The four-loop six-gluon NMHV ratio function

By L. Dixon, M. Hippel, Andrew J. McLeod. 2015

150 citations recorded by the source corpus.

A bstractWe use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar N=4$$ \mathcal{N}=4 $$ super-Yang-Mills theory at four loops. A powerful constraint comes from dual superconformal invariance, in the form of a Q¯$$ \overline{Q} $$ differential equation, which heavily constrains the first derivatives of the transcendental functions entering the ratio function. At four loops, it leaves only a 34-parameter space of functions. Constraints from the collinear limits, and from the multi-Regge limit at the leading-logarithmic (LL) and next-to-leading-logarithmic (NLL) order, suffice to fix these parameters and obtain a unique result. We test the result against multi-Regge predictions at NNLL and N3LL, and against predictions from the operator product expansion involving one and two flux-tube excitations; all cross-checks are satisfied. We study the analytical and numerical behavior of the parity-even and parity-odd parts on various lines and surfaces traversing the three-dimensional space of cross ratios. As part of this program, we characterize all irreducible hexagon functions through weight eight in terms of their coproduct. We also provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/515048808020f94b8af7f0140944a64b7ea304d4

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In Nuclear and High Energy Physics

Citations in the corpus

Heptagons from the Steinmann cluster bootstrap (2016, methodology): “havior than U 6. The Lloop contribution U(L) is also a polynomial in log(uw=v), but it has only degree Lat Lloops, for L>1. This three-loop result was later found to hold also at four and ve loops [15,35]. Because U(L) has weight 2L, but a maximum of Lpowers of log(uw=v) for L>1, every term in”