Role of $f_0(980)$ and $a_0(980)$ in the $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to {\pi }^{-}{K}^0{\bar{K}}^0$ reactions

Abstract

In this work we study the role of the $f_0(980)$ and $a_0(980)$ resonances in the low $K^{+}{K}^{-}$ and $K^0{\bar{K}}^0$ invariant-mass region of the $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to {\pi }^{-}{K}^0{\bar{K}}^0$ reactions. The amplitudes are calculated by using the chiral unitary $\mathrm{SU}(3)$ formalism, in which these two resonances are dynamically generated from the unitary pseudocalar-pseudoscalar coupled-channel approach. The amplitudes are then used as input in the evaluation of the mass distributions with respect to the $K^{+}{K}^{-}$ and $K^0{\bar{K}}^0$ invariant-masses, where the contributions coming from the $I=0$ and $I=1$ components are explicitly assessed. Furthermore, the contribution of the $K^{\ast }(892{)}^0{K}^{-}$ production and its influence on the ${\pi }^{-}{K}^{+}$ and $K^{+}{K}^{-}$ systems are also evaluated, showing that there is no significant strength for small $K^{+}{K}^{-}$ invariant mass. Lastly, the final distributions of $M_{\mathrm{inv}}^2(K^{\pm }{K}^{\mp })$ for the $B^{\mp }\to {\pi }^{\mp }{K}^{\pm }{K}^{\mp }$ reactions are estimated and compared with the LHCb data. Our results indicate that the $I=0$ component tied to the $f_0(980)$ excitation generates the dominant contribution in the range of low $K^{+}{K}^{-}$ invariant-mass.

Comments: 11 pages, 10 figures