$B\to K^\ast_2(1430)\ell^+\ell^-$ 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 $K^\ast_2$ meson. This allows us to construct observables where at leading order in $\Lambda_{\rm QCD}/m_b$ and $\alpha_s$ the form factor dependence involving the $B\to K^\ast_2$ 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.