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SUMMARY:Making Sense of Divergent Series: Resummation of Logarithms in the
Nonrelativistic Expansions of Light-Cone Amplitudes
DTSTART;VALUE=DATE-TIME:20180805T142000Z
DTEND;VALUE=DATE-TIME:20180805T144000Z
DTSTAMP;VALUE=DATE-TIME:20191120T001559Z
UID:indico-contribution-3032743@indico.cern.ch
DESCRIPTION:Speakers: Geoffrey Bodwin (Argonne National Laboratory)\nLogar
ithms of the hard-scattering scale that appear in light-cone\namplitudes c
an be resummed by making use of the\nEfremov-Radyushkin-Brodsky-Lepage (ER
BL) evolution equation for the\nlight-cone distribution amplitude (LCDA).
The standard method for\ncarrying out the evolution is to decompose the LC
DA in a series of\neigenfunctions of the lowest-order evolution kernel (Ge
genbauer\npolynomials). When the LCDA is expressed as a nonrelativistic ex
pansion\,\nas in applications to heavy quarkonia\, the eigenfunction serie
s can\nbecome divergent because the unevolved LCDA contains generalized\nf
unctions\, such as the Dirac delta-function and its derivatives. We show\n
that the divergent eigenfunction series can be regulated in a way that is\
nconsistent with the definition of the generalized functions by making\nus
e of Abel summation and that the regularization can be made\ncomputational
ly efficient through the use of Pade approximants. We\npresent results fro
m the application of our method to the calculation of\nthe rates for Z-bos
on decays to a vector quarkonium plus a photon.\n\nhttps://indico.cern.ch/
event/648004/contributions/3032743/
LOCATION:Arts Bldg. Hall H
URL:https://indico.cern.ch/event/648004/contributions/3032743/
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