The isospin asymmetry in $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ using AdS/QCD

Abstract

We compute the isospin asymmetry distribution in the rare dileptonic decay $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$, in the dimuon mass squared ($q^2$) region below the $J/\Psi$ resonance, using non-perturbative inputs as predicted by the anti-de Sitter/Quantum Chromodynamics (AdS/QCD) correspondence and by Sum Rules. We predict a positive asymmetry at $q^2=0$ which flips sign in the region $q^2\in [1,2]\text{mbox}{GeV}^2$ to remain small ($\le 2\%$) and negative for larger $q^2$. While our predictions are distinct as $q^2\to 0$, they become hardly model-dependent $q^2\ge 4\text{mbox}{GeV}^2$. We compare our predictions to the most recent LHCb data.

Comments: 18 pages, 7 figures