Neutron electric dipole moment from lattice QCD

Abstract

We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the $\theta$ term. We develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic form factor $F_3$ at small $\theta$, in which NEDM is given by ${\lim }_{q^2\to 0}\theta F_3(q^2)/(2m_N)$ where $q$ is the momentum transfer and $m_N$ is the nucleon mass. We first derive a formula which relates $F_3$, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/or the current. In the expansion of $\theta$, the parity-odd part of the nucleon-current-nucleon three-point function contains contributions not only from the parity-odd form factors but also from the parity-even form factors multiplied by the parity-odd part of the nucleon two-point function, and therefore the latter contribution must be subtracted to extract $F_3$. We then perform an explicit lattice calculation employing the domain-wall quark action with the RG improved gauge action in quenched QCD at $a^{-1}\simeq 2$ GeV on a $16^3\times 32\times 16$ lattice. At the quark mass $m_{f}a=0.03$, corresponding to $m_{\pi }/m_{\rho }\simeq 0.63$, we accumulate 730 configurations, which allow us to extract the parity-odd part in both two- and three-point functions. Employing two different Dirac $\gamma$ matrix projections, we show that a consistent value for $F_3$ cannot be obtained without the subtraction described above. We obtain $F_3(q^2\simeq 0.58{\text{GeV}}^2)/(2m_N)=$ $-$0.024(5) $e\cdot$fm for the neutron and $F_3(q^2\simeq 0.58{\text{GeV}}^2)/(2m_N)=$ 0.021(6) $e\cdot$fm for the proton.

arXiv commentLaTeX2e, 43 pages, 42 eps figures, uses revtex4 and graphicx, comments added and typos corrected, final version to appear in Phys. Rev. D

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• Renormalization Group Running of Dimension-Six Sources of Parity and Time-Reversal Violation
• QCD corrections to the electric dipole moment of the neutron in the MSSM
• Baryon electric dipole moments from strong CP violation
• Neutron-Electron EDM Correlations in Supersymmetry and Prospects for EDM Searches
• Topics in Effective Field Theory for Lattice QCD
• Computing Nucleon Electric Dipole Moment from lattice QCD