The chiral transitions in heavy-light mesons

The mass shifts of the $P$-wave $D_s$ and $B_s$ mesons due to coupling to $DK$, $D^{\ast }K$ and $BK$, $B^{\ast }K$ channels are studied using the chiral quark-pion Lagrangian without fitting parameters. The strong mass shifts down $\sim 140$ MeV and $\sim 100$ MeV for $D_s^{\ast }(0^{+})$ and $D_s(1^{{+}^{\mathrm{\prime }}})$ and $\sim 100$ MeV for $B_s^{\ast }(0^{+})$ and $B_s(1^{{+}^{\mathrm{\prime }}})$ are calculated. Two factors are essential for large mass shifts: strong coupling of the $0^{+}$ and $1^{{+}^{\mathrm{\prime }}}$ 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 $M(B_s^{\ast }(0^{+}))=5695(10)$ MeV and $M(B_s(1^{{+}^{\mathrm{\prime }}}))=5730(15)$ MeV,very close to $M(B(0^{+}))$ and $M(B(1^{{+}^{\mathrm{\prime }}}))$, are predicted. Experimental limit on the width $\mathrm{\Gamma }(D_{s1}(2536))<2.3$ MeV puts strong restrictions on admittable mixing angle between the $1^{+}$ and $1^{{+}^{\mathrm{\prime }}}$ states, $\mathrm{\mid }\varphi \mathrm{\mid }<6^{\circ }$, which corresponds to the mixing angle $\theta$ between the ${}^3{P}_1$ and ${}^1{P}_1$ states, ${29}^{\circ }<\theta <{41}^{\circ }$.