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Holomorphy without Supersymmetry in the Standard Model Effective Field Theory

Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar

(Submitted on 2 Sep 2014 (v1), last revised 6 Nov 2014 (this version, v2))

The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. The holomorphy conditions are reminiscent of supersymmetry, even though the SMEFT is not a supersymmetric theory.

http://arxiv.org/abs/1412.7151

One-loop non-renormalization results in EFTs

J. Elias-Miro, J. R. Espinosa, A. Pomarol

(Submitted on 22 Dec 2014 (v1), last revised 17 Feb 2015 (this version, v2))

In Effective Field Theories (EFTs) with higher-dimensional operators many anomalous dimensions vanish at the one-loop level for no apparent reason. With the use of supersymmetry, and a classification of the operators according to their embedding in super-operators, we are able to show why many of these anomalous dimensions are zero. The key observation is that one-loop contributions from superpartners trivially vanish in many cases under consideration, making supersymmetry a powerful tool even for non-supersymmetric models. We show this in detail in a simple U(1) model with a scalar and fermions, and explain how to extend this to SM EFTs and the QCD Chiral Langrangian. This provides an understanding of why most "current-current" operators do not renormalize "loop" operators at the one-loop level, and allows to find the few exceptions to this ubiquitous rule.

http://arxiv.org/abs/1505.01844

Non-renormalization Theorems without Supersymmetry

Clifford Cheung, Chia-Hsien Shen

(Submitted on 7 May 2015)

We derive a new class of one-loop non-renormalization 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 anti-holomorphic weights, (w,wbar)=(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 wbar_{i}≥wbar_{j}, absent non-holomorphic 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.

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# New properties of "standard model effective field theory"

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