One-loop amplitudes of gluons in supersymmetric QCD

Abstract

One-loop amplitudes of gluons in supersymmetric Yang-Mills are four-dimensional cut-constructible. This means that they can be determined from their unitarity cuts.We present a new systematic procedure to explicitly carry out any finite unitarity cut integral. The procedure naturally separates the contributions from bubble, triangle and box scalar integrals. This technique allows the systematic calculation of N = 1 amplitudes of gluons. As an application we compute all next-to-MHV six-gluon amplitudes in N = 1 super-Yang-Mills.

The rational parts of one-loop QCD amplitudes III: The six-gluon case

“…For MHV helicity configurations, explicit results were obtained for A N =4 in [15]. The recent development of using MHV vertices to compute one-loop amplitudes leads to many new results for the cut-constructible part [22,23,24,25,26,27,28,29,30,31,32]. In particular, Bedford, Brandhuber, Spence and Travaglini [22,26] applied the MHV vertices to one-loop calculations.…”

“…In particular, Bedford, Brandhuber, Spence and Travaglini [22,26] applied the MHV vertices to one-loop calculations. Britto, Buchbinder, Cachazo, Feng and Mastrolia [31,32,33] developed an efficient technique for evaluating the rational coefficients in an expansion of the one-loop amplitude in terms of scalar box, triangle and bubble integrals (the cut-constructible part, see [1] for details). By using their technique, it is much easier to calculate the coefficients of box integrals without doing any integration.…”

The rational parts of one-loop QCD amplitudes I: The general formalism

“…Even for the scalar part which is not cut-constructible, we can still split it into two parts: a cut-constructible part and a rational part. As we said before, the recent development inspired by twistor string theory has lead to very efficient techniques to compute the cut-constructible part [38,39,40]. To complete the program it is quite important to have efficient and powerful methods to compute the rational part.…”

“…Following Witten's twistor string theory [18], the CSW approach [19] and the use of maximally-helicity-violating (MHV) 1 vertices [21,22], there has been spectacular progress [23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47] in the perturbative QCD computations in the last two years or so, by using the unitarity cut method of Bern, Dunbar, Dixon and Kosower [3,48,50] and the spinor-helicity formalism [51,52] (see [53] for a review). In particular, Bedford, Brandhuber, Spence and Travaglini [28,31] applied the MHV vertices to one-loop calculations.…”

“…In particular, Bedford, Brandhuber, Spence and Travaglini [28,31] applied the MHV vertices to one-loop calculations. Britto, Buchbinder, Cachazo, Feng and Mastrolia [38,39,40] developed an efficient technique for evaluating the rational coefficients in an expansion of the oneloop amplitude in terms of scalar box, triangle and bubble integrals (the cut-constructible part, see below and Sect. 4).…”