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Nonrenormalization Theorems without Supersymmetry

Cheung, Clifford and Shen, Chia-Hsien (2015) Nonrenormalization Theorems without Supersymmetry. Physical Review Letters, 115 (7). Art. No. 071601. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20150601-134624745

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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¯) = (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¯_i ≥ w¯_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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.115.071601 DOIArticle
https://arxiv.org/abs/1505.01844arXivDiscussion Paper
ORCID:
AuthorORCID
Shen, Chia-Hsien0000-0002-5138-9971
Alternate Title:Non-renormalization Theorems without Supersymmetry
Additional Information:© 2015 American Physical Society. Received 20 May 2015; published 13 August 2015. We would like to thank Rodrigo Alonso, Zvi Bern, Lance Dixon, Yu-tin Huang, Elizabeth Jenkins, David Kosower, and Aneesh Manohar for useful discussions. C. C. and C.-H. S. are supported by a DOE Early Career Award under Grant No. DE-SC0010255. C. C. is also supported by a Sloan Research Fellowship.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0010255
Alfred P. Sloan FoundationUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2015-024
Issue or Number:7
Classification Code:PACS numbers: 11.10.Gh
Record Number:CaltechAUTHORS:20150601-134624745
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150601-134624745
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:57923
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:01 Jun 2015 21:31
Last Modified:09 Mar 2020 13:19

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