Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space

Understand

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 $zt$ ($z \leq 1$).