Estimating decay rate of $X^{\pm}(5568)\to B_sπ^{\pm}$ while assuming them to be molecular states

Abstract: Discovery of $X(5568)$ brings up a tremendous interest because it is very special, i.e. made of four different flavors. The D0 collaboration claimed that they observed this resonance through portal $X(5568)\to B_s\pi$, but unfortunately, later the LHCb, CMS, CDF and ATLAS collaborations' reports indicate that no such state was found. Almost on the Eve of 2017, the D0 collaboration reconfirmed existence of $X(5568)$ via the semileptonic decay of $B_s$. To further reveal the discrepancy, supposing $X(5568)$ as a molecular state, we calculate the decay rate of $X(5568)\rightarrow B_s\pi^+$ in an extended light front model. Numerically, the theoretically predicted decay width of $\Gamma(X(5568)\rightarrow B_s\pi^+)$ is $20.28$ MeV which is consistent with the result of the D0 collaboration ($\Gamma=18.6^{+7.9}{-6.1}(stat)^{+3.5}{-3.8}(syst)$ MeV). Since the resonance is narrow, signals might be drowned in a messy background. In analog, two open-charm molecular states $DK$ and $BD$ named as $X_a$ and $X_b$, could be in the same situation. The rates of $X_a\to D_s\pi^0$ and $X_b\to B_c\pi^0$ are estimated as about 30 MeV and 20 MeV respectively. We suggest the experimental collaborations round the world to search for these two modes and accurate measurements may provide us with valuable information.