Covariant Spectator Theory of heavy–light and heavy mesons and the predictive power of covariant interaction kernels

Abstract

The Covariant Spectator Theory (CST) is used to calculate the mass spectrum and vertex functions of heavy-light and heavy mesons in Minkowski space. The covariant kernel contains Lorentz scalar, pseudoscalar, and vector contributions. The numerical calculations are performed in momentum space, where special care is taken to treat the strong singularities present in the confining kernel. The observed meson spectrum is very well reproduced after fitting a small number of model parameters. Remarkably, a fit to a few pseudoscalar meson states only, which are insensitive to spin-orbit and tensor forces and do not allow to separate the spin-spin from the central interaction, leads to essentially the same model parameters as a more general fit. This demonstrates that the covariance of the chosen interaction kernel is responsible for the very accurate prediction of the spin-dependent quark-antiquark interactions.

Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons

“…In [57] we found that fits to a small number of pseudoscalar states alone already yield a model that predicts all other considered mesons with J ≤ 1 with almost the same accuracy as more general fits, indicating that the covariance of the kernel correctly determines the spin-dependence of the interaction. The CST wave functions are then analyzed in detail.…”

“…We chose three different sets of data to fit our model parameters to: the set called S1 consists of pseudoscalar meson states only (it is identical to the one used in [57] to fit the model named P1), the set S2 includes pseudoscalar, scalar, and vector states, and the largest set, S3, adds a number of axial vector states to the states contained in S2. A list of these states and their masses is given in Table I.…”

“…In this work we go beyond [57] in several aspects. In addition to the previously used scalar+pseudoscalar Lorentz structure, we introduce a vector interaction, whose relative weight can be altered through a continuous mixing parameter y.…”

Heavy and Heavy--Light Mesons and the Lorentz Structure of the Quark--Antiquark Interaction

“…Fitting the quark masses does not lead to a significant improvement over the results of [19]. The light and charm quark masses can be varied by a few hundred MeV (the bottom quark mass to a somewhat lesser degree) without noticeably deteriorating the quality of the fit.…”

“…The data set S1 contains 9 meson states with 0 − , the set S2 (S2 ) contains 25 (24) states with 0 ± and 1 − , and the set S3 contains 39 states with 0 ± and 1 ± (the states are listed in [17]). Table 1 shows the parameters of the various models determined in our fits, which include the ones found in [19], M0 S1 and M0 S2 , for comparison. The results of four of our models are compared to the data in Fig.…”