We compute the axial, scalar, tensor and pseudoscalar isovector couplings of the nucleon as well as the induced tensor and pseudoscalar charges in lattice simulations with N f = 2 massdegenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions. The simulations are carried out down to a pion mass of 150 MeV and linear spatial lattice extents of up to 4.6 fm at three different lattice spacings ranging from approximately 0.08 fm to 0.06 fm. Possible excited state contamination is carefully investigated and finite volume effects are studied. The couplings, determined at these lattice spacings, are extrapolated to the physical pion mass. In this limit we find agreement with experimental results, where these exist, with the exception of the magnetic moment. A proper continuum limit could not be performed, due to our limited range of lattice constants, but no significant lattice spacing dependence is detected. Upper limits on discretization effects are estimated and these dominate the error budget.
We analyze N f = 2 nucleon mass data with respect to their dependence on the pion mass down to m π = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion-nucleon σ-term. Our lattice data below m π = 435 MeV is well described by O(p 4 ) BChPT and we find σ = 37(8)(6) MeV for the σ-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r 0 = 0.501(10)(11) fm.
Using an SU(3) flavour symmetry breaking expansion in the quark mass, we determine the QCD component of the nucleon, Sigma and Xi mass splittings of the baryon octet due to up-down (and strange) quark mass differences in terms of the kaon mass splitting. Provided the average quark mass is kept constant, the expansion coefficients in our procedure can be determined from computationally cheaper simulations with mass degenerate sea quarks and partially quenched valence quarks. Both the linear and quadratic terms in the SU(3) flavour symmetry breaking expansion are considered; it is found that the quadratic terms only change the result by a few percent, indicating that the expansion is highly convergent.Comment: 31 pages, 8 figures, published versio
We determine the second Mellin moment of the isovector quark parton distribution function x u−d from lattice QCD with N f = 2 sea quark flavours, employing the non-perturbatively improved Wilson-Sheikholeslami-Wohlert action at a pseudoscalar mass mπ = 157(6) MeV. The result is converted non-perturbatively to the RI'-MOM scheme and then perturbatively to the MS scheme at a scale µ = 2 GeV. As the quark mass is reduced we find the lattice prediction to approach the value extracted from experiments. PACS numbers: 12.38.Gc,14.20.Dh Almost all visible matter is composed of protons and neutrons. Analyses of the scattering of cosmic ray particles off nuclei or of results from fixed target and colliding hadron beam experiments require a quantitative understanding of the partonic structure of nucleons. The theoretical framework for this is known [1, 2] since the inception of quantum chromodynamics (QCD); see also [3,4].Of particular importance for the experimental programmes at the Large Hadron Collider are unpolarized parton distribution functions (PDFs). These, in the lightcone frame, parameterize the likelihood of a parton to carry the Bjorken momentum fraction x at a renormalization scale µ. While these PDFs have been mapped out very well from fits to experimental data, ideally one would wish to evaluate them directly from the underlying fundamental theory, QCD.The present method of choice is lattice QCD, where in principle all approximations can be removed and systematic uncertainties controlled by taking the limits of infinite volume, of vanishing lattice spacing (a → 0) and of physical quark masses. However, in this Monte Carlo simulation approach to QCD, the statistical errors and the reliability of the extrapolation to the physical point are limited by the power of available computers and the efficiency of numerical algorithms. Moreover, only Mellin moments of the PDFs can be accessed. Thus, present-day lattice simulation cannot compete in terms of precision with determinations of isovector unpolarized PDFs from fits to experimental photon-nucleon scattering data that have been collected over decades of dedicated effort. For a summary of the present status of PDF parametrizations, see [5].The possibility to predict averages over the momentum fraction, however, is complementary to experimental measurements that can only cover a limited range of x values. In particular, the strangeness and gluonic PDFs are determined rather indirectly from experiment, with large uncertainties [6]. Consequently, lattice QCD is already on the verge of becoming essential to constrain these and other less well known quantities, e.g., the pion nucleon σ term [7][8][9][10][11], the strangeness fraction of the mass of the proton f Ts [8][9][10][11][12][13], the strange quark contribution to the spin of the proton ∆s + ∆s [13,14] or individual (valence and sea) quark contributions to the proton's momentum x u , x d and x s [15]. Naturally, for lattice predictions of such quantities to be trusted, lattice QCD needs to demonstrate its ab...
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.