Next-to-leading-order QCD calculations of $B \to A$ form factors with higher-twist corrections

Abstract

Applying the light-cone sum rules (LCSR) approach, the next-to-leading-order (NLO) corrections to $B \to A$ form factors are calculated with the twist-two and twist-three $B$ meson light-cone distribution amplitudes (LCDAs) at leading power in $\Lambda / m_b$. At one-loop level, the vacuum-to-$B$-meson correlation functions defined with interpolating currents for the $p$-wave axial-vector meson are factorized into short-distance coefficients and the distribution amplitudes (DAs) of the $B$ meson, among which the hard coefficients for A0-type currents and $\mu$ dependent jet functions entering correlation functions $\Pi_{\mu,\|}^{(T+\tilde{T})}$, $\Pi_{\delta\mu,\perp}^{(V-A)}$ and $\Pi_{\delta\mu,\perp}^{(T+\tilde{T})}$ are identical to the corresponding ones of $B \to V$ in SCET. In addition, $\Pi_{\mu,\|}^{(V-A)}$ and $\Pi_{\mu,\|}^{(T+\tilde{T})}$ coincide with the results of $B\to \pi,K$ under the limit $m_q \to 0$ up to one-loop accuracy. Then the subleading power corrections to $B \to A$ form factors are computed with the higher-twist $B$ meson LCDAs at tree level up to the twist-six accuracy. Furthermore, we predict the $q^2$ dependence of $B \to A$ form factors via the Bourrely-Caprini-Lellouch (BCL) $z$-series expanding parameterization to compute several physical observables including branching ratios of semileptonic $B\to A \ell \bar{\nu}_{\ell} $ and $B\to A \nu_{\ell} \bar{\nu}_{\ell} $ processes, transverse asymmetries, forward-backward asymmetries and lepton flavor universality observables employing the given mixing angles $\theta_K=-34^\circ$, $\theta_{1_{P_1}}=28^\circ$, $\theta_{3_{P_1}}=23^\circ$. We also compare our theory calculations with the results from other methods.