Semileptonic decays of the scalar tetraquark Z_{bc;overline{u}overline{d}}^{0}

Abstract

We study semileptonic decays of the scalar tetraquark Z_{bc;overline{u} overline{d}}^{0} to final states T_{bs;overline{u}overline{d} }^{-}e^{+}nu _{e} and T_{bs;overline{u}overline{d}}^{-}mu ^{+}nu _{mu } , which run through the weak transitions crightarrow se^{+}nu _{e} and crightarrow smu ^{+}nu _{mu }, respectively. To this end, we calculate the mass and coupling of the final-state scalar tetraquark T_{bs;overline{u}overline{d} }^{-} by means of the QCD two-point sum rule method: these spectroscopic parameters are used in our following investigations. In calculations we take into account the vacuum expectation values of the quark, gluon, and mixed operators up to dimension ten. We use also three-point sum rules to evaluate the weak form factors G_{i}(q^2) (i=1,~2) that describe these decays. The sum rule predictions for G_{i}(q^2) are employed to construct fit functions F_{i}(q^2), which allow us to extrapolate the form factors to the whole region of kinematically accessible q^2. These functions are required to get partial widths of the semileptonic decays Gamma left( Z_{bc}^{0}rightarrow Te^{+}nu _{e}right) and Gamma left( Z_{bc}^{0}rightarrow Tmu ^{+}nu _{mu }right) by integrating corresponding differential rates. We analyze also the two-body nonleptonic decays Z_{bc;overline{u}overline{d}}^{0} rightarrow T_{bs;overline{u}overline{d }}^{-}pi ^{+} and Z_{bc;overline{u}overline{d}}^{0} rightarrow T_{bs;overline{u }overline{d}}^{-}K^{+}, which are necessary to evaluate the full width of the Z_{bc;overline{u}overline{d}}^{0}. The obtained results for Gamma _{mathrm {full}}=(3.18pm 0.39)times 10^{-11}~{mathrm {MeV}} and mean lifetime 20.7_{-2.3}^{+2.9}~{mathrm {ps}} of the tetraquark Z_{bc;overline{u} overline{d}}^{0} can be used in experimental investigations of this exotic state.