Calculation of the neutron electric dipole moment with two dynamical flavors of domain wall fermions

Abstract

We present a study of the neutron electric dipole moment (${\stackrel{\ensuremath{\rightarrow}}{d}}_{N}$) within the framework of lattice QCD with two flavors of dynamical light quarks. The dipole moment is sensitive to the topological structure of the gauge fields, and accuracy can only be achieved by using dynamical, or sea quark, calculations. However, the topological charge evolves slowly in these calculations, leading to a relatively large uncertainty in ${\stackrel{\ensuremath{\rightarrow}}{d}}_{N}$. It is shown, using quenched configurations, that a better sampling of the charge distribution reduces this problem, but because the $CP$ even part of the fermion determinant is absent, both the topological charge distribution and ${\stackrel{\ensuremath{\rightarrow}}{d}}_{N}$ are pathological in the chiral limit. We discuss the statistical and systematic uncertainties arising from the topological charge distribution and unphysical size of the quark mass in our calculations and prospects for eliminating them. Our calculations employ the RBC collaboration two flavor domain wall fermion and DBW2 gauge action lattices with inverse lattice spacing ${a}^{\ensuremath{-}1}\ensuremath{\approx}1.7\text{ }\text{ }\mathrm{GeV}$, physical volume $V\ensuremath{\approx}(2\text{ }\text{ }\mathrm{fm}{)}^{3}$, and light quark mass roughly equal to the strange quark mass (${m}_{\mathrm{sea}}=0.03$ and 0.04). We determine a value of the electric dipole moment that is zero within (statistical) errors, from which we obtain the bound $|{\stackrel{\ensuremath{\rightarrow}}{d}}_{N}|\ensuremath{\lesssim}0.02e\mathrm{\text{\ensuremath{-}}}\ensuremath{\theta}\mathrm{\text{\ensuremath{-}}}\mathrm{fm}$. Satisfactory results for the magnetic and electric form factors of the proton and neutron are also obtained and presented.