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.

fNπN:From quarks to the pion derivative coupling

“…Although the theoretical results did not differ too much from the experimental ones it was shown in Ref. [5] in the context of a more general potential, that we will still need a coulomb force if we want to get a correct value for the R parameter (which is related with the mass splittings of the 3 P J triplet). And this happened despite the fact that, individually, the theoretically obtained masses were quite good when compared with the experimental ones.…”

“…Then the axial and vectorial Ward identities would have constrained the parameters s, p, a, v and t to obey the following equations, [5] s + p + 6t = 0; s − p = 0.…”

“…On the other hand the bare rho-pion mass difference is completely controlled by the extent of chiral symmetry breaking and this mechanism when understood in terms of quarks, amounts to a specific connection between the chiral condensate and the strength of the microscopic hyperfine interaction s · s [3][4][5]. It happens that the obtained strength of this s · s when considered in the exotic K-n s-wave system yields good phase shifts provided we have a small bare nucleon core.…”

Spectra of heavy mesons in the Bethe-Salpeter approach

“…Nevertheless, when it comes to the quantitative details such as the spin-orbit splitting, sizeable corrections occur. On the other hand, it has been argued in [29] that the constraints of chiral symmetry still play an important role in the heavy quark region. We conclude from this that systematic studies of the feasibility of the rainbow-ladder scheme in the heavy quark region provide an important systematic link between the chiral and the static limit of QCD.…”

Chiral-symmetry breaking and confinement in Minkowski space

“…We start from the most general Lorentz structure for the qq interaction and then determine the constraints imposed by SχSB, similarly to what has been done in Ref. [24]. It turns out that a CST model with scalar confinement, together with an equal-weighted pseudoscalar part satisfies the SχSB condition of the Adler consistency zero [25] in π-π scattering in the chiral limit.…”