Abstract
Abstract We compute the next-to-maximally-helicity-violating one-loop n-gluon amplitudes in $ \mathcal{N} $ = 1 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and constitute the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We assemble ingredients from the $ \mathcal{N} $ = 4 NMHV tree super-amplitude into previously unwritten double cuts and use the spinor integration technique to calculate all bubble coefficients. We also derive the missing box coefficients from quadruple cuts. Together with the known formula for three-mass triangles, this completes the set of NMHV one-loop master integral coefficients in $ \mathcal{N} $ = 1 SYM. To facilitate further use of our results, we provide their Mathematica implementation.
Highlights
In the last couple of decades, there have been impressive achievements in taming gauge theory amplitudes analytically for increasing and in some cases arbitrary number of particles
Together with the known formula for three-mass triangles, this completes the set of NMHV one-loop master integral coefficients in N = 1 SYM
For all other integrands one needs to sew NMHV tree amplitudes, which we describe in detail
Summary
In the last couple of decades, there have been impressive achievements in taming gauge theory amplitudes analytically for increasing and in some cases arbitrary number of particles. We use spinor integration [6, 11] which provides a sleek way to compute amplitude coefficients of one-loop master integrals from unitarity cuts in a purely algebraic manner. The main difficulty in finding universal NMHV formulas is that even at 7 points general patterns are not yet obvious, because the numbers of minus and plus helicities are still comparable to each other, whereas MHV amplitudes become “saturated” by positive helicities already for 6 external gluons. We hope that our all-multiplicity results will provide a helpful testing ground for further theoretic developments. It is an interesting question whether any kind of onshell recursion relations can be established between the coefficients we have found.
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