV is an infrared value of the dressed-quark mass, results obtained using a symmetry-preserving regularisa-tion of the contact-interaction 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 one-loop QCD renormalisation-group-improved kernels. This owes to the necessary presence in pseudoscalar meson Bethe-Salpeter amplitudes of terms that may be described as pseudovector in character. In this con-text, 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 fully-consistent treatment of a momentum-dependent kernel that behaves as1/k2in the ultraviolet. From a modern perspective, however, the omission might be used judiciously in order to build effica-cious 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 distri-bution of a dressed-u-quark in the K+is very similar to that of the dressed-u-quark in the π+, whereas the charge distribution of the dressed-s-quark in the K+is noticeably harder than that of its u-quark 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 current-quark mass and the interaction-generated 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 associat-ed 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.