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Title: Bootstrapping an NMHV Amplitude through Three Loops

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Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); High Energy Physics (HEP)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: JHEP1410:65, 2014
Country of Publication:
United States

Citation Formats

Dixon, Lance J., /SLAC, von Hippel, Matt, and /Stony Brook U., New York, SCGP. Bootstrapping an NMHV Amplitude through Three Loops. United States: N. p., 2014. Web. doi:10.1007/JHEP10(2014)065.
Dixon, Lance J., /SLAC, von Hippel, Matt, & /Stony Brook U., New York, SCGP. Bootstrapping an NMHV Amplitude through Three Loops. United States. doi:10.1007/JHEP10(2014)065.
Dixon, Lance J., /SLAC, von Hippel, Matt, and /Stony Brook U., New York, SCGP. Mon . "Bootstrapping an NMHV Amplitude through Three Loops". United States. doi:10.1007/JHEP10(2014)065.
title = {Bootstrapping an NMHV Amplitude through Three Loops},
author = {Dixon, Lance J. and /SLAC and von Hippel, Matt and /Stony Brook U., New York, SCGP},
abstractNote = {},
doi = {10.1007/JHEP10(2014)065},
journal = {JHEP1410:65, 2014},
number = ,
volume = ,
place = {United States},
year = {Mon Aug 11 00:00:00 EDT 2014},
month = {Mon Aug 11 00:00:00 EDT 2014}
  • We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parametersmore » uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.« less
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  • Here, the analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.
  • We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both ourmore » ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3 {yields} 3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.« less