A high-statistics study of the nucleon EM form factors, axial charge and quark momentum fraction

Abstract

We present updated results for the nucleon axial charge and electromagnetic (EM) form factors, which include a significant increase in statistics for all ensembles (up to 4000 measurements), as well as the addition of ensembles with pion masses down to m π ∼ 195 MeV. We also present results for the average quark momentum fraction. The new data allows us to perform a thorough study of the systematic effects encountered in the lattice extraction. We concentrate on systematic effects due to excited-state contaminations for each of the quantities, which we check using several different time separations between the operators at the source and sink through a comparison of plateau fits and the summed operator insertion method (which provides a mechanism to suppress the excited-state contamination). We confirm our earlier finding [1] that a reliable extraction of the axial charge must be based on a method which eliminates excited-state contaminations. Similar conclusions apply to our EM form factor calculations [2]. The measurements are calculated using the CLS ensembles with non-perturbatively O(a) improved Wilson fermions in N f = 2 QCD.

Nucleon structure from Lattice QCD using a nearly physical pion mass

“…None of the other observables show this kind of reversal in behavior between 254 MeV and lower pion masses. Excluding our two lightest m π ensembles, our results are consistent with a recent calculation [9,42] that uses O(a) improved Wilson fermions and the summation method for 195 MeV m π 649 MeV. In that calculation, chiral extrapolation to the physical mass is statistically consistent with experiment and g A (∆t) typically increases 10% when ∆t increases by 0.5 fm, which is the behavior for our 254 MeV ensemble.…”

“…The presence of substantial excited-state contaminations in x u−d was first hinted at in Ref. [40] for m π = 493 MeV, later substantiated by an early report from the present study [15] and at m π = 373 MeV [41], and recently further confirmed at m π ≥ 195 MeV [42].…”

Nucleon matrix elements from lattice QCD with all-mode-averaging and a domain-decomposed solver: An exploratory study

“…In this paper, we study the efficiency of AMA when combined with the highly efficient locally deflated SAP-preconditioned GCR solver. In an extension of our previous studies [13,24,25], we apply AMA to the calculation of the axial charge of the nucleon from three-point functions with large source-sink separations of around 1.5 fm and above on large lattices satisfying m π L > 4 with N f = 2 flavours of dynamical quarks. In addition, we also determine the scalar and tensor charges of the nucleon on the same configurations.…”

“…We find that for the axial charge as extracted from ratios of correlation functions, large source-sink separations are required to reliably suppress excited-state contaminations, which become visible only at high enough statistics, and that values close to the experimental one are obtained from the largest source-sink separations studied. The summation method [9,13,25] is able to extract the asymptotic behaviour already from moderate source-sink separations, but still profits greatly from having precise measurements at large separations.…”

Chiral corrections to nucleon two- and three-point correlation functions

“…For pion masses at the physical point, however, nucleon correlation functions suffer from a well-known signal-to-noise problem [5], which is only exacerbated in the calculation of nucleon three-point functions. For many years, lattice computations of the axial charge have been subject to underestimation, with a variety of systematic sources investigated for this effect, such as: finite volume [6][7][8][9][10], excited-state contamination [11][12][13] and even thermal effects [14]. Not all collaborations, however, have obtained consistent results, for example, finite volume effects could not be substantiated [15], excited-state effects were not seen in the studies [16,17], and thermal effects could not be reproduced [18].…”