Scale-dependence of the $B$-meson LCDA beyond leading order from conformal symmetry

Abstract

We argue that the evolution kernel for the scale-dependence of the $B$-meson light-cone distribution amplitude (LCDA) can be written, to all orders in perturbation theory, in terms of the generator of special conformal transformations in a modified theory: QCD at critical coupling in non-integer $d\ne 4$ dimensions. Explicit expression for the eigenfunctions of the evolution kernel is derived that is valid, again, to all orders. From a practitioner's point of view the utility of this representation is that it allows to "save one loop" and obtain the evolution kernel to a given order of perturbation theory, up to a constant term, from the calculation of the conformal anomaly at one order less. This construction is verified by explicit calculation at two-loop level.

arXiv comment8 pages, talk presented at RADCOR 2019, 9-13 September 2019

References in corpus (13)

• Asymptotics of Heavy-Meson Form Factors
• The Uses of Conformal Symmetry in QCD
• The B-Meson Distribution Amplitude in QCD
• Renormalization-Group Evolution of the B-Meson Light-Cone Distribution Amplitude
• Broken conformal invariance and spectrum of anomalous dimensions in QCD
• Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons
• Evolution equations beyond one loop from conformal symmetry
• Two-loop evolution equation for the B-meson distribution amplitude
• Conformal symmetry of the Lange-Neubert evolution equation
• Two-loop conformal generators for leading-twist operators in QCD
• Renormalisation of heavy-light light ray operators
• Conformal symmetry of QCD in $d$-dimensions
• Integrability in heavy quark effective theory