A non-planar two-loop three-point function beyond multiple polylogarithms
High Energy Physics - Theory
Physics
ddc:530
FOS: Physical sciences
QC770-798
QCD Phenomenology
530
01 natural sciences
High Energy Physics - Phenomenology
High Energy Physics - Phenomenology (hep-ph)
High Energy Physics - Theory (hep-th)
Nuclear and particle physics. Atomic energy. Radioactivity
NLO Computations
0103 physical sciences
info:eu-repo/classification/ddc/530
DOI:
10.1007/jhep06(2017)127
Publication Date:
2017-06-24T07:13:45Z
AUTHORS (2)
ABSTRACT
27 pages, 1 figure, 1 ancillary file<br/>We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for $t \bar{t}$ production and $����$ production in gluon fusion through a massive top-quark loop. All subtopology integrals can be written in terms of multiple polylogarithms over an irrational alphabet and we employ a new method for the integration of the differential equations which does not rely on the rationalization of the latter. The top topology integrals, instead, in spite of the absence of a massive three-particle cut, cannot be evaluated in terms of multiple polylogarithms and require the introduction of integrals over complete elliptic integrals and polylogarithms. We provide one-fold integral representations for the solutions and continue them analytically to all relevant regions of the phase space in terms of real function, extracting all imaginary parts explicitly. The numerical evaluation of our expressions becomes straightforward in this way.<br/>
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