Experimental constraint on quark electric dipole moments

The electric dipole moments (EDMs) of nucleons are sensitive probes of additional $CP$ violation sources beyond the standard model to account for the baryon number asymmetry of the universe. As a fundamental quantity of the nucleon structure, tensor charge is also a bridge that relates nucleon EDMs to quark EDMs. With a combination of nucleon EDM measurements and tensor charge extractions, we investigate the experimental constraint on quark EDMs, and its sensitivity to $CP$ violation sources from new physics beyond the electroweak scale. We obtain the current limits on quark EDMs as $1.27\times {10}^{-24}e·\mathrm{cm}$ for the up quark and $1.17\times {10}^{-24}e·\mathrm{cm}$ for the down quark at the scale of $4{\mathrm{GeV}}^2$. We also study the impact of future nucleon EDM and tensor charge measurements, and show that upcoming new experiments will improve the constraint on quark EDMs by about 3 orders of magnitude leading to a much more sensitive probe of new physics models.

Figure 1

Tensor charge results. The left panel shows the values of $u$ and $d$ quark tensor charges, and the right panel shows the values of the isovector tensor charge. The round (green) points are from Dyson-Schwinger equation calculations [31, 44], the square (blue) points are from lattice QCD calculations [45, 46, 47, 48, 49, 50], the triangle (magenta) points are from model calculations [34, 35, 36, 37, 38, 39, 40, 41, 42, 43], the filled diamond (black) points are phenomenological extractions from data [51, 52, 53, 54, 55], and the hollow diamond (red) points are the projection of JLab-12 GeV SoLID experiments based on the most recent global analysis [52]. The results quoted from the references are evaluated at different scales as explained in the text.

Figure 2

Constraints on quark EDMs with the upper limits on nucleon EDMs and the tensor charge extractions. The left panel shows the constraints by the upper limit on the proton EDM, and the right panel shows the constraints by the upper limit on the neutron EDM. The current tensor charge precision refers to $g_T^u=0.405\pm 0.130$ and $g_T^d=-0.225\pm 0.092$, and the future tensor charge precision refers to $g_T^u=0.405\pm 0.018$ and $g_T^d=-0.225\pm 0.008$ [52]. The strange quark tensor charge $g_T^s=0.008\pm 0.015$ [18] is used for both current and future tensor charge precisions. The current nucleon EDM limit refers to $|d_p|\le 2.6\times {10}^{-25}e·\mathrm{cm}$ derived from mercury atomic EDM measurement [24] and $|d_n|\le 3.0\times {10}^{-26}e·\mathrm{cm}$ from neutron EDM measurement [22], and the future nucleon EDM limit means $|d_p|\le 2.6\times {10}^{-29}e·\mathrm{cm}$ and $|d_n|\le 3.0\times {10}^{-28}e·\mathrm{cm}$. The constraints are understood at the scale of $4{\mathrm{GeV}}^2$.

Figure 3

The constraint on the split-supersymmetric model. The left panel is the constraint from the proton EDM, and the right panel is the constraint from the neutron EDM. The dotted (black) curves are constraints with precise tensor charge values, i.e. zero tensor charge uncertainties, the solid (blue) curves are those with current tensor charge uncertainties, and the dashed (red) curves are those with future tensor charge uncertainties. The nucleon EDM limit values marked on curves are in units of $e·\mathrm{cm}$. The area below the curves represents the excluded parameter space.