$B\to K_2^{\ast }(1430){\ell }^{+}{\ell }^{-}$ distributions in Standard Model at large recoil

Abstract

We study the rare decay $B\to K_2^{\ast }(1430)(\to K\pi ){\ell }^{+}{\ell }^{-}$ in the Standard Model and beyond. Working in the transversity basis, we exploit the relations between the heavy-to-light form factors in the limit of heavy quark ($m_b\to \infty$) and large energy ($E_{K_2^{\ast }}\to \infty$) of the $K_2^{\ast }$ meson. This allows us to construct observables where at leading order in ${\Lambda }_{\mathrm{QCD}}/m_b$ and ${\alpha }_s$ the form factor dependence involving the $B\to K_2^{\ast }$ transitions cancels. Higher order corrections are systematically incorporated in the numerical analysis. In the Standard Model the decay has a sizable branching ratio and therefore a large number of events can be expected at LHCb. Going beyond the Standard Model, we explore the implications of the global fit to presently available $b\to s{\ell }^{+}{\ell }^{-}$ data on the $B\to K_2^{\ast }{\ell }^{+}{\ell }^{-}$ observables.