The moment⟨x⟩u−dof the nucleon fromNf

Abstract

We present an update of our analysis [1] which includes additional ensembles at different quark masses, lattice spacings and volumes, all with high statistics. We use N f ¼ 2 mass-degenerate quark flavors, employing the nonperturbatively improved clover action. The lattice matrix elements are converted to the MS scheme via renormalization factors determined nonperturbatively in the RI 0 -MOM scheme. We have systematically investigated excited state contributions, in particular, at the smallest, near physical, pion mass. While our results (with much increased precision) are consistent with Ref.[1], comparing to previous determinations we find that excited state contributions can be significant if the quark smearing is not suitably optimized, in agreement with other recent studies. The difference with respect to the value for hxi u−d extracted from experimental data is reduced but not resolved. Using lattice sizes in the range Lm π ∼ 3.4-6.7, no significant finite volume effects have been observed. Performing a controlled continuum limit that may remove the discrepancy will require simulations at lattice spacings a < 0.06 fm.

Nucleon Spin and Momentum Decomposition Using Lattice QCD Simulations

“…Determinations of hxi u−d within lattice QCD using simulations with larger than physical pion masses have yielded larger values, an effect that is partly understood to be due to the contribution of excited states to the ground state matrix element [48]. We note that our value is in agreement with that determined by the RQCD Collaboration using N f ¼ 2 clover fermions at pion mass of 151 MeV [49], and that lattice QCD results for hxi u−d and J u−d for ensembles with larger than physical pion masses including ours are in overall agreement [40]. Results within lattice QCD for the individual quark hxi q and J q contributions are scarce.…”

Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass

“…Also shown are results from RBC-UKQCD using N f ¼ 2 þ 1 DWF (magenta right pointing triangle) [74], from LHPC using DWF on N f ¼ 2 þ 1 staggered sea (blue crosses) [67], and QCDSF/UKQCD using N f ¼ 2 clover fermions (filled magenta diamond) [75]. For hxi u−d , we also show results from LHPC using an N f ¼ 2 þ 1 clover with 2-HEX smearing (filled black triangles) [66] and an N f ¼ 2 clover (open black circle) [72]. All values are extracted using the plateau method and t s ∼ ð1 − 1.2Þ fm, except our result at the physical point for which t s ∼ 1.3 fm was used.…”

“…These are from Ref. [72], which is an update of Ref. [73] for m π ∼ 160 MeV and from LHPC at m π ∼ 150 MeV using N f ¼ 2 þ 1 clover fermions with 2-HEX smeared gauge action [66].…”

Erratum: Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass [Phys. Rev. D92, 114513 (2015)]

“…Also shown are results from RBC-UKQCD using N f ¼ 2 þ 1 DWF (magenta right pointing triangle) [1], from LHPC using DWF on N f ¼2þ1 staggered sea (blue crosses) [2] and QCDSF/UKQCD using N f ¼2 clover fermions (filled magenta diamond) [3]. For hxi u−d we also show results from LHPC using N f ¼2þ1 clover with 2-HEX smearing (filled black triangles) [4] and N f ¼ 2 clover (open black circle) [5]. All values are extracted using the plateau method and t s ∼ð1-1.2Þfm, except our result at the physical point for which t s ∼1.3 fm was used.…”