Hexagon functions and the three-loop remainder function
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We present the three-loop remainder function, which describes the
scattering of six gluons in the maximally-helicity-violating
configuration in planar = 4 super-Yang-Mills theory, as a function of
the three dual conformal cross ratios. The result can be expressed in
terms of multiple Goncharov polylogarithms. We also employ a more
restricted class of hexagon functions which have the correct branch cuts
and certain other restrictions on their symbols. We classify all the
hexagon functions through transcendental weight five, using the
coproduct for their Hopf algebra iteratively, which amounts to a set of
first-order differential equations. The three-loop remainder function is
a particular weight-six hexagon function, whose symbol was determined
previously. The differential equations can be integrated numerically for
generic values of the cross ratios, or analytically in certain kinematic
limits, including the near-collinear and multi-Regge limits. These
limits allow us to impose constraints from the operator product
expansion and multi-Regge factorization directly at the function level,
and thereby to fix uniquely a set of Riemann ζ valued constants
that could not be fixed at the level of the symbol. The near-collinear
limits agree precisely with recent predictions by Basso, Sever and
Vieira based on integrability. The multi-Regge limits agree with the
factorization formula of Fadin and Lipatov, and determine three
constants entering the impact factor at this order. We plot the
three-loop remainder function for various slices of the Euclidean region
of positive cross ratios, and compare it to the two-loop one. For large
ranges of the cross ratios, the ratio of the three-loop to the two-loop
remainder function is relatively constant, and close to -7.
Originalsprog | Engelsk |
---|---|
Artikelnummer | 049 |
Tidsskrift | Journal of High Energy Physics |
Vol/bind | 2013 |
Udgave nummer | 12 |
Antal sider | 95 |
ISSN | 1126-6708 |
DOI | |
Status | Udgivet - 1 dec. 2013 |
Eksternt udgivet | Ja |
ID: 279626009