Form Factors and Differential Branching Ratio of $B \to K \mu^+ \mu^-$ in AdS/QCD

TL;DR

This paper uses AdS/QCD to calculate form factors and differential branching ratios for the decay $B o K \, \mu^+ \, \mu^-$, comparing predictions with other models and experiments.

Contribution

It introduces a novel AdS/QCD approach to compute transition form factors and decay observables for $B o K \, \mu^+ \, \mu^-$ decay, incorporating dynamical spin effects.

Findings

AdS/QCD predictions agree well with experimental data.

The model provides reliable form factors for semileptonic B decays.

Comparison with LCSR and lattice QCD shows consistent results.

Abstract

The light-front distribution amplitudes (LFDAs) and the decay constant of the $K $ pseudoscalar meson are extracted within the framework of the AdS/QCD correspondence. For the LFDAs calculation, we consider a momentum-dependent (dynamical) helicity wave function which contains the dynamical spin effects. We use the LFDAs to predict the transition form factors of the semileptonic $B\to K \ell^{+}\ell^{-}$ decay. With the help of these form factors, the differential branching ratio of the $B\to K\, \mu^+ \mu^-$ on $q^2$ is plotted. A comparison is made between our prediction in AdS/QCD and the results obtained from two models including the light-cons sum rules (LCSR) and lattice QCD as well as the experimental values.