Non-perturbative renormalization scheme for the C P -odd three-gluon operator
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Received: April 27, 2020 Accepted: August 23, 2020 Published: September 14, 2020
Vincenzo Cirigliano,a Emanuele Mereghettia and Peter Stofferb a
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A. b Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0319, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: We define a regularization-independent momentum-subtraction scheme for the CP -odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of CP -violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to MS at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment. Keywords: Non-perturbative renormalization ArXiv ePrint: 2004.03576
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)094
JHEP09(2020)094
Non-perturbative renormalization scheme for the CP -odd three-gluon operator
Contents 1 Introduction
1
2 Operator mixing
3 5 6 8 8 11
4 Renormalization scheme 4.1 Counterterm vertex rules 4.2 Projection of scalar structures Ė 4.3 Renormalization conditions in the RI-SMOM scheme 4.3.1 Conditions for the gCEDM 4.3.2 Conditions for the qCEDM 4.3.3 Condition for the qEDM 4.3.4 Conditions for the remaining operators
12 13 19 23 24 24 24 24
5 Matching at one loop 5.1 Gauge fixing 5.2 Dimensional regularization and renormalization 5.3 Results 5.3.1 Covariant gauge 5.3.2 Background-field method
25 25 26 28 29 31
6 Conclusions
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A Construction of gauge-invariant operator basis A.1 Symmetries and building blocks A.2 Pure gauge operators A.3 Two-quark operators A.4 Four-quark operators A.5 Intermediate summary
34 34 36 39 43 44
B BRST invariance and nuisance operators B.1 Gauge fixing and equations of motion B.2 Slavnov-Taylor identities B.3 Construction of nuisance operators B.4 Symmetry properties of sources and building blocks B.5 Seed operators
45 45 46 49 50 52
āiā
JHEP09(2020)094
3 Construction of the operator basis 3.1 Gauge-invariant operators 3.2 Nuisance operators 3.3 Operator basis 3.4 Mixing structure
B.6 Nuisance operators B.7 Redundancies
56 57
C Mixing with evanescent operators C.1 Generalities C.2 Definition of evanescent operators
Introduction
Permanent electric dipole moments (EDMs) of non-degenerate systems break the symmetries of parity (P ) and time reversal (T
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