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.

arXiv comment23 pages, 3 figures

References in corpus (71)

• Properties and uses of the Wilson flow in lattice QCD
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Measurement of the permanent electric dipole moment of the neutron
• Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond
• A Revised Experimental Upper Limit on the Electric Dipole Moment of the Neutron
• Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles
• 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
• Two-loop mixing of dimension-five flavor-changing operators
• Chiral symmetry and the Yang--Mills gradient flow
• Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation
• The gradient flow coupling in the Schrödinger Functional
• Studying the gradient flow coupling in the Schrödinger functional
• QCD corrections to the electric dipole moment of the neutron in the MSSM
• Hadronic EDMs, the Weinberg Operator, and Light Gluinos
• The lattice gradient flow at tree-level and its improvement
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
• Thermodynamics of SU(3) Gauge Theory from Gradient Flow
• Symanzik improvement of the gradient flow in lattice gauge theories
• Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Non-Perturbative Renormalization of Lattice Four-Fermion Operators without Power Subtractions
• The electric dipole moment of the neutron from 2+1 flavor lattice QCD
• Dimension-5 CP-odd operators: QCD mixing and renormalization
• Quasi parton distributions and the gradient flow
• Sp(4) gauge theories on the lattice: $N_f=2$ dynamical fundamental fermions
• The Nucleon Electric Dipole Form Factor From Dimension-Six Time-Reversal Violation
• Space-time symmetries and the Yang-Mills gradient flow
• On Lattice Calculation of Electric Dipole Moments and Form Factors of the Nucleon
• Calculation of the neutron electric dipole moment with two dynamical flavors of domain wall fermions
• Nonperturbative beta function of twelve-flavor SU(3) gauge theory
• Reexamination of The Standard Model Nucleon Electric Dipole Moment
• The Electric Dipole Form Factor of the Nucleon in Chiral Perturbation Theory to Sub-leading Order
• The two-loop energy-momentum tensor within the gradient-flow formalism
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Exploring Nf=2+1 QCD thermodynamics from the gradient flow
• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• 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
• Future applications of the Yang-Mills gradient flow in lattice QCD
• Neutron electric dipole moment using $N_f=2+1+1$ twisted mass fermions
• The nucleon electric dipole moment with the gradient flow: the $\theta$-term contribution
• Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
• Correlations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
• Non-perturbative renormalization of lattice operators in coordinate space
• Sum rules for CP-violating operators of Weinberg type
• Neutron and proton electric dipole moments from $N_f=2+1$ domain-wall fermion lattice QCD
• Thermodynamics in quenched QCD: energy--momentum tensor with two-loop order coefficients in the gradient flow formalism
• The gradient flow running coupling with twisted boundary conditions
• SMD-based numerical stochastic perturbation theory
• Small flow-time representation of fermion bilinear operators
• Results and techniques for higher order calculations within the gradient-flow formalism
• Gradient flow step-scaling function for SU(3) with twelve flavors
• The gradient flow coupling at high-energy and the scale of SU(3) Yang-Mills theory
• Gradient-flowed thermal correlators: how much flow is too much?
• Non-perturbative determination of the $\Lambda$-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling
• The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box
• Non-perturbative renormalization scheme for the CP-odd three-gluon operator
• Universal formula for the flavor non-singlet axial-vector current from the gradient flow
• Themodynamics for pure SU($2$) gauge theory using gradient flow
• $O(4)$-symmetric position-space renormalization of lattice operators
• Investigation of New Methods for Numerical Stochastic Perturbation Theory in ${\phi }^4$ Theory
• Topological susceptibility in QCD with two flavors and 3-5 colors -- a pilot study
• Simple chromatic properties of gradient flow
• The twisted gradient flow coupling at one loop
• Electric Dipole Moment Results from lattice QCD
• Scale setting for $N_f=3+1$ QCD
• Neutron Electric Dipole Moment on the Lattice
• Improvements to Nucleon Matrix Elements within a $\theta$ Vacuum from Lattice QCD

Cited by in corpus (19)

• Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow
• Opportunities for Fundamental Physics Research with Radioactive Molecules
• Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
• Weinberg operator contribution to the nucleon electric dipole moment in the quark model
• Computing Tools for Effective Field Theories
• Non-perturbative renormalization scheme for the CP-odd three-gluon operator
• Moments of parton distribution functions of any order from lattice QCD
• Effective electroweak Hamiltonian in the gradient-flow formalism
• Nucleon electric dipole moment from polarized deep inelastic scattering
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow
• Lattice QCD and the Neutron Electric Dipole Moment
• ftint: Calculating gradient-flow integrals with pySecDec
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• 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
• Weinberg Operator Contribution to the Hadronic CP Violation
• Applications of the Perturbative Gradient Flow
• Quark model analysis of the Weinberg operator contribution to the nucleon EDM
• The gradient flow formulation of the electroweak Hamiltonian