Abstract
We present state-of-the-art results for the matrix elements of flavor diagonal tensor operators within the nucleon state. The calculation of the dominant connected contribution is done using eleven ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quark (HISQ) action with 2+1+1 dynamical flavors. The calculation of the disconnected contributions is done using seven (six) ensembles for the strange (light) quarks. These high-statistics simulations allowed us to address various systematic uncertainties. A simultaneous fit in the lattice spacing and the light-quark mass is used to extract the tensor charges in the continuum limit and at $M_\pi=135$ MeV. Results for the proton in the $\overline{MS}$ scheme at 2~GeV are: $g_T^u = 0.784(28)(10)$, $g_T^d = -0.204(11)(10)$ and $g_T^s = -0.0027(16)$. Implications of these results for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed.
Highlights
High-precision calculations of the matrix elements of flavor diagonal quark bilinear operators q Γq, where Γ is one of the 16 Dirac matrices, within the nucleon state provide a quantitative understanding of a number of properties of nucleons and their interactions with electrically neutral probes
We present results for the tensor charges guT, gdT and gsT that give the contribution of the electric dipole moment (EDM) of these quark flavors to the EDM of the nucleon
We report a signal in the still smaller gsT, whose contribution to the neutron EDM can be enhanced versus guT by ms=mu ≈ 40 in models in which the chirality flip is provided by the Standard Model Yukawa couplings
Summary
High-precision calculations of the matrix elements of flavor diagonal quark bilinear operators q Γq, where Γ is one of the 16 Dirac matrices, within the nucleon state provide a quantitative understanding of a number of properties of nucleons and their interactions with electrically neutral probes. We present results for the tensor charges guT, gdT and gsT that give the contribution of the electric dipole moment (EDM) of these quark flavors to the EDM of the nucleon. They are defined as the nucleon matrix elements of the renormalized tensor operator. ZTqσμνq with σμν 1⁄4 i1⁄2γμ; γν=2, ZT the renormalization constant and q the bare quark field: hNðp; sÞjZTqσμνqjNðp; sÞi 1⁄4 gqTu Nðp; sÞσμνuNðp; sÞ: ð1Þ They can be extracted from semi-inclusive deep-inelastic scattering data [1,2,3]. Quarks, the corresponding number of random sources (Nsrc) sampled, and the ratio NLP=NHP of low- to high-precision measurements made to estimate the disconnected quark loop contribution on each configuration
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