The coupled-channel analysis of $D_s$ and $B_s$ mesons

Abstract

In the framework of the coupled channel model the mass shifts of the $P$--wave excitations of $D_s$ and $B_s$ mesons have been calculated. The corresponding coupling to $DK$ and $BK$ channels is provided by the effective chiral Lagrangian which is deduced from QCD and does not contain fitting parameters. The strong mass shifts down for $0^+$ and ${1^+}'$ states have been obtained, while ${1^+}"$ and $2^+$ states remain almost at rest. Two factors are essential for large mass shifts: strong coupling of the $0^+$ and $1^{+'}$ states to the $S$-wave decay channel, containing a Nambu-Goldstone meson, and the chiral flip transitions due to the bispinor structure of both heavy-light mesons. The masses $M(B^*_s(0^+))=5710(15)$ MeV and $M(B_s(1^{+'}))=5730(15)$ MeV are predicted. Experimental limit on the width $\Gamma(D_{s1}(2536))<2.3$ MeV puts strong restrictions on admittable mixing angle between the $1^+$ and $1^{+'}$ states.