# Two-loop evolution equation for the B-meson distribution amplitude

## TL;DR

This paper derives the two-loop evolution equation for the B-meson distribution amplitude, completing the necessary components for NNLL resummation of QCD corrections in B decays.

## Contribution

It presents the first derivation of the two-loop evolution equation for the B-meson light-cone distribution amplitude, linking the kernel to conformal symmetry and cusp anomalous dimension.

## Key findings

- Derived the two-loop evolution equation for B-meson distribution amplitude.
- Connected the evolution kernel to conformal transformations and cusp anomalous dimension.
- Provided a scheme-dependent expression for the evolution kernel.

## Abstract

We derive the two-loop evolution equation of the B-meson light-cone distribution amplitude which is the last missing element for the next-to-next-to-leading logarithmic resummation of QCD corrections to B decays in QCD factorization. We argue that the evolution kernel to all orders in perturbation theory can be written as a logarithm of the generator of special conformal transformations times the cusp anomalous dimension, up to a scheme-dependent overall constant. Up to this constant term, the evolution kernel to a given order in perturbation theory can be obtained from the calculation of special conformal anomaly at one order less.