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 ${1^{+}}^{\prime }$ 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 $1^{{+}^{\prime }}$ 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 $M(B_s^{\ast }(0^{+}))=5710(15)$ MeV and $M(B_s(1^{{+}^{\prime }}))=5730(15)$ 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 $1^{{+}^{\prime }}$ states.

Comments: to be published in the Proceedings of the Conference QUARKS-2008, Sergiev Posad, Russia, 23rd-29th May 2008