$\bar{B}^0$, $\bar{B}^0_s$ and $B^-$ decays into $\eta_c$ plus a scalar meson

Abstract

We investigate the decays of $\bar{B}^0_s$, $\bar{B}^0$ and $B^-$ into $\eta_c$ plus a scalar meson in a theoretical framework by taking into account the dominant process for the weak decay of $\bar{B}$ meson into $\eta_c$ and a $q\bar{q}$ pair. After hadronization of this $q\bar{q}$ component into pairs of pseudoscalar mesons we obtain certain weights for the pseudoscalar meson-pseudoscalar meson components. The calculation is based on the postulation that the scalar mesons $f_0(500)$, $f_0(980)$ and $a_0(980)$ are dynamically generated states from the pseudoscalar meson-pseudoscalar meson interactions in $S$-wave. Up to a global normalization factor, the $\pi \pi$, $K \bar{K}$ and $\pi \eta$ invariant mass distributions for the decays of $\bar B^0_s \to \eta_c \pi^+ \pi^-$, $\bar{B}^0_s \to \eta_c K^+ K^-$, $\bar B^0 \to \eta_c \pi^+ \pi^-$, $\bar{B}^0 \to \eta_c K^+ K^-$, $\bar{B}^0 \to \eta_c \pi^0 \eta$, $B^- \to \eta_c K^0 K^-$ and $B^- \to \eta_c \pi^- \eta$ are predicted. Comparison is made with the limited experimental information available and other theoretical calcualtions. Further comparison of these results with coming LHCb measurements will be very valuable to make progress in our understanding of the nature of the low lying scalar mesons, $f_0(500), f_0(980)$ and $a_0(980)$.