Radiative and semileptonicBdecays involving the tensor mesonK2*(1430)in the standard model and beyond

Abstract

We study semileptonic and radiative $B$ decays involving the strange tensor meson ${K}_{2}^{*}(1430)$ in the final state. Using the large energy effective theory (LEET) techniques, we formulate the $B\ensuremath{\rightarrow}{K}_{2}^{*}$ transition form factors in large recoil region. All the form factors can be parametrized in terms of two independent LEET functions ${\ensuremath{\zeta}}_{\ensuremath{\perp}}$ and ${\ensuremath{\zeta}}_{\ensuremath{\parallel}}$. The magnitude of ${\ensuremath{\zeta}}_{\ensuremath{\perp}}$ is estimated from the data for $\mathcal{B}(B\ensuremath{\rightarrow}{K}_{2}^{*}(1430)\ensuremath{\gamma})$. Assuming a dipole ${q}^{2}$ dependence for the LEET functions and ${\ensuremath{\zeta}}_{\ensuremath{\parallel}}/{\ensuremath{\zeta}}_{\ensuremath{\perp}}=1.0\ifmmode\pm\else\textpm\fi{}0.2$, for which the former consists with the QCD counting rules, and the latter is favored by the $B\ensuremath{\rightarrow}\ensuremath{\phi}{K}_{2}^{*}$ data, we investigate the decays $B\ensuremath{\rightarrow}{K}_{2}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ and $B\ensuremath{\rightarrow}{K}_{2}^{*}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, where the contributions due to ${\ensuremath{\zeta}}_{\ensuremath{\parallel}}$ are suppressed by ${m}_{{K}_{2}^{*}}/{m}_{B}$. For the $B\ensuremath{\rightarrow}{K}_{2}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decay, in the large recoil region where the hadronic uncertainties are considerably reduced, the longitudinal distribution $d{F}_{L}/ds$ is reduced by 20\char21{}30% due to the flipped sign of ${c}_{7}^{\mathrm{eff}}$ compared with the standard model result. Moreover, the forward-backward asymmetry zero is about $3.4\text{ }\text{ }{\mathrm{GeV}}^{2}$ in the standard model, but changing the sign of ${c}_{7}^{\mathrm{eff}}$ yields a positive asymmetry for all values of the invariant mass of the lepton pair. We calculate the branching fraction for $B\ensuremath{\rightarrow}{K}_{2}^{*}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ in the standard model. Our result exhibits the impressed resemblance between $B\ensuremath{\rightarrow}{K}_{2}^{*}(1430){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, $\ensuremath{\nu}\overline{\ensuremath{\nu}}$, and $B\ensuremath{\rightarrow}{K}^{*}(892){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, $\ensuremath{\nu}\overline{\ensuremath{\nu}}$.