Chiral symmetry breaking and meson wave functions in soft-wall AdS/QCD

Abstract

We consider mesons composed of light and heavy quarks and discuss the construction of the corresponding meson wave functions in soft-wall AdS/QCD. We specifically take care that constraints imposed by chiral symmetry breaking and by the heavy quark limit are fulfilled. The main results are (i) the wave functions of light mesons have a nontrivial dependence on the current quark mass, which gives rise to a mass spectrum consistent with the one including explicit breaking of chiral symmetry; (ii) the wave functions of heavy-light mesons generate their correct mass spectrum, the mass splittings of vector and pseudoscalar states, and the correct scaling of leptonic decay constants ${f}_{Q\overline{q}}\ensuremath{\sim}1/\sqrt{{m}_{Q}}$; (iii) the wave functions of heavy quarkonia produce their correct mass spectrum and lead to a scaling behavior of the leptonic decay constants ${f}_{Q\overline{Q}}\ensuremath{\sim}\sqrt{{m}_{Q}}$ and ${f}_{c\overline{b}}\ensuremath{\sim}{m}_{c}/\sqrt{{m}_{b}}$ at ${m}_{c}\ensuremath{\ll}{m}_{b}$, consistent with potential models and QCD sum rules.