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.

中文翻译：

---

具有一般螺旋度的自举单环 QCD 振幅

最近开发的用于在非超对称理论（如 QCD）中计算单环幅度的壳上引导程序将幺正性方法与环级壳上递归相结合。对于通用螺旋度配置，递归关系可能涉及来自非标准复奇点或位移参数的大值的不确定贡献。在这里，我们开发了一种通过使用成对递归关系来回避困难的策略。为了说明该策略，我们提出了在 QCD 中获得 n-胶子振幅所需的一组递归关系。我们给出了具有三个或四个颜色相邻的负螺旋度胶子和其余正螺旋度的胶子的单环 n-胶子 QCD 振幅的递归解决方案。我们为 QCD 振幅 A{sub 6;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup +}, 5{sup +}, 6{sup +})，以及 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 +})。我们希望壳上引导方法在对撞机的现象学研究中得到广泛应用。