Nonlinear Regge trajectories with AdS/QCD

Abstract

In this work, we consider a nonquadratic dilaton $\mathrm{\ensuremath{\Phi}}(z)=(\ensuremath{\kappa}z{)}^{2\ensuremath{-}\ensuremath{\alpha}}$ in the context of the static soft wall model to describe the mass spectrum of a wide range of vector mesons from the light up to the heavy sectors. The effect of this nonquadratic approach is translated into nonlinear Regge trajectories with the generic form ${M}^{2}=a(n+b{)}^{\ensuremath{\nu}}$. We apply this sort of fits for the isovector states of $\ensuremath{\omega}$, $\ensuremath{\phi}$, $J/\ensuremath{\psi}$, and $\mathrm{\ensuremath{\Upsilon}}$ mesons and compare with the corresponding holographic duals. We also extend these ideas to the heavy-light sector by using the isovector set of parameters to extrapolate the proper values of $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ through the average constituent mass $\overline{m}$ for each mesonic specie considered. In the same direction, we address the description of possible non-$q\overline{q}$ candidates using $\overline{m}$ as a holographic threshold, associated with the structure of the exotic state, to define the values of $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$. We study the ${\ensuremath{\pi}}_{1}$ mesons in the light sector and the ${Z}_{c}$, $Y$, and ${Z}_{b}$ mesons in the heavy sector as possible exotic vector states. Finally, the RMS error for describing these twenty-seven states with fifteen parameters (four values for $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ respectively and seven values for $\overline{m}$) is 12.61%.

Topics & Concepts