Mesons in the Low-Energy Limit of QCDh

Abstract

Quark-antiquark bound states are described within the Bethe-Salpeter approach for a class of quark models with instantaneous 4-quark interaction. Thereby decompositions of the Bethe-Salpeter vertex and wave functions according to their Lorentz structures and the particle content are used. Normalization conditions for the bound state functions are given. As an application of the general scheme, we determine the mass spectrum of low-lying mesons without expanding in energy. This calculation is performed for a special Nambu-Jona-Lasinio model which follows from the so-called QCD for hadrons, QCD,, by a localization of the potential. Furthermore the pion and kaon decay constants are determined. We receive good agreement with the experimental data.

Mesons as bilocal fields in the harmonic approximation: A reassessment

“…Pervushin and collaborators [2][3][4][5]131 have shown that with kernels of the form (61, this BSE is also manifestly 1 Lorentz covariant. E ( k ) = r n s i n p ( k ) + k cosp(k)-fp'(k)-=cos2p(k) , To solve the BSE, we should decompose $Lb) over the n Dirac y matrices [4,5,9,13]. Since in this work we are in-(1 1) terested only in the pseudoscalar mesons r , r 1 , K , K ' , we simply have Our solutions for p ( k ) , E T ( k ) , L l ( k ) , and L 2 ( k ) (obtained by the Adams-Bashfort method) agree with the ones in Ref.…”

“…Choosing an instantaneous interaction leads to a potential model. For the covariant generalization of the potential approach to the bound states, Pervushin and co-workers [4,5,13,14] found that the kernel should be of a special form [15], K-KT:…”

Charmless three-body decays ofBmesons

“…DP and PP ! PP scattering at energies m D have been made by several authors [18][19][20][21][22] to calculate the nonresonant D decays, though in principle it is not justified to employ the SU(4) chiral symmetry. As shown in [21,22], the predictions of the nonresonant decay rates in chiral perturbation theory are in general too small when compared with experiment.…”

Heavy-light mesons in a bilocal effective theory

“…To incorporate the spontaneous breaking of chiral symmetry, we use a Lorentz-vector effective interaction motivated by QCD. A special feature of our approach is that we take the interaction to be instantaneous in the rest frame of the meson bound state [11,12,13]. There are a number of reasons for this choice.…”

“…The equations for wave functions written down in[13] apply only to this case of equal quark flavors, since the L-N mixing term has been omitted there.…”