One-Loop Gluonic Amplitudes from Single Unitarity Cuts

We show that one-loop amplitudes in massless gauge theories can be determined from single cuts. By cutting a single propagator and putting it on-shell, the integrand of an n-point one-loop integral is transformed into an (n+2)-particle tree level amplitude. The single-cut approach described here is complementary to the double or multiple unitarity cut approaches commonly used in the literature. In common with these approaches, if the cut is taken in four dimensions, one finds only the cut-constructible parts of the amplitude, while if the cut is in D=4-2 epsilon dimensions, both rational and cut-constructible parts are obtained. We test our method by reproducing the known results for the fully rational all-plus and mostly-plus QCD amplitudes A^{(1)}_4(1^+,2^+,3^+,4^+) and A^{(1)}_5(1^+,2^+,3^+,4^+,5^+). We also rederive expressions for the scalar loop contribution to the four-gluon MHV amplitude, A_4^{(1,N=0)}(-,-,+,+) which has both cut-constructible and rational contributions, and the fully cut-constructible n-gluon MHV amplitude in N=4 Supersymetric Yang-Mills, A_4^{(1,N=4)}(-,-,+,...,+).

MHV amplitudes in N=2 SQCD and in N=4 SYM at one loop

Using four-dimensional unitarity and MHV-rules we calculate the one-loop MHV amplitudes with all external particles in the adjoint representation for N=2 supersymmetric QCD with N_f fundamental flavours. We start by considering such amplitudes in the superconformal N=4 gauge theory where the N=4 supersymmetric Ward identities (SWI) guarantee that all MHV amplitudes for all types of external particles are given by the corresponding tree-level result times a universal helicity- and particle-type-independent contribution. In N=2 SQCD the MHV amplitudes differ from those for N=4 for general values of N_f and N_c. However, for N_f=2N_c where the N=2 SQCD is conformal, the N=2 MHV amplitudes (with all external particles in the adjoint representation) are identical to the N=4results. This factorisation at one-loop motivates us to pose a question if there may be a BDS-like factorisation for these amplitudes which also holds at higher orders of perturbation theory in superconformal N=2 theory.