Abstract
We report on lattice QCD calculations of the nucleon isovector axial, scalar, and tensor charges. Our calculations are performed on two 2+1-flavor ensembles generated using a 2-HEX-smeared Wilson-clover action at the physical pion mass and lattice spacings $a\approx$ 0.116 and 0.093 fm. We use a wide range of source-sink separations - eight values ranging from roughly 0.4 to 1.4 fm on the coarse ensemble and three values from 0.9 to 1.5 fm on the fine ensemble - which allows us to perform an extensive study of excited-state effects using different analysis and fit strategies. To determine the renormalization factors, we use the nonperturbative Rome-Southampton approach and compare RI'-MOM and RI-SMOM intermediate schemes to estimate the systematic uncertainties. Our final results are computed in the MS-bar scheme at scale 2 GeV. The tensor and axial charges have uncertainties of roughly 4%, $g_T=0.972(41)$ and $g_A=1.265(49)$. The resulting scalar charge, $g_S=0.927(303)$, has a much larger uncertainty due to a stronger dependence on the choice of intermediate renormalization scheme and on the lattice spacing.
Highlights
Nucleon charges quantify the coupling of nucleons to quark-level interactions and play an important role in the analysis of the Standard Model and beyond the Standard Model (BSM) physics
We present a lattice QCD calculation of the isovector axial, scalar, and tensor charges of the nucleon using two ensembles at the physical pion mass with different lattice spacings
In Ref. [31] a model was used to study corrections to the LO chiral perturbation theory (ChPT) result for the axial charge; it was found that high-momentum Nπ states with energies larger than about 1.5MN can be the cause for the underestimating of the axial charge observed in lattice QCD calculations
Summary
Nucleon charges quantify the coupling of nucleons to quark-level interactions and play an important role in the analysis of the Standard Model and beyond the Standard Model (BSM) physics. The isovector charges, gX, are associated with the β-decay of the neutron into a proton and are defined via the transition matrix elements, hpðP; sÞju ΓXdjnðP; sÞi 1⁄4 gXupðP; sÞΓXunðP; sÞ; ð1Þ where the Dirac matrix ΓX is 1, γμγ and σμν for the scalar (S), the axial (A) and the tensor (T) operators, respectively They are straightforward to calculate in lattice QCD since. The nucleon scalar and tensor charges are difficult to directly measure in experiments Computations of those observables within lattice QCD will provide useful input for ongoing experimental searches for BSM physics. We present a lattice QCD calculation of the isovector axial, scalar, and tensor charges of the nucleon using two ensembles at the physical pion mass with different lattice spacings. In Appendix B, we list the bare charges determined on the two ensembles studied in this work, along with data used in previous publications [2,3]
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