Bootstrapping an NMHV amplitude through three loops
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- Dixon-Hippel2014_Article_BootstrappingAnNMHVAmplitudeTh
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We extend the hexagon function bootstrap to the
next-to-maximally-helicity-violating (NMHV) configuration for six-point
scattering in planar = 4 super-Yang-Mills theory at three loops.
Constraints from the 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 R 6 at one higher loop, which works through three
loops for V (four loops for R 6).
Originalsprog | Engelsk |
---|---|
Artikelnummer | 065 |
Tidsskrift | Journal of High Energy Physics |
Vol/bind | 2014 |
Udgave nummer | 10 |
Antal sider | 64 |
ISSN | 1126-6708 |
DOI | |
Status | Udgivet - 1 okt. 2014 |
Eksternt udgivet | Ja |
ID: 279625576