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Register a new userSubleading power corrections to the pion-photon transition form factor in QCD
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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.
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In this paper we calculate the power corrections to the pion transition form factor within the framework of perturbative QCD approach on the basis of $k_T$ factorization. The power suppressed contributions from higher twist pion wave functions and the hadronic structure of photon are investigated. We find that there exists strong cancellation between the two kinds contributions, thus the total power corrections considered currently are very small, and the prediction of the leading power contribution with joint resummation improved perturbative QCD approach is almost unchanged. This result confirms that the pion transition form factor is a good platform to constrain the nonperturbative parameters in pion wave functions. Moreover, our result can accommodate the anomalous data from BaBar, or agrees with results from Belle according to the choice of Gegebauer moment in the pion wave function, and the more precise experimental data from Belle-II is expected.
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.
In this paper we investigate the power suppressed contributions from two-particle and three-particle twist-4 light-cone distribution amplitudes (LCDAs) of photon within the framework of light-cone sum rules. Compared with leading twist LCDA result, the contribution from three-particle twist-4 LCDAs is not suppressed in the expansion by $1/Q^2$, so that the power corrections considered in this work can give rise to a sizable contribution, especially at low $Q^2$ region. According to our result, the power suppressed contributions should be included in the determination of the Gegenbauer moments of pion LCDAs with the pion transition form factor.
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.
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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