Bootstrapping one-loop QCD amplitudes with general helicities

The recently developed on-shell bootstrap for computing one-loop amplitudes in nonsupersymmetric 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 nonstandard complex singularities or from large values of the shift parameter. Here we develop a strategy for sidestepping difficulties through the 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(6;1)(1(-),2(-),3(-),4(+),5(+),6(+)), as well as numerical results for A(7;1)(1(-),2(-),3(-),4(+),5(+),6(+),7(+)), A(8;1)(1(-),2(-),3(-),4(+),5(+),6(+),7(+),8(+)), and A(8;1)(1(-),2(-),3(-),4(-),5(+),6(+),7(+),8(+)). We expect the on-shell bootstrap approach to have widespread applications to phenomenological studies at colliders.