Heavy-Heavy-Light Quark Potential in Two Approaches

Abstract

There are a large number of studies about the interquark potential in hadrons. The interquark potential is mainly generated by gluon dynamics reflecting the SU(3) gauge symmetry. In particular, as many lattice QCD studies, the static and quenched approximation produces the only gluonic potential. However, realistic hadrons include not only gluons but also quarks, and quarks affect the interquark potential. We can consider two types of the quark effects, dynamical quark effects and valence quark effects. An example of the dynamical quark effects is the string breaking, which is obtained by unquenched calculation. In this study, we focus on the motional effects of finite-mass valence quarks, that is, valence quarks are not static but have a finite mass. To investigate such quark effects, we define the heavy-heavy-light (QQq) quark potential VQQq(R). It is defined as the energy of QQq systems in terms of the interheavy-quark distance R. The QQq system is constructed from two heavy quarks which are infinitely heavy and spatially fixed, and one light quark which is finite mass and moving around. Since this QQq potential effectively includes the lightquark motional effect, we can investigate the finite-mass valence quark effects to the interquark force. This QQq system is also related to the doubly charmed baryon, which has been recently discovered at the SELEX experiment.1),2) To calculate the QQq potential, we adopt the two approaches, SU(3) lattice QCD3) and a non-relativistic potential model.4) Lattice QCD is the first principle calculation based on QCD. The potential model, or the quark model, is one of the most successful analytical approaches for the low-energy hadron physics.