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 ${\Pi }_{\mu ,\Vert }^{(T+\tilde{T})}$, ${\Pi }_{\delta \mu ,\perp }^{(V-A)}$ and ${\Pi }_{\delta \mu ,\perp }^{(T+\tilde{T})}$ are identical to the corresponding ones of $B\to V$ in SCET. In addition, ${\Pi }_{\mu ,\Vert }^{(V-A)}$ and ${\Pi }_{\mu ,\Vert }^{(T+\tilde{T})}$ 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.

Comments: 70 pages, 23 figures, 23 tables