Speaker
Description
Logarithms of the hard-scattering scale that appear in light-cone
amplitudes can be resummed by making use of the
Efremov-Radyushkin-Brodsky-Lepage (ERBL) evolution equation for the
light-cone distribution amplitude (LCDA). The standard method for
carrying out the evolution is to decompose the LCDA in a series of
eigenfunctions of the lowest-order evolution kernel (Gegenbauer
polynomials). When the LCDA is expressed as a nonrelativistic expansion,
as in applications to heavy quarkonia, the eigenfunction series can
become divergent because the unevolved LCDA contains generalized
functions, such as the Dirac delta-function and its derivatives. We show
that the divergent eigenfunction series can be regulated in a way that is
consistent with the definition of the generalized functions by making
use of Abel summation and that the regularization can be made
computationally efficient through the use of Pade approximants. We
present results from the application of our method to the calculation of
the rates for Z-boson decays to a vector quarkonium plus a photon.
