On the Electromagnetic Interactions in the B and D Mesons and Their Structure

Abstract

It is shown that there are serious discrepancies between the empirical values and our theoretical estimates on the magnitude of of the Band D mesons and the radiative decays of the D* mesons. A light quark is described in our theoretical model by the Dirac equation with the same color potential as in heavy quarkonia, whose center is put on a heavy quark. It is pointed out that one of the common reasons for the discrepancies is in too narrow wave functions of the light quark. potentials with almost the same magnitude in the range from 0.1 to 1.0 fm, where heavy quarks are treated non-relativistically. The form of the potential is consistent with the QCD prediction; it tends to a linear confining potential in the long range and a color Coulomb potential in the short range. On the other hand, a light quark and antiquark in a light meson should be treated relativistically in its essence. The bag model and the approach using the Sal peter or the Bethe-Salpeter equation have been succeeded in describing such mesons to a certain extent. 2 ) There seem to be more ambiguous ingredients in the light mesons than in the heavy quarkonia; effective masses of the light quarks are often introduced by hands up to a few hundred MeV, and there are issues concerning chiral symmetry and the separation of the center-of-mass motion from the relative motion. In this sense the so-called atom-like mesons such as Band D mesons seem to offer a charming and beautiful field to examine the light quark behavior. They' are composed of the heavy c - or b-antiquark almost sitting near the center of mass and the light u- or d-quark moving around the heavy antiquark. The light quark with a small current mass would be well described by the Dirac equation with the potential centered at the heavy quark.3) It is examined whether the same potential as in the heavy quarkonia could be used also in atom-like mesons. The heavier the mass of the heavy quark is, the smaller the effect of its motion on the behavior of the light quark is. The behaviors of the light quark in the Band D mesons would, therefore, be similar. Since the charge of the charmed quark is different from that of the bottom quark, the comparison of the mass splittings of the isomultiplets is expected to give valuable information on the u - d quark mass difference, the magnitude of the electric Cotilomb interaction and the size of the mesons. A phenomenological analysis shows that there is an apparent discrepancy between the Coulomb energy derived from the experimental data on the mass split-