A Phenomenological Study of Semileptonic $B^+$ and $B_s^0$ Decays into Axial-Vector Mesons $\big(D_1(2420),\, D_1^\prime(2430),\, D_{s1}(2460),\, \text{and } D_{s1}^\prime(2536)\big)$ within the Standard Model

Abstract

We study semileptonic $B$ meson decays $B^+ \to D_1^{(\prime)}\ell^+\nu_\ell$ and $B_s^0 \to D_{s1}^{-(\prime)}\ell^+\nu_\ell$, where $\ell=\mu,\tau$. The final state axial vector mesons are treated as mixtures of the heavy quark basis states with light degree of freedom angular momenta $j_\ell=1/2$ and $j_\ell=3/2$, parametrized by the mixing angle $\theta_{D_1}$. Using form factors obtained in the covariant light front quark model, we analyze the dependence of various observables on $\theta_{D_1}$ such as polarized and unpolarized branching ratios, the lepton forward-backward asymmetry, the longitudinal polarization fraction, and the lepton flavor universality ratios. In addition, we also discuss correlations among different observables. We study these observables in the experimentally motivated mixing angle regions as well as over a wider range of $\theta_{D_1}$. Our results show that branching ratios and other observables are sensitive to the axial-vector mixing structure. These predictions provide useful Standard Model benchmarks for future measurements of semileptonic $B_{(s)}$ decays into orbitally excited mesons and may help to clarify the long standing $1/2$ vs. $3/2$ puzzle through semileptonic $B$ decays.