Moments of nucleon isovector structure functions in 2+1+1 -flavor QCD

Abstract

We present results on the isovector momentum fraction, hxi u−d , helicity moment, hxi Δu−Δd , and the transversity moment, hxi δu−δd , of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC Collaboration using 2 þ 1 þ 1-flavors of dynamical highly improved staggered quarks. The correlation functions are calculated using the Wilson-Clover action, and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI 0-MOM scheme. The data have been collected at lattice spacings a ≈ 0.15, 0.12, 0.09, and 0.06 fm and M π ≈ 310, 220, and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in the MS scheme at 2 GeV, are hxi u−d ¼ 0.173ð14Þð07Þ, hxi Δu−Δd ¼ 0.213ð15Þð22Þ, and hxi δu−δd ¼ 0.208ð19Þð24Þ, where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.

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

“…(4.1), couples to the nucleon, all its excitations and multiparticle states with the same quantum numbers. Previous lattice calculations have shown that these ESC can be large [16,[33][34][35]. The strategy to remove these artifacts in this work is the same as described in ref.…”

“…The strategy to remove these artifacts in this work is the same as described in ref. [16]: 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 (eqs. (5.1) and (5.2)) keeping as many excited states as possible without overparameterizing the fits.…”

“…We update the comparison of lattice QCD calculations on ensembles with dynamical fermions presented in ref. [16] in the top half of table 5 and in figure 4. Our new results, eq.…”

“…in a clover-on-clover unitary formulation of lattice QCD, whereas the clover-on-HISQ formulation was used in ref. [16]. The clover action includes one iteration of stout smearing with weight ρ = 0.125 for the staples [17].…”

“…The parameters used to construct the Gaussian smeared sources [14,16,24,25] are given in table 2. To construct the smeared source, the gauge links were first smoothened using twenty hits of the stout algorithm with ρ = 0.08 and only the spatial staples were included [17].…”