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