Bootstrapping an NMHV amplitude through three loops

By L. Dixon, M. Hippel. 2014

175 citations recorded by the source corpus.

A bstractWe extend the hexagon function bootstrap to the next-to-maximally-helicity-violating (NMHV) configuration for six-point scattering in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at three loops. Constraints from the Q¯$$ \overline{Q} $$ differential equation, from the operator product expansion (OPE) for Wilson loops with operator insertions, and from multi-Regge factorization, lead to a unique answer for the three-loop ratio function. The three-loop result also predicts additional terms in the OPE expansion, as well as the behavior of NMHV amplitudes in the multi-Regge limit at one higher logarithmic accuracy (NNLL) than was used as input. Both predictions are in agreement with recent results from the flux-tube approach. We also study the multi-particle factorization of multi-loop amplitudes for the first time. We find that the function controlling this factorization is purely logarithmic through three loops. We show that a function U , which is closely related to the parity-even part of the ratio function V , is remarkably simple; only five of the nine possible final entries in its symbol are non-vanishing. We study the analytic and numerical behavior of both the parity-even and parity-odd parts of the ratio function on simple lines traversing the space of cross ratios (u, v, w), as well as on a few two-dimensional planes. Finally, we present an empirical formula for V in terms of elements of the coproduct of the six-gluon MHV remainder function R6 at one higher loop, which works through three loops for V (four loops for R6).

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fb8f23ebe0e1ac2c521d609a42653e4da4fe8c8e

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In Nuclear and High Energy Physics

Citations in the corpus

PolyLogTools — polylogs for the masses (2019, background): “J H E P 0 8 ( 2 0 1 9 ) 1 3 5 In[5]:= ansatz = c[1] PolyLog[4,x] + c[2] PolyLog[4,1-x] + c[3] PolyLog[4,x/(x-1)] + c[4] Log[1-x] PolyLog[3,x] + c[5] Log[x] PolyLog[3,x] + c[6] Log[1-x] PolyLog[3,1-x] + c[7] Log[x] PolyLog[3,1-x] + c[8] PolyLog[2,x]^2 + c[9] PolyLog[2,x] Log[1-x]^2 + c[10] PolyLog[2,”
A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, methodology): “This hypothesis has been successfully tested for the MHV remainder function through four loops [16, 18, 19] and the NMHV ratio function through three loops [17, 21].”
Heptagons from the Steinmann cluster bootstrap (2016, methodology): “[11], has an even simpler behavior than U6.”