Isospin violating decays of positive parity $$B_s$$ B s mesons in HM $$\chi $$ χ PT

Svjetlana Fajfer,Anita Prapotnik Brdnik

doi:10.1140/epjc/s10052-016-4377-1

Abstract

Recent lattice QCD results suggest that the masses of the first two positive parity $B_s$ mesons lie below the BK threshold, similar to the case of $D^*_{s0}(2317)^+$ and $D_{s1}(2460)^+$ mesons. The mass spectrum of $B_s$ mesons seems to follow the pattern of a $D_s$ mass spectrum. As in the case of charmed mesons, the structure of positive parity $B_s$ mesons is very intriguing. To shed more light on this issue, we investigate the strong isospin violating decays $B_{s0}^{*0} \rightarrow B_s^0 \pi ^0$, $B_{s1}^{0} \rightarrow B_s^{*0} \pi ^0$, and $B_{s1}^{0} \rightarrow B_s^0 \pi \pi $ within heavy meson chiral perturbation theory. The two-body decay amplitude arises at tree level and we show that the loop corrections give significant contributions. On the other hand, in the case of three-body decay $B_{s1}^{0} \rightarrow B_s^0 \pi \pi $ the amplitude occurs only at loop level. We find that the decay widths for these decays are $\Gamma (B_{s1}^{0} \rightarrow B_s^0 \pi \pi )\sim 10^{-3}\,$ keV, and $\Gamma (B_{s0}^{*0} \rightarrow B_s^0 \pi ^0) \le 55\,$ keV, $\Gamma (B_{s1}^{0} \rightarrow B_s^{*0} \pi ^0) \le 50\,$ keV. More precise knowledge of the coupling constant describing the interaction of positive and negative parity heavy mesons with light pseudo-scalar mesons would help to increase the accuracy of our calculation.

Highlights

Recent lattice QCD results suggest that the masses of the first two positive parity Bs mesons lie below the B K threshold, similar to the case of Ds∗0(2317)+ and Ds1(2460)+ mesons
The two-body decay amplitude arises at tree level and we show that the loop corrections give significant contributions
We find that the decay widths for these decays are (Bs01 → Bs0π π ) ∼ 10−3 keV, and (Bs∗00 → Bs0π 0) ≤ 55 keV, (Bs01 → Bs∗0π 0) ≤ 50 keV

Summary

Introduction

It was already suggested by the authors of [19] that a study of the strong and radiative decay modes of positive parity Ds states might help in differentiating between these scenarios. These authors determined the spectrum of Bs 1P states and they found that the masses of Bs1(5830)0 and Bs∗2(5840)0 agree very well with the experimental results [1,2,3,4] They predicted the existence of the spin zero positive parity state (J P = 0+) with the mass m Bs0 = 5.711(13)(19) GeV and the state J P = 1+ with the mass m Bs0 = 5.750(17)(19) GeV. In the isospin violating two-body decays of Ds∗0(2317) and Ds1(2460) mesons, chiral loops contribute significantly [21].

Framework

The amplitudes and the decay widths of two-body decay modes

The three-body decays: amplitudes and decay widths

Comments and discussion

Method