Flavor diagonal tensor charges of the nucleon from ( 2 + 1 + 1 )-flavor lattice QCD

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 11 ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quark 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 Mπ=135 MeV. Results for the proton in the MS¯ scheme at 2 GeV are gTu=0.784(28)(10), gTd=−0.204(11)(10) and gTs=−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.