Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD

Tanmoy Bhattacharya; Vincenzo Cirigliano; Saul Cohen; Rajan Gupta; Huey-Wen Lin; Boram Yoon

doi:10.1103/PhysRevD.94.054508

paper

Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD

arXiv:1606.07049 · doi:10.1103/PhysRevD.94.054508

Abstract

We present results for the isovector axial, scalar and tensor charges $g_{A}^{u - d}$ , $g_{S}^{u - d}$ and $g_{T}^{u - d}$ of the nucleon needed to probe the Standard Model and novel physics. The axial charge is a fundamental parameter describing the weak interactions of nucleons. The scalar and tensor charges probe novel interactions at the TeV scale in neutron and nuclear $β$ -decays, and the flavor-diagonal tensor charges $g_{T}^{u}$ , $g_{T}^{d}$ and $g_{T}^{s}$ are needed to quantify the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The 9 ensembles, generated by the MILC Collaboration using the HISQ action with 2+1+1 dynamical flavors, span three lattice spacings $a \approx 0.06, 0.09$ and 0.12 fm and light-quark masses corresponding to the pion masses $M_{π} \approx 135, 225$ and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses for the connected contributions. Our final estimates, in the $MS$ scheme at 2 GeV, of the isovector charges are $g_{A}^{u - d} = 1.195 (33) (20)$ , $g_{S}^{u - d} = 0.97 (12) (6)$ and $g_{T}^{u - d} = 0.987 (51) (20)$ . The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for $g_{S}^{u - d}$ with the difference of light quarks masses $(m_{d} - m_{u})^{QCD} = 2.67 (35)$ MeV given by FLAG, we obtain $(M_{N} - M_{P})^{QCD} = 2.59 (49)$ MeV. Estimates of the connected part of the flavor-diagonal tensor charges of the proton are $g_{T}^{u} = 0.792 (42)$ and $g_{T}^{d} = - 0.194 (14)$ . Combining our new estimates with precision low-energy experiments, we update constraints on novel scalar and tensor interactions, $ε_{S, T}$ , at the TeV scale.

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Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD

Abstract

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