Meson spectra and mass splitting of $ \eta_{c}^{}$ - J/ $ \psi$ calculated with a regularized quark potential

Abstract

The complete Breit potential contains the terms of spin-spin, spin-orbit, orbit-orbit, and tensor force interactions which become singular at short distance. Most of previous calculations of the non-relativistic potential quark model considered only the spin-spin interaction and substituted the \( \delta\)(r) -function by the Gaussian or Yukawa potential in coordinate space. Recently, a method to regularize the Breit potential consists of subtracting terms that cancel the singularity at the origin but leave the intermediate- and long-distance behavior unchanged. Motivated by this work we regularize the Breit potential by multiplying the singular terms in momentum space identically by the form factor [\( \mu^{2}_{}\)/(q2 + \( \mu^{2}_{}\))]2 of the momentum transfer q , where the screened mass μ increases with the reduced mass of the meson. With the regularized Breit potential we calculate the masses of 30 common mesons and the new \( \eta_{b}^{}\) meson. We find that the calculated masses from light to heavy mesons agree well with experimental data. The inclusion of such a dependence of the reduced mass in the potential regularization improves the spin-spin splittings of \( \eta_{c}^{}\) -J/\( \psi\) and \( \eta_{b}^{}\) - \( \Upsilon\)(1S) . The spin-orbit and tensor force interactions in the Breit potential lead to the splittings of \( \chi_{{c0}}^{}\) , \( \chi_{{c1}}^{}\) , and \( \chi_{{c2}}^{}\) .