Model independent evaluation of the Wilson coefficient of the Weinberg operator in QCD
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Springer
Received: January 10, Revised: March 8, Accepted: March 23, Published: March 28,
2018 2018 2018 2018
Tomohiro Abe,a,b Junji Hisanob,c,d and Ryo Nagaie a
Institute for Advanced Research, Nagoya University, Furo-cho Chikusa-ku, Nagoya, Aichi, 464-8602 Japan b Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Furo-cho Chikusa-ku, Nagoya, Aichi, 464-8602 Japan c Department of Physics, Nagoya University, Furo-cho Chikusa-ku, Nagoya, Aichi, 464-8602, Japan d Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa, Chiba 277-8584, Japan e Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan
E-mail: [email protected], [email protected], [email protected] Abstract: We derive a Wilson coefficient of a CP-violating purely gluonic dimension-6 ˜ generated by a scalar and two fermions at operator called the Weinberg operator (GGG) the two-loop level. We do not specify the representation of SU(3)c for the scalar and the fermions, and thus our result can be applied to a variety of models beyond the standard model. We estimate the nucleon EDMs induced by the Weinberg operator in some examples and discuss the importance of measuring EDMs. It is found that future measurements of the EDMs can probe physics at higher energy scale beyond the reach of collider experiments. Keywords: Beyond Standard Model, CP violation ArXiv ePrint: 1712.09503
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)175
JHEP03(2018)175
Model independent evaluation of the Wilson coefficient of the Weinberg operator in QCD
Contents 1
2 Setup
2
3 Evaluation of diagrams ˜ from DGDG ˜ terms 3.1 GGG 3.2 Diagrams with three external gluon fields
3 4 5
4 Results
8
5 A view point from effective theory
8
6 Numerical analysis
10
7 Summary
14
A One gluon field from the scalar field in Fock-Schwinger gauge
15
B Some formulae of integrals
16
C Approximate formulae
17
D A relation among X † TS X, X † TB X, and XTA TA X †
17
1
Introduction
Measurements of electric dipole moments (EDMs) are very powerful for exploring physics beyond the standard model (SM). The SM predicts small values of EDMs. Its prediction for the neutron EDM is dn ' 10−32 e cm [1–5], and for the electron EDM is de ≤ 10−38 e cm [5, 6]. It is much smaller than the current upper bounds, |dn | < 2.9 × 10−26 e cm (90% CL) [7], and |de | < 8.7 × 10−29 e cm (90% CL) [8]. On the other hand, models beyond the SM often have new CP violation sources, and they can predict larger values of EDMs compared to the SM. Therefore observation of EDMs is equivalent to a discovery of physics beyond the SM. Moreover, EDMs can probe physics at higher energy scale beyond the reach of collider experiments. The current data of the Large Hadron Collider (LHC) experiment imply that the scale of new physics is higher than O(1) TeV. Thus the importance of measuring EDMs is increasing. This situation motivates us to evaluate EDMs in a variety of models with small
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