Walter Burke Institute for Theoretical Physics California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev Lett. 2015 Aug 14;115(7):071601. doi: 10.1103/PhysRevLett.115.071601. Epub 2015 Aug 13.
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w,w[over ¯])=(n-h,n+h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_{i} can only be renormalized by an operator O_{j} if w_{i}≥w_{j} and w[over ¯]{i}≥w[over ¯]{j}, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.
我们推导出一类新的单圈非重整化定理，这些定理对一般的四维量子场论中更高维算符的跑动行为施加了很强的约束。我们的逻辑源于幺正性：单圈振幅的割线是树振幅的乘积，因此如果后者为零，那么相关的发散也为零。通过简单的选择定则，有限性就得到了保证，这些定则将某些螺旋度配置的树振幅清零。对于每个算子，我们定义了全纯和反全纯权，(w,w[over ¯])=(n-h,n+h)，其中 n 和 h 是由该算子产生的粒子的数量和螺旋度之和。我们认为，如果不存在非全纯 Yukawa 耦合，算子 O_{i} 只能被算子 O_{j} 重整化，当且仅当 w_{i}≥w_{j} 且 w[over ¯]{i}≥w[over ¯]{j}。这些结果解释并推广了在标准模型中六维算子重整化中发现的令人惊讶的消去现象。由于我们的结论依赖于幺正性和螺旋度，而不是显式对称性，因此它们具有广泛的适用性。
