Short flow-time coefficients of CP-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-chromo electric dipole moment (qCEDM) operator and the three-gluon Weinberg operator. The non-perturbative 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 non-zero 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 ${\gamma }_5$ in generic d dimensions. We show that leading contributions in the external momenta can be reproduced by defining ${\gamma }_5$ using the 't Hooft-Veltman-Breitenlohner-Maison scheme.

23 pages, 3 figures

References in corpus (17)

• Measurement of the permanent electric dipole moment of the neutron
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
• The lattice gradient flow at tree-level and its improvement
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• The Nucleon Electric Dipole Form Factor From Dimension-Six Time-Reversal Violation
• The Electric Dipole Form Factor of the Nucleon in Chiral Perturbation Theory to Sub-leading Order
• Reexamination of The Standard Model Nucleon Electric Dipole Moment
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Massless correlators of vector, scalar and tensor currents in position space at orders alpha_s^3 and alpha_s^4: explicit analytical results
• The perturbative QCD gradient flow to three loops
• Step scaling and the Yang-Mills gradient flow
• Correlations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
• The gradient flow running coupling with twisted boundary conditions
• Topological susceptibility in QCD with two flavors and 3-5 colors -- a pilot study
• The twisted gradient flow coupling at one loop

Cited by in corpus (4)

• Weinberg operator contribution to the nucleon electric dipole moment in the quark model
• Nucleon electric dipole moment from polarized deep inelastic scattering
• Nonperturbative Renormalization of the Quark Chromoelectric Dipole Moment with the Gradient Flow:Power Divergences
• Weinberg operator contribution to the CP-odd nuclear force in the quark model