Confirming the existence of the strong CP problem in lattice QCD with the gradient flow

• DOI: 10.1103/physrevc.103.015202
• Publication Date: 2021-01-19T15:42:05Z
• Authors: Jack Dragos; Thomas Luu; Andrea Shindler; Jordy de Vries; Ahmed Yousif
• Keywords: Lattice (music); Quenched approximation; Bar (unit)

We calculate the electric dipole moment of nucleon induced by quantum chromodynamics $\ensuremath{\theta}$ term. use gradient flow to define topological charge and ${N}_{f}=2+1$ flavors dynamical quarks corresponding pion masses 700, 570, $410\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, perform an extrapolation physical point based on chiral perturbation theory. calculations at three different lattice spacings in range $0.07\phantom{\rule{0.16em}{0ex}}\mathrm{fm}<a<0.11\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$ a single value mass, enable control discretization effects. also investigate finite-size effects using two volumes. A novel technique is applied improve signal-to-noise ratio form factor calculations. The very mild observed suggest continuumlike behavior toward limit. Under this assumption our results read ${d}_{n}=\ensuremath{-}0.00152(71)\phantom{\rule{4pt}{0ex}}\overline{\ensuremath{\theta}}\phantom{\rule{4pt}{0ex}}e\phantom{\rule{0.16em}{0ex}}\text{fm}$ ${d}_{p}=0.0011(10)\phantom{\rule{4pt}{0ex}}\overline{\ensuremath{\theta}}\phantom{\rule{4pt}{0ex}}e\phantom{\rule{0.16em}{0ex}}\text{fm}$. Assuming term only source CP violation, experimental bound neutron limits $\left|\overline{\ensuremath{\theta}}\right|<1.98\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ ($90%$ CL). first attempt calculating Schiff continuum resulted ${S}_{p}=0.50(59)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{4pt}{0ex}}\overline{\ensuremath{\theta}}\phantom{\rule{4pt}{0ex}}e\phantom{\rule{0.16em}{0ex}}{\text{fm}}^{3}$ ${S}_{n}=\ensuremath{-}0.10(43)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{4pt}{0ex}}\overline{\ensuremath{\theta}}\phantom{\rule{4pt}{0ex}}e\phantom{\rule{0.16em}{0ex}}{\text{fm}}^{3}$.