Rapidity resummation for BB-meson wave functions

Transverse-momentum dependent (TMD) hadronic wave functions develop light-cone divergences under QCD corrections, which are commonly regularized by the rapidity $\zeta$ of gauge vector defining the non-light-like Wilson lines. The yielding rapidity logarithms from infrared enhancement need to be resummed for both hadronic wave functions and short-distance functions, to achieve scheme-independent calculations of physical quantities. We briefly review the recent progress on the rapidity resummation for $B$-meson wave functions which are the key ingredients of TMD factorization formulae for radiative-leptonic, semi-leptonic and non-leptonic $B$-meson decays. The crucial observation is that rapidity resummation induces a strong suppression of $B$-meson wave functions at small light-quark momentum, strengthening the applicability of TMD factorization in exclusive $B$-meson decays. The phenomenological consequence of rapidity-resummation improved $B$-meson wave functions is further discussed in the context of $B \to \pi$ transition form factors at large hadronic recoil.Comment: 6 pages, 2 figures, Conference proceedings for the workshop of QCD@work, Giovinazzo (Italy), June 16-19, 201

QCD corrections to B→πB \to \pi form factors from light-cone sum rules

We compute perturbative corrections to $B \to \pi$ form factors from QCD light-cone sum rules with $B$-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-$B$-meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for $f_{B \pi}^{+}(q^2)$ and $f_{B \pi}^{0}(q^2)$ at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of $B \to \pi$ form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract $|V_{ub}|= \left(3.05^{+0.54}_{-0.38} |_{\rm th.} \pm 0.09 |_{\rm exp.}\right) \times 10^{-3}$ with the inverse moment of the $B$-meson distribution amplitude $\phi_B^{+}(\omega)$ determined by reproducing $f_{B \pi}^{+}(q^2=0)$ obtained from the light-cone sum rules with $\pi$ distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for $B \to \pi \ell \nu_{\ell}$ ($\ell= \mu \,, \tau$) in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the $B \to \pi$ form factors $f_{B \pi}^{+}(q^2)$ and $f_{B \pi}^{0}(q^2)$ in brief.Comment: 44 pages, 12 figure

Joint resummation for pion wave function and pion transition form factor

We construct an evolution equation for the pion wave function in the $k_T$ factorization theorem, whose solution sums the mixed logarithm $\ln x\ln k_T$ to all orders, with $x$ ($k_T$) being a parton momentum fraction (transverse momentum). This joint resummation induces strong suppression of the pion wave function in the small $x$ and large $b$ regions, $b$ being the impact parameter conjugate to $k_T$, and improves the applicability of perturbative QCD to hard exclusive processes. The above effect is similar to those from the conventional threshold resummation for the double logarithm $\ln^2 x$ and the conventional $k_T$ resummation for $\ln^2 k_T$. Combining the evolution equation for the hard kernel, we are able to organize all large logarithms in the $\gamma^{\ast} \pi^{0} \to \gamma$ scattering, and to establish a scheme-independent $k_T$ factorization formula. It will be shown that the significance of next-to-leading-order contributions and saturation behaviors of this process at high energy differ from those under the conventional resummations. It implies that QCD logarithmic corrections to a process must be handled appropriately, before its data are used to extract a hadron wave function. Our predictions for the involved pion transition form factor, derived under the joint resummation and the input of a non-asymptotic pion wave function with the second Gegenbauer moment $a_2=0.05$, match reasonably well the CLEO, BaBar, and Belle data.Comment: 31 pages, 7 figure