Branching Ratios, Forward-backward Asymmetry and Angular Distributions of $B\to K_1l^+l^-$ Decays

TL;DR

This paper analyzes semileptonic B decays to K1 mesons using perturbative QCD, focusing on decay distributions, asymmetries, and the impact of mixing angles on observable quantities.

Contribution

It provides a detailed study of B to K1 l+ l- decays, including decay amplitudes, distributions, and the effects of mixing angle ambiguities, using helicity amplitudes and form factors.

Findings

Branching ratios vary significantly with mixing angle sign.

Polarizations and forward-backward asymmetries are insensitive to mixing angles.

Resonant contributions alter dilepton mass distributions dramatically.

Abstract

Using the $B\to K_1$ form factors evaluated in the perturbative QCD approach, we study semileptonic $B\to K_1(1270)l^+l^-$ and $B\to K_1(1400)l^+l^-$ decays, where $K_1(1270)$ and $K_1(1400)$ are mixtures of $K_{1A}$ and $K_{1B}$ which are $^3P_1$ and $^1P_1$ states, respectively. Using the technique of helicity amplitudes, we express the decay amplitudes in terms of several independent and Lorentz invariant pieces. We study the dilepton invariant mass distributions, branching ratios, polarizations and forward-backward asymmetries of $ B\to K_1l^+l^-$ decays. The ambiguity in the sign of the mixing angle will induce much large differences to branching ratios of semileptonic B decays: branching ratios without resonant contributions either have the order of $10^{-6}$ or $10^{-8}$. But the polarizations and the forward-backward asymmetries are not sensitive to the mixing angles. We find that the resonant contributions will dramatically change the dilepton invariant mass distributions in the resonant region. We also provide the angular distributions of $ B\to K_1l^+l^-\to (K\pi\pi)l^+l^-$ decays.