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Register a new userEvolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space
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Authors
Hiroyuki Kawamura
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The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the quasilocal kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate-space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation $t$ in terms of the DA at a lower renormalization scale $mu$ with smaller interquark separations $zt$ ($z leq 1$). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale $sim sqrt{m_b Lambda_{rm QCD}}$ for $t$ less than $sim 1$ GeV^{-1}, using the recently obtained operator product expansion of the DA as the input at $mu sim 1$ GeV. We also derive the master formula, which reexpresses the integrals of the DA at $mu sim sqrt{m_b Lambda_{rm QCD}}$ for the factorization formula by the compact integrals of the DA at $mu sim 1$ GeV.
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We find that the evolution equation for the three-particle quark-gluon B-meson light-cone distribution amplitude (DA) of subleading twist is completely integrable in the large $N_c$ limit and can be solved exactly. The lowest anomalous dimension is separated from the remaining, continuous, spectrum by a finite gap. The corresponding eigenfunction coincides with the contribution of quark-gluon states to the two-particle DA $phi_-(omega)$ so that the evolution equation for the latter is the same as for the leading-twist DA $phi_+(omega)$ up to a constant shift in the anomalous dimension. Thus, ``genuine three-particle states that belong to the continuous spectrum effectively decouple from $phi_-(omega)$ to the leading-order accuracy. In turn, the scale dependence of the full three-particle DA turns out to be nontrivial so that the contribution with the lowest anomalous dimension does not become leading at any scale. The results are illustrated on a simple model that can be used in studies of $1/m_b$ corrections to heavy-meson decays in the framework of QCD factorization or light-cone sum rules.
We present a general study on exclusive semileptonic decays of heavy (B, D, B_s) to light (pi, rho, K, K^*) mesons in the framework of effective field theory of heavy quark. Transition matrix elements of these decays can be systematically characterized by a set of wave functions which are independent of the heavy quark mass except for the implicit scale dependence. Form factors for all these decays are calculated consistently within the effective theory framework using the light cone sum rule method at the leading order of 1/m_Q expansion. The branching ratios of these decays are evaluated, and the heavy and light flavor symmetry breaking effects are investigated. We also give comparison of our results and the predictions from other approaches, among which are the relations proposed recently in the framework of large energy effective theory.
Based on the dual representation in terms of the recently established eigenfunctions of the evolution kernel in heavy-quark effective theory, we investigate the description of the B-meson light-cone distribution amplitude (LCDA) beyond tree-level. In particular, in dual space, small and large momenta do not mix under renormalization, and therefore perturbative constraints from a short-distance expansion in the parton picture can be implemented independently from non-perturbative modelling of long-distance effects. It also allows to (locally) resum perturbative logarithms from large dual momenta at fixed values of the renormalization scale. We construct a generic procedure to combine perturbative and non-perturbative information on the B-meson LCDA and compare different model functions and the resulting logarithmic moments which are the relevant hadronic parameters in QCD factorization theorems for exclusive B-meson decays.
The scaling behavior of semileptonic form-factors in Heavy to Light transitions is studied in the Heavy Quark Effective Theory. In the case of $Hrightarrow pi e u$ it is shown that the same scaling violations affecting the heavy meson decay constant will be present in the semileptonic form-factors.
A new method for the model-independent determination of the light-cone distribution amplitude (LCDA) of the $B$-meson in heavy quark effective theory (HQET) is proposed by combining the large momentum effective theory (LaMET) and the numerical simulation technique on the Euclidean lattice. We demonstrate the autonomous scale dependence of the non-local quasi-HQET operator with the aid of the auxiliary field approach, and further determine the perturbative matching coefficient entering the hard-collinear factorization formula for the $B$-meson quasi-distribution amplitude at the one-loop accuracy. These results will be crucial to explore the partonic structure of heavy-quark hadrons in the static limit and to improve the theory description of exclusive $B$-meson decay amplitudes based upon perturbative QCD factorization theorems.
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