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Authors
Hiroyuki Kawamura
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The $B$-meson light-cone distribution amplitude (LCDA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory (HQET) and is a building block of QCD factorization formula for exclusive $B$-meson decays. When the corresponding bilocal HQET operator has a light-like distance $t$ between the quark and antiquark fields, the scale $sim 1/t$ separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat the bilocal HQET operator based on the operator product expansion (OPE), disentangling the singularities from the IR and UV regions systematically. The matching at the next-to-leading order $alpha_s$ is performed in the $overline{rm MS}$ scheme with a complete set of local operators of dimension $d le 5$, through a manifestly gauge-invariant calculation organizing all contributions in the coordinate space. The result exhibits the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This OPE yields the $B$-meson LCDA for $t$ less than $sim 1$ GeV$^{-1}$, in terms of $bar{Lambda}= m_B - m_b$ and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive $B$ decays, $lambda_B$, is also discussed.
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When the bilocal heavy-quark effective theory (HQET) operator for the B-meson distribution amplitude has a light-like distance t between the quark and antiquark fields, the scale sim 1/t separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat these notorious UV and IR behaviors simultaneously using the operator product expansion, with the local operators of dimension $d le 5$ and radiative corrections at order alpha_s for the corresponding Wilson coefficients. The result is derived in the coordinate space, which manifests the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This result yields the B-meson distribution amplitude for t less than sim 1 GeV^{-1}, in terms of $bar{Lambda}=m_B - m_b$ and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive B decays, lambda_B, is also discussed.
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 discuss the B-meson light-cone wavefunction relevant for QCD factorization approach for exclusive B-meson decays. We derive the operator product expansion for the B-meson light-cone wavefunction, taking into account the local composite operators of dimension less than 6 and calculating the radiative corrections at order alpha_s for the corresponding Wilson coefficients. The result embodies peculiar UV and IR behaviors of the B-meson light-cone wavefunction, the Sudakov-type double logarithmic effects and the mixing of the multiparticle states with additional gluons inside the B meson. The former effects are induced from the cusp singularity in the radiative corrections, while the latter is manifested by the participation of the higher-dimensional operators associated with the nonperturbative structure of the B meson.
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.
The $Bto gamma ell u_ell$ decay at large energies of the photon receives a numerically important soft-overlap contribution which is formally of the next-to-leading order in the expansion in the inverse photon energy. We point out that this contribution can be calculated within the framework of heavy-quark expansion and soft-collinear effective theory, making use of dispersion relations and quark-hadron duality. The soft-overlap contribution is obtained in a full analogy with the similar contribution to the $gamma^* gamma to pi$ transition form factor. This result strengthens the case for using the $Bto gamma ell u_ell$ decay to constrain the $B$-meson distribution amplitude and determine its most important parameter, the inverse moment $lambda_B$.
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