Nonrenormalization Theorems without Supersymmetry

Physical Review Letters
Clifford Cheung, Chia-Hsien Shen

Abstract

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.

References

May 1, 1994·Physical Review. D·G Mahlon
May 3, 1993·Physical Review Letters·Z BernD A Kosower
Apr 4, 1994·Physical Review Letters·Z BernD A Kosower

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Citations

Apr 8, 2017·Physical Review Letters·Clifford Cheung, Chia-Hsien Shen
Feb 23, 2020·Physical Review Letters·Zvi BernEric Sawyer
Feb 25, 2017·Physical Review Letters·Rutger H Boels, Ricardo Medina
Jan 23, 2021·Physical Review Letters·Minyuan JiangYu-Hui Zheng
Aug 24, 2021·Physical Review Letters·T HeinzlB King

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