Contribution of the QCD $\Theta$-term to nucleon electric dipole moment

Abstract

We present a calculation of the contribution of the $\Theta$-term to the neutron and proton electric dipole moments using seven 2+1+1-flavor HISQ ensembles. We also estimate the topological susceptibility for the 2+1+1 theory to be ${\chi }_Q=(66(9)(4)\mathrm{MeV}{)}^4$ in the continuum limit at $M_{\pi }=135$ MeV. The calculation of the nucleon three-point function is done using Wilson-clover valence quarks. The CP-violating form factor $F_3$ is calculated by expanding in small $\Theta$. We show that lattice artifacts introduce a term proportional to $a$ that does not vanish in the chiral limit, and we include this in our chiral-continuum fits. A chiral perturbation theory analysis shows that the $N(0)\pi (0)$ state should provide the leading excited state contribution, and we study the effect of such a state. Detailed analysis of the contributions to the neutron and proton electric dipole moment using two strategies for removing excited state contamination are presented. Using the excited state spectrum from fits to the two-point function, we find $d_n^{\Theta }$ is small, $|d_n^{\Theta }|\lesssim 0.01\overline{\Theta }e$ fm, whereas for the proton we get $|d_p^{\Theta }|\sim 0.02\overline{\Theta }e$ fm. On the other hand, if the dominant excited-state contribution is from the $N\pi$ state, then $|d_n^{\Theta }|$ could be as large as $0.05\overline{\Theta }e$ fm and $|d_p^{\Theta }|\sim 0.07\overline{\Theta }e$ fm. Our overall conclusion is that present lattice QCD calculations do not provide a reliable estimate of the contribution of the $\Theta$-term to the nucleon electric dipole moments, and a factor of ten higher statistics data are needed to get better control over the systematics and possibly a $3\sigma$ result.

27 pages, 21 figures

References in corpus (10)

• Measurement of the permanent electric dipole moment of the neutron
• CP Violation and Neutrino Oscillations
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• 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
• Neutron Electric Dipole Moment Induced by the Strangeness Revisited
• A Fresh Look into the Neutron EDM and Magnetic Susceptibility
• Neutron electric dipole moment using lattice QCD simulations at the physical point
• Neutron Electric Dipole Moment from Beyond the Standard Model

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