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

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-vector 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 $K_S=K_P=-3\mathrm{}{K}_T$. Within the validity domain of the ladder approximation, this result is independent of the quark current masses. While the vector and axial-vector parts, $K_V$ and $K_A$, 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.