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Title: Short flow-time coefficients of C P -violating operators

Abstract

Measurements of a permanent neutron electric dipole moment (EDM) potentially probe beyond-the-Standard Model (BSM) sources of CP-violation. At low energy the CP-violating BSM interactions are parametrized by flavor-conserving CP-violating operators of dimension higher than four. QCD calculations of the nucleon matrix elements of these operators are required to fully reconstruct the sources and magnitudes of the different CP-violating contributions to the nucleon EDM. Herein we study the quark-chromoelectric dipole moment (qCEDM) operator and the three-gluon Weinberg operator. The nonperturbative determination, using lattice QCD, of the nucleon matrix elements of these CP-violating operators is hampered by their short-distance behavior. Under renormalization these operators mix with lower-dimensional operators, which induces power divergences in the lattice spacing, as the continuum limit is approached. We study the short-distance behavior of the qCEDM and the Weinberg operators using the gradient flow. We perform a short flow time expansion and determine, in perturbation theory, the expansion coefficients of the linearly divergent terms stemming from the mixing with the pseudoscalar density and the topological charge, confirming the expectations of the operator product expansion. We introduce a new method to perform calculations at nonzero flow-time for arbitrary values of the external momenta. This method allows us to workmore » in four dimensions for most of the calculations described in this paper, avoiding the complications associated with defining γ5 in generic d dimensions. We show that leading contributions in the external momenta can be reproduced by defining γ5 using the t Hooft-Veltman-Breitenlohner-Maison scheme.« less

Authors:
ORCiD logo; ORCiD logo; ORCiD logo;
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)
OSTI Identifier:
1650700
Alternate Identifier(s):
OSTI ID: 1656459
Report Number(s):
JLAB-THY-20-3191; DOE/OR-23177-4968; arXiv:2005.04199
Journal ID: ISSN 2470-0010; PRVDAQ; 034509
Grant/Contract Number:  
AC05-06OR23177; PHY-1913287
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Feynman diagrams; lattice field theory; perturbation theory; renormalization; symmetries

Citation Formats

Rizik, Matthew D., Monahan, Christopher J., Shindler, Andrea, and SymLat Collaboration. Short flow-time coefficients of C P -violating operators. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.102.034509.
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Rizik, Matthew D., Monahan, Christopher J., Shindler, Andrea, & SymLat Collaboration. Short flow-time coefficients of C P -violating operators. United States. https://doi.org/10.1103/PhysRevD.102.034509
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Rizik, Matthew D., Monahan, Christopher J., Shindler, Andrea, and SymLat Collaboration. Wed . "Short flow-time coefficients of C P -violating operators". United States. https://doi.org/10.1103/PhysRevD.102.034509.
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@article{osti_1650700,
title = {Short flow-time coefficients of C P -violating operators},
author = {Rizik, Matthew D. and Monahan, Christopher J. and Shindler, Andrea and SymLat Collaboration},
abstractNote = {Measurements of a permanent neutron electric dipole moment (EDM) potentially probe beyond-the-Standard Model (BSM) sources of CP-violation. At low energy the CP-violating BSM interactions are parametrized by flavor-conserving CP-violating operators of dimension higher than four. QCD calculations of the nucleon matrix elements of these operators are required to fully reconstruct the sources and magnitudes of the different CP-violating contributions to the nucleon EDM. Herein we study the quark-chromoelectric dipole moment (qCEDM) operator and the three-gluon Weinberg operator. The nonperturbative determination, using lattice QCD, of the nucleon matrix elements of these CP-violating operators is hampered by their short-distance behavior. Under renormalization these operators mix with lower-dimensional operators, which induces power divergences in the lattice spacing, as the continuum limit is approached. We study the short-distance behavior of the qCEDM and the Weinberg operators using the gradient flow. We perform a short flow time expansion and determine, in perturbation theory, the expansion coefficients of the linearly divergent terms stemming from the mixing with the pseudoscalar density and the topological charge, confirming the expectations of the operator product expansion. We introduce a new method to perform calculations at nonzero flow-time for arbitrary values of the external momenta. This method allows us to work in four dimensions for most of the calculations described in this paper, avoiding the complications associated with defining γ5 in generic d dimensions. We show that leading contributions in the external momenta can be reproduced by defining γ5 using the t Hooft-Veltman-Breitenlohner-Maison scheme.},
doi = {10.1103/PhysRevD.102.034509},
journal = {Physical Review D},
number = 3,
volume = 102,
place = {United States},
year = {Wed Aug 26 00:00:00 EDT 2020},
month = {Wed Aug 26 00:00:00 EDT 2020}
}
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https://doi.org/10.1103/PhysRevD.102.034509
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