Heavy Meson Description with a Screened Potential.pdf

a r X i v : h e p - p h / 0 3 0 7 3 1 0 v 1 2 5 J u l 2 0 0 3 Heavy Meson Description with a Screened Potential P. Gonza?lez(1), A. Valcarce(2), H.Garcilazo(3), and J. Vijande(2) (1) Dpto. de F??sica Teo?rica and IFIC Universidad de Valencia - CSIC, E-46100 Burjassot, Valencia, Spain (2) Grupo de F??sica Nuclear Universidad de Salamanca, E-37008 Salamanca, Spain (3) Escuela Superior de F??sica y Matema?ticas Instituto Polite?cnico Nacional, Edificio 9, 07738 Me?xico D.F., Mexico Abstract We perform a quark model calculation of the bb and cc spectra from a screened funnel potential form suggested by unquenched lattice calculations. A con- nection between the lattice screening parameter and an effective gluon mass directly derived from QCD is established. Spin-spin energy splittings, lep- tonic widths and radiative decays are also examined providing a test for the description of the states. Keywords: phenomenological quark models, meson properties Pacs: 12.39.-x, 14.40.-n, 13.40.Hq 1 I. INTRODUCTION Heavy quarkonia, bb and to a lesser extent cc (for tt the weak decay rates are too large for these resonances to be observed), are ideal systems to test quark potential models derived from QCD. Actually for the low-lying states (the ground state for cc and the ground and first excited states for bb) one can test the theory itself at the perturbative regime [1]. This may provide a quantitative estimate of the approximations involved when using a potential model interaction derived from QCD to describe heavy quarkonia. At very short distances a nonrelativistic coulombic potential, with strength proportional to αs, the quark-gluon-quark coupling constant, is derived perturbatively from the one- gluon exchange interaction in QCD. Relativistic corrections involve spin-independent, spin- spin, spin-orbit and tensor terms. Radiative corrections have been estimated as well. At long distances nonperturbative effects involving multigluon interactions, in particular those relate