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Register a new userSubleading-power corrections to the radiative leptonic $B to gamma ell u$ decay in QCD
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Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic $B to gamma ell u$ decay, at next-to-leading order in QCD for the twist-two contribution and at leading order in $alpha_s$ for the higher-twist contributions, induced by the hadronic component of the collinear photon. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two $B to gamma$ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30% correction to the leading-power direct photon effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of ${cal O} (3 sim 5%)$ with the light-cone sum rule approach. We further predict the partial branching fractions of $B to gamma ell u $ with a photon-energy cut $E_{gamma} geq E_{rm cut}$, which are of interest for determining the inverse moment of the leading-twist $B$-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.
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We reconsider the QCD predictions for the radiative decay $Bto gamma ell u_ell$ with an energetic photon in the final state by taking into account the $1/E_gamma, 1/m_b$ power-suppressed hard-collinear and soft corrections from higher-twist $B$-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA $phi_+(omega)$ shows that the latter dominates. The radiative leptonic decay is therefore well suited to constrain the parameters of $phi_+(omega)$, including the first inverse moment, $1/lambda_B$, from the expected high-statistics data of the BELLE II experiment.
We reconsider QCD factorization for the leading power contribution to the $gamma^{ast} gamma to pi^0$ form factor $F_{gamma^{ast} gamma to pi^0} (Q^2)$ at one loop using the evanescent operator approach, and demonstrate the equivalence of the resulting factorization formulae derived with distinct prescriptions of $gamma_5$ in dimensional regularization. Applying the light-cone QCD sum rules (LCSRs) with photon distribution amplitudes (DAs) we further compute the subleading power contribution to the pion-photon form factor induced by the hadronic component of the real photon at the next-to-leading-order in ${cal O}(alpha_s)$, with both naive dimensional regularization and t Hooft-Veltman schemes of $gamma_5$. Confronting our theoretical predictions of $F_{gamma^{ast} gamma to pi^0} (Q^2)$ with the experimental measurements from the BaBar and the Belle Collaborations implies that a reasonable agreement can be achieved without introducing an exotic end-point behaviour for the twist-2 pion DA.
We revisit QCD calculations of radiative heavy meson decay form factors by including the subleading power corrections from the twist-two photon distribution amplitude at next-to-leading-order in $alpha_s$ with the method of the light-cone sum rules (LCSR). The desired hard-collinear factorization formula for the vacuum-to-photon correlation function with the interpolating currents for two heavy mesons is constructed with the operator-product-expansion technique in the presence of evanescent operators. Applying the background field approach, the higher twist corrections from both the two-particle and three-particle photon distribution amplitudes are further computed in the LCSR framework at leading-order in QCD, up to the twist-four accuracy. Combining the leading power point-like photon contribution at tree level and the subleading power resolved photon corrections from the newly derived LCSR, we update theory predictions for the nonperturbative couplings describing the electromagnetic decay processes of the heavy mesons $H^{ast , pm} to H^{pm} , gamma$, $H^{ast , 0} to H^{0} , gamma$, $H_s^{ast , pm} to H_s^{pm} , gamma$ (with $H=D, , B$). Furthermore, we perform an exploratory comparisons of our sum rule computations of the heavy-meson magnetic couplings with the previous determinations based upon different QCD approaches and phenomenological models.
The leptonic radiative decay $B to gamma l u$ is of great importance in the determination of $B$ meson wave functions, and evaluating the form factors $ F_{V,A}$ are the essential problem on the study of this channel. We computed next-to-leading power corrections to the form factors within the framework of PQCD approach, including the power suppressed hard kernel, the contribution from a complete set of three-particle $B$ meson wave functions up to twist-4 and two-particle off light-cone wave functions, the $1/m_b$ corrections in heavy quark effective theory, and the contribution from hadronic structure of photon. In spite of large theoretical uncertainties, the overall power suppressed contributions decreases about $50%$ of the leading power result. The $lambda_B$ dependence of the integrated branching ratio is reduced after including the subleading power contributions, thus the power corrections lead to more ambiguity in the determination of $lambda_B$ from $B to gamma l u$ decay.
We compute perturbative QCD corrections to $B to D$ form factors at leading power in $Lambda/m_b$, at large hadronic recoil, from the light-cone sum rules (LCSR) with $B$-meson distribution amplitudes in HQET. QCD factorization for the vacuum-to-$B$-meson correlation function with an interpolating current for the $D$-meson is demonstrated explicitly at one loop with the power counting scheme $m_c sim {cal O} left (sqrt{Lambda , m_b} right ) $. The jet functions encoding information of the hard-collinear dynamics in the above-mentioned correlation function are complicated by the appearance of an additional hard-collinear scale $m_c$, compared to the counterparts entering the factorization formula of the vacuum-to-$B$-meson correction function for the construction of $B to pi$ from factors. Inspecting the next-to-leading-logarithmic sum rules for the form factors of $B to D ell u$ indicates that perturbative corrections to the hard-collinear functions are more profound than that for the hard functions, with the default theory inputs, in the physical kinematic region. We further compute the subleading power correction induced by the three-particle quark-gluon distribution amplitudes of the $B$-meson at tree level employing the background gluon field approach. The LCSR predictions for the semileptonic $B to D ell u$ form factors are then extrapolated to the entire kinematic region with the $z$-series parametrization. Phenomenological implications of our determinations for the form factors $f_{BD}^{+, 0}(q^2)$ are explored by investigating the (differential) branching fractions and the $R(D)$ ratio of $B to D ell u$ and by determining the CKM matrix element $|V_{cb}|$ from the total decay rate of $B to D mu u_{mu}$.
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