Light scalar mesons and charmless hadronicBc→SP,SVdecays in the perturbative QCD approach

Abstract

The scalar productions in heavy meson decays can provide a good platform to study not only heavy flavor physics but also their own physical properties in a dramatically different way. In this work, based on the assumption of two-quark structure of the scalars, the charmless hadronic ${B}_{c}\ensuremath{\rightarrow}SP,SV$ decays (here, $S$, $P$, and $V$ denote the light scalar, pseudoscalar, and vector mesons, respectively) are investigated by employing the perturbative QCD (pQCD) factorization approach. In the standard model all these considered ${B}_{c}$ meson decays can only occur through the annihilation diagrams. From our numerical evaluations and phenomenological analysis, we find that (a) the pQCD predictions for the $CP$-averaged branching ratios (BRs) of the considered ${B}_{c}$ decays vary in the range of ${10}^{\ensuremath{-}5}$ to ${10}^{\ensuremath{-}8}$, which will be tested in the ongoing LHCb and forthcoming Super-B experiments, while the $CP$-violating asymmetries for these modes are absent naturally in the standard model because only one type tree operator is involved; (b) for ${B}_{c}\ensuremath{\rightarrow}SP,SV$ decays, the BRs of $\ensuremath{\Delta}S=0$ processes are basically much larger than those of $\ensuremath{\Delta}S=1$ as generally expected because the different Cabibbo-Kobayashi-Maskawa factors are involved; (c) analogous to $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\eta}}^{(\ensuremath{'})}$ decays, $\mathrm{Br}({B}_{c}\ensuremath{\rightarrow}{\ensuremath{\kappa}}^{+}\ensuremath{\eta})\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}\mathrm{Br}({B}_{c}\ensuremath{\rightarrow}{\ensuremath{\kappa}}^{+}{\ensuremath{\eta}}^{\ensuremath{'}})$ in the pQCD approach, which can be understood by the constructive and destructive interference between the ${\ensuremath{\eta}}_{q}$ and ${\ensuremath{\eta}}_{s}$ contributions to the ${B}_{c}\ensuremath{\rightarrow}{\ensuremath{\kappa}}^{+}\ensuremath{\eta}$ and ${B}_{c}\ensuremath{\rightarrow}{\ensuremath{\kappa}}^{+}{\ensuremath{\eta}}^{\ensuremath{'}}$ decays, however, $\mathrm{Br}({B}_{c}\ensuremath{\rightarrow}{K}_{0}^{*}(1430)\ensuremath{\eta})$ is approximately equal to $\mathrm{Br}({B}_{c}\ensuremath{\rightarrow}{K}_{0}^{*}(1430){\ensuremath{\eta}}^{\ensuremath{'}})$ in both scenarios because the factorizable contributions from the ${\ensuremath{\eta}}_{s}$ term play the dominant role in the considered two channels; (d) if ${a}_{0}(980)$ and $\ensuremath{\kappa}$ are the $q\overline{q}$ bound states, the pQCD predicted BRs for ${B}_{c}\ensuremath{\rightarrow}{a}_{0}(980)(\ensuremath{\pi},\ensuremath{\rho})$ and ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\kappa}{K}^{(*)}$ decays will be in the range of ${10}^{\ensuremath{-}6}\ensuremath{\sim}{10}^{\ensuremath{-}5}$, which are within the reach of the LHCb experiments and could be measured in the near future; and (e) for the ${a}_{0}(1450)$ and ${K}_{0}^{*}(1430)$ channels, the BRs for ${B}_{c}\ensuremath{\rightarrow}{a}_{0}(1450)(\ensuremath{\pi},\ensuremath{\rho})$ and ${B}_{c}\ensuremath{\rightarrow}{K}_{0}^{*}(1430){K}^{(*)}$ modes in the pQCD approach are found to be $(5\ensuremath{\sim}47)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $(0.7--36)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, respectively. A measurement of them at the predicted level will favor the $q\overline{q}$ structure and help understand the physical properties of the scalars and the involved QCD dynamics in the modes, especially the reliability of the pQCD approach to these ${B}_{c}$ meson decays.