Abstract
The Lange–Neubert evolution equation describes the scale dependence of the wave function of a meson built of an infinitely heavy quark and light antiquark at light-like separations, which is the hydrogen atom problem of QCD. It has numerous applications to the studies of B-meson decays. We show that the kernel of this equation can be written in a remarkably compact form, as a logarithm of the generator of special conformal transformation in the light-ray direction. This representation allows one to study solutions of this equation in a very simple and mathematically consistent manner. Generalizing this result, we show that all heavy–light evolution kernels that appear in the renormalization of higher-twist B-meson distribution amplitudes can be written in the same form.
Highlights
The Lange–Neubert evolution equation describes the scale dependence of the wave function of a meson built of an infinitely heavy quark and light antiquark at light-like separations, which is the hydrogen atom problem of QCD
We show that the kernel of this equation can be written in a remarkably compact form, as a logarithm of the generator of special conformal transformation in the light-ray direction. This representation allows one to study solutions of this equation in a very simple and mathematically consistent manner. Generalizing this result, we show that all heavy–light evolution kernels that appear in the renormalization of higher-twist B-meson distribution amplitudes can be written in the same form
We define the B-meson distribution amplitude (DA) as the renormalized matrix element of the bilocal operator built of an effective heavy quark field hv (0) and a light antiquark q(zn) at a light-like separation: 0|q(zn)n/[zn, 0]Γ hv (0)|B (v)
Summary
We show that the kernel of this equation can be written in a remarkably compact form, as a logarithm of the generator of special conformal transformation in the light-ray direction. This representation allows one to study solutions of this equation in a very simple and mathematically consistent manner. The integration goes over all possible eigenvalues of the step-up generator S+ that corresponds to special conformal transformations along the light-ray nμ This representation is very similar to the one suggested in Ref. Cusp anomalous dimension [9,10]
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