Completing the scalar and fermionic universal one-loop effective action
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Springer
Received: September 2, 2019 Accepted: December 19, 2019 Published: January 15, 2020
Michael Kr¨ amer, Benjamin Summ and Alexander Voigt Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen University, 52074 Aachen, Germany
E-mail: [email protected], [email protected], [email protected] Abstract: We extend the known Universal One-Loop Effective Action (UOLEA) by all operators which involve scalars and fermions, not including contributions arising from open covariant derivatives. Our generic analytic expressions for the one-loop Wilson coefficients of effective operators up to dimension six allow for an application of the UOLEA to a broader class of UV-complete models. We apply our generic results to various effective theories of supersymmetric models, where different supersymmetric particles are integrated out at a high mass scale. Keywords: Effective Field Theories, Beyond Standard Model ArXiv ePrint: 1908.04798
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)079
JHEP01(2020)079
Completing the scalar and fermionic universal one-loop effective action
Contents 1
2 Calculation of the scalar and fermionic UOLEA 2.1 Functional matching in a scalar theory 2.2 Fermionic contributions to the UOLEA
3 3 5
3 Discussion of the result 3.1 Published operators and coefficients 3.2 Infrared and ultra-violet divergences 3.3 Application to models with massive vector fields 3.4 Extraction of β-functions
12 12 14 15 15
4 Applications 4.1 Integrating out the top quark from the Standard Model 4.2 MSSM threshold correction to the quartic Higgs coupling 4.3 Integrating out stops and the gluino from the MSSM 4.4 Integrating out the gluino from the MSSM with light stops
16 16 17 23 26
5 Conclusions
32
A Fermionic shifts
33
B Loop functions
35
C Useful relations for spinors and SU(N ) groups
36
D Dimensional regularization and dimensional reduction
37
1
Introduction
With the discovery of the Higgs boson at the Large Hadron Collider (LHC) [1, 2], the Standard Model of Particle Physics (SM) is formally complete. While existing deviations between some SM predictions and experiment, such as for the anomalous magnetic moment of the muon (see for example [3, 4]), are not conclusive, the SM is not a complete description of nature as it neither accounts for astrophysical phenomena such as dark matter, nor does it incorporate gravity. Searches for physics beyond the SM have not been successful thus far. Exclusion limits for new particles introduced by SM extensions often exceed the TeV scale. These results suggest that new physics either interacts weakly with the SM, or that the masses
–1–
JHEP01(2020)079
1 Introduction
of new particles are significantly above the electroweak scale. A well-known example is the Minimal Supersymmetric Standard Model (MSSM) [5], which requires at least TeV-scale stops in order to correctly predict the mass of the SM-like Higgs boson of about 125 GeV, see for example [6, 7]. Th
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