Chiral symmetry and spin dependence of the quark-antiquark forces in quarkonium

Abstract

Within the ladder approximation, the general form of the quark-antiquark interaction kernel,consistent with chiral symmetry, is investigated through the combined use of Ward identities for theaxial and vector currents. In the charm and bottom sectors we show that chiral symmetry still playsan important role, through the functional form of the quark-antiquark forces. To maintain the chiralsymmetry the scalar, pseudoscalar and tensor terms of the local interaction kernel must appear ina combination consistent with the equation Ks = Kp = 3Kt. Within the validity domain of theladder approximation, this result is independent of the quark current masses. While the vectorand axial parts, Kv and Ka, are not constrained by chiral symmetry, they are needed in order toimplement spontaneous chiral-symmetry breaking, since the above terms alone would not do. Inaddition to the usual spin-spin, spin-orbit and tensor interactions, the existence of a Lorentz-tensorterm in the kernel gives rise to a second tensor force which does not appear in previous studies ofmesonic spectroscopy.