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SUMMARY:Non-global logarithms in recoil-sensitive observables
DTSTART;VALUE=DATE-TIME:20170825T120000Z
DTEND;VALUE=DATE-TIME:20170825T130000Z
DTSTAMP;VALUE=DATE-TIME:20170920T002400Z
UID:indico-event-660427@cern.ch
DESCRIPTION:Speakers: Dingyu Shao (University of Bern)\nThe jet shape prob
es the average energy profile inside jet of radius R\, which describes the
energy distribution within a smaller cone of r. When r << R\, the perturb
ative prediction suffers from large logarithms of r/R\, where the non-glob
al property of this observable makes the soft gluon resummation complicate
d. Meanwhile\, the rapidity logarithms from soft recoiling effects would i
nterplay with the non-global structure. In this talk I will introduce our
recent work (1708.04516) in which we developed a framework to resum all ra
pidity and non-global logarithms at the same time based on the Soft-Collin
ear Effective Theory. In this work we chose event shape narrow jet broad
ening as an example. I will show that our framework could be easily genera
lised to the recoil-sensitive non-global jet shape resummation. \nhttps:/
/indico.cern.ch/event/660427/
LOCATION:4-3-006 - TH Conference Room (CERN)
URL:https://indico.cern.ch/event/660427/
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SUMMARY:Iterated Elliptic and Hypergeometric Integrals for Feynman Diagram
s
DTSTART;VALUE=DATE-TIME:20171013T120000Z
DTEND;VALUE=DATE-TIME:20171013T130000Z
DTSTAMP;VALUE=DATE-TIME:20170920T002400Z
UID:indico-event-654175@cern.ch
DESCRIPTION:Speakers: Johannes Bluemlein (DESY)\nWe calculate 3-loop maste
r integrals for heavy quark correlators and the 3-loop QCD corrections to
the rho-parameter. They obey non-factorizing differential equations of sec
ond order with more than three singularities\, which cannot be factorized
in Mellin-N space either. The solution of the homogeneous equations is pos
sible in terms of convergent close integer power series as 2_F_1 Gauss hyp
ergeometric functions at rational argument. In some cases\, integrals of t
his type can be mapped to complete elliptic integrals at rational argument
. This class of functions appears to be the next one arising in the calcul
ation of more complicated Feynman integrals following the harmonic polylog
arithms\, generalized polylogarithms\, cyclotomic harmonic polylogarithms\
, square-root valued iterated integrals\, and combinations thereof\, which
appear in simpler cases. The inhomogeneous solution of the corresponding
differential equations can be given in terms of iterative integrals\, wher
e the new innermost letter itself is not an iterative integral. A new clas
s of iterative integrals is introduced containing letters in which (multip
le) definite integrals appear as factors. For the elliptic case\, we also
derive the solution in terms of integrals over modular functions and also
modular forms\, using q-product and series representations implied by Jaco
bi's theta_i functions and Dedekind's eta-function. The corresponding repr
esentations can be traced back to polynomials out of Lambert--Eisenstein s
eries\, having representations also as elliptic polylogarithms\, a q-facto
rial 1/eta^k(\\tau)\, logarithms and polylogarithms of q and their q-int
egrals. Due to the specific form of the physical variable x(q) for differe
nt processes\, different representations do usually appear. The present re
sults cover classes of elliptic solutions of a more general kind than thos
e of the well-known sunrise and kite diagrams. Numerical results for the s
olutions are also presented.\nhttps://indico.cern.ch/event/654175/
LOCATION:4-3-006 - TH Conference Room (CERN)
URL:https://indico.cern.ch/event/654175/
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