The four-loop six-gluon NMHV ratio function
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- Dixon2016_Article_TheFour-loopSix-gluonNMHVRatio
Final published version, 1.9 MB, PDF document
We use the hexagon function bootstrap to compute the ratio function
which characterizes the next-to-maximally-helicity-violating (NMHV)
six-point amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory
at four loops. A powerful constraint comes from dual superconformal
invariance, in the form of a $\bar{Q}$ 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 N$^3$LL, 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.
Original language | English |
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Article number | 053 |
Journal | Journal of High Energy Physics (Online) |
Volume | 2016 |
Issue number | 01 |
Number of pages | 66 |
ISSN | 1126-6708 |
DOIs | |
Publication status | Published - 11 Jan 2016 |
Externally published | Yes |
- High Energy Physics - Theory
Research areas
ID: 279625505