Bethe-Salpeter Equations And Their Applications To Meson Spectrums

Quantum Chromodynamics(QCD) is a fundamental field theory of hadron physics. It describes the color interaction between quarks and gluons. QCD is an asymptotically free gauge theory, the high-energy problem of quark and gluon can be calculated pertur-batively. Dynamical chiral symmetry breaking is another feature of QCD, which can be learnt via Dyson-Schwinger equations.Hadrons can be divided into two classes, baryons and mesons, which can be distin-guished since the baryon number is a conserved quantum number. Thus, a baryon is characterized as a hadron with baryon number one, while a meson is characterized as a hadron with baryon number zero. Also a baryon is a fermion while a meson is a boson. A meson, in their simplest form, can be considered as a bound state of a quark with baryon number-and an antiquark with baryon number-1/3, in the constituent quark model. These type of models are very successfully in describing the hadron spectrum and provid-ing a consistent classification scheme for mesonic states according to their flavor content via group theory argument. Nevertheless, the calculation of the meson spectrum in terms of constitute quarks has certain drawbacks. Especially the masses of the low-lying pseu-doscalar meson octet(π, K,η, η’mesons) are not easily described by constituents with masses of approximately300MeV.The strong interaction is well described by the relativistic quantum field theory of QCD. And the elementary degrees of freedom of QCD are quarks and gluons. In low-energy region, the dynamical chiral symmetry breaking characterizes the QCD. The ap-peared (pseudo) Goldstone bosons are taken as the light pseudoscalar mesons, so they have the comparatively light masses. These particles can still be classified in the same way as in the quark model.In order to provide a consistent description of mesons within the standard model of particle physics, it is necessary to treat the pseudoscalar mesons as composite states in the framework of QCD. Non-perturbative methods are necessary in this context, and lattice-regularized QCD has successfully described the hadron spectrum for ground states and some excited states. Here we use a different approach which is provided by the Dyson-Schwinger equation and Bethe-Salpeter equation formalism, and we employ them in the following to study the mesons as relativistic bound states of strong interaction. In solving the quark DSE and meson BSE, we use the rainbow-ladder truncation and Maris-Tandy model in which the enhancement of the effective interaction in the infrared region plays a significant impact on the dynamical chiral symmetry breaking. The rainbow-ladder truncation is only suitable for the flavor-nonsinglet states in pseudoscalar and vector channel. For the mass splitting of pion and kaon, we introduce the electromagnetic interaction into both DSE and BSE and consider the isospin symmetry breaking. And the results for the pseudoscalar mesons are good while it is not the case for the vector mesons.