Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow

Abstract

We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f=2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ MeV, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at $3$ different lattice spacings in the range of $0.07\mathrm{fm}<a<0.11$ fm at a single value of the pion mass, to enable control on discretization effects. We also investigate finite size effects using $2$ different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuum-like behavior of the nucleon EDM towards the chiral limit. Under this assumption our results read $d_n=-0.00152(71)\bar{\theta }e\text{fm}$ and $d_p=0.0011(10)\bar{\theta }e\text{fm}$. Assuming the theta term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $\left|\bar{\theta }\right|<1.98\times 10^{-10}$ ($90\%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_p=0.50(59)\times 10^{-4}\bar{\theta }e{\text{fm}}^3$ and $S_n=-0.10(43)\times 10^{-4}\bar{\theta }e{\text{fm}}^3$.

arXiv commentUpdated version submitted to journal. Added extraction of CP-odd pion-nucleon coupling and details about chiral extrapolation. Fixed bug in analysis code. Results mostly unchanged. Minor changes in the wording

References in corpus (42)

• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• Properties and uses of the Wilson flow in lattice QCD
• 2+1 Flavor Lattice QCD toward the Physical Point
• Ab initio calculation of the neutron-proton mass difference
• 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
• Monte Carlo errors with less errors
• An Improved Limit on the Muon Electric Dipole Moment
• Critical slowing down and error analysis in lattice QCD simulations
• A new method of measuring electric dipole moments in storage rings
• Lattice QCD without topology barriers
• Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass
• Highly-improved lattice field-strength tensor
• Electric Dipole Moments of Light Nuclei From Chiral Effective Field Theory
• New insights into the neutron electric dipole moment
• The electric dipole moment of the neutron from 2+1 flavor lattice QCD
• Building the International Lattice Data Grid
• New method for a continuous determination of the spin tune in storage rings and implications for precision experiments
• Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
• Dimension-5 CP-odd operators: QCD mixing and renormalization
• Light quark masses from unquenched lattice QCD
• The Effective Chiral Lagrangian From the Theta Term
• Baryon mass splittings and strong CP violation in SU(3) Chiral Perturbation Theory
• Calculation of the neutron electric dipole moment with two dynamical flavors of domain wall fermions
• The Nucleon Electric Dipole Form Factor From Dimension-Six Time-Reversal Violation
• On Lattice Calculation of Electric Dipole Moments and Form Factors of the Nucleon
• Magnetic form factors of the octet baryons from lattice QCD and chiral extrapolation
• The Electric Dipole Form Factor of the Nucleon in Chiral Perturbation Theory to Sub-leading Order
• Baryon electric dipole moments from strong CP violation
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• The electric dipole moment of the deuteron from the QCD $\theta$-term
• The electric dipole form factor of the nucleon
• The nucleon electric dipole moment with the gradient flow: the $\theta$-term contribution
• Neutron electric dipole moment using $N_f=2+1+1$ twisted mass fermions
• Variance Reduction and Cluster Decomposition
• Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
• Neutron and proton electric dipole moments from $N_f=2+1$ domain-wall fermion lattice QCD
• Short flow-time coefficients of CP-violating operators
• Indirect Signs of the Peccei-Quinn Mechanism
• Neutron Electric Dipole Moment on the Lattice
• New Physics Searches from Nucleon Matrix Elements in Lattice QCD

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