Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

Abstract

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, 〈x〉u − d, helicity moment, 〈x〉Δu − Δd, and the transversity moment, 〈x〉δu − δd, of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass Mπ. The final results are obtained using a simultaneous fit in the lattice spacing a, pion mass Mπ and the finite volume parameter MπL keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme at 2 GeV, are 〈x〉u − d = 0.155(17)(20), 〈x〉Δu − Δd = 0.183(14)(20) and 〈x〉δu − δd = 0.220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

Octet baryon charges with Nf=2+1 non-perturbatively improved Wilson fermions

“…The filled ETM (2022) [34] point is obtained from a continuum limit extrapolation of results determined on three physical point ensembles with large spatial volumes. Right: Second isovector helicity moment ⟨𝑥⟩ 𝑁 Δ𝑢−Δ𝑑 with 𝑁 𝑓 = 2 + 1 [21,37,[40][41][42] and 𝑁 𝑓 = 2 + 1 + 1 [43,45,46] dynamical fermions. Recent phenomenological estimates are also displayed for comparison [11,13,54].…”

All about the neutron from lattice QCD

“…Changing the operator to a scalar, Ŝ = du or tensor, T = dσ µν u, gives us nucleon's scalar and tensor charges that are also probed in precision measurements of neutron decay distributions [9]. One link operators give us the momentum fraction, helicity and transversity moments [10]. And the list continues.…”

Nucleon isovector momentum fraction, helicity and transversity moment using Lattice QCD

“…(ii) The Clover-on-Clover calculation, published in [2] (NME 20), used seven Clover ensembles generated by the JLab/W&M/LANL/MIT collaboration [8]. Here (NME 21) we include two new ensembles, one at physical 𝑀 𝜋 and the other at smaller lattice spacing 𝑎 = 0.056 fm which gives us better control over chiral and continuum extrapolations, respectively.…”

“…The strategy to remove these artifacts are described in Refs. [1,2]: reduce ESC by using smeared sources in the generation of quark propagators and then fit the data at multiple source-sink separations 𝜏 using the spectral decomposition of the correlation functions keeping as many excited states as possible without over-parameterizing the fits. The spectral decomposition of the zero-momentum two-point function, 𝐶 2pt , truncated at four states, is given by…”