Bootstrapping One-Loop QCD Amplitudeswith General Helicities

Abstract

The recently developed on-shell bootstrap for computing one-loop amplitudes in non-supersymmetric theories such as QCD combines the unitarity method with loop-level on-shell recursion. For generic helicity configurations, the recursion relations may involve undetermined contributions from non-standard complex singularities or from large values of the shift parameter. Here we develop a strategy for sidestepping difficulties through use of pairs of recursion relations. To illustrate the strategy, we present sets of recursion relations needed for obtaining n-gluon amplitudes in QCD. We give a recursive solution for the one-loop n-gluon QCD amplitudes with three or four color-adjacent gluons of negative helicity and the remaining ones of positive helicity. We provide an explicit analytic formula for the QCD amplitude A{sub 6;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup +}, 5{sup +}, 6{sup +}), as well as numerical results for A{sub 7;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup +}, 5{sup +}, 6{sup +}, 7{sup +}), A{sub 8;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup +}, 5{sup +}, 6{sup +}, 7{sup +}, 8{sup +}), and A{sub 8;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup -}, 5{sup +}, 6{sup +}, 7{sup +}, 8{sup +}). We expect the on-shell bootstrap approach to have widespread applications to phenomenological studies at colliders.