The moment $⟨x{⟩}_{u-d}$ of the nucleon from $N_f=2$ lattice QCD down to nearly physical quark masses

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 $N_f=2$ mass-degenerate quark flavours, employing the non-perturbatively improved clover action. The lattice matrix elements are converted to the $\overline{\mathrm{MS}}$ scheme via renormalization factors determined non-perturbatively in the RI${}^{\prime }$-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 with 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 $⟨x{⟩}_{u-d}$ extracted from experimental data is reduced but not resolved. Using lattice sizes in the range $L{m}_{\pi }\sim 3.4-6.7$, no significant finite volume effects were observed. Performing a controlled continuum limit that may remove the discrepancy will require simulations at lattice spacings $a<0.06$ fm.

arXiv commentv2, labelling and visibility of figures improved, very minor changes to text

References in corpus (27)

• Parton distributions with LHC data
• The Chroma Software System for Lattice QCD
• Ab-initio Determination of Light Hadron Masses
• The CT10 NNLO Global Analysis of QCD
• Uncertainties on alpha_S in global PDF analyses and implications for predicted hadronic cross sections
• The ABM parton distributions tuned to LHC data
• Lattice QCD with open boundary conditions and twisted-mass reweighting
• Light Hadron Masses from Lattice QCD
• The nucleon axial charge from lattice QCD with controlled errors
• Gauge-Invariant Smearing and Matrix Correlators using Wilson Fermions at beta=6.2
• Nucleon Charges and Electromagnetic Form Factors from 2+1+1-Flavor Lattice QCD
• Nucleon form factors and moments of generalized parton distributions using $N_f=2+1+1$ twisted mass fermions
• Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions
• Strangeness Contribution to the Proton Spin from Lattice QCD
• Renormalisation and off-shell improvement in lattice perturbation theory
• Disconnected quark loop contributions to nucleon observables in lattice QCD
• The strange and light quark contributions to the nucleon mass from Lattice QCD
• Nucleon Structure from Lattice QCD Using a Nearly Physical Pion Mass
• Perturbative and Nonperturbative Renormalization in Lattice QCD
• Moments of nucleon generalized parton distributions from lattice QCD
• Nucleon strangeness form factors from N_f=2+1 clover fermion lattice QCD
• Variational Approach to the Calculation of gA
• Precision Study of Excited State Effects in Nucleon Matrix Elements
• Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD
• <x>_{u-d} from lattice QCD at nearly physical quark masses
• A Stochastic Method for Computing Hadronic Matrix Elements
• Hadron Physics and Lattice QCD

Cited by in corpus (34)

• Parton distributions and lattice QCD calculations: a community white paper
• Large-Momentum Effective Theory
• The Structure of the Proton in the LHC Precision Era
• Novel quark smearing for hadrons with high momenta in lattice QCD
• The nucleon spin and momentum decomposition using lattice QCD simulations
• Nucleon isovector couplings from $N_f=2$ lattice QCD
• Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass
• Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
• Direct determinations of the nucleon and pion $\sigma$ terms at nearly physical quark masses
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• Improved Parton Distribution Functions at Physical Pion Mass
• FLAG Review 2024
• Nucleon isovector charges and twist-2 matrix elements with $N_f=2+1$ dynamical Wilson quarks
• Pion distribution amplitude from Euclidean correlation functions
• Quark propagator with two flavors of O(a)-improved Wilson fermions
• Lattice QCD Determination of the Bjorken-$x$ Dependence of Parton Distribution Functions at Next-to-next-to-leading Order
• Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors
• Nucleon generalized form factors from two-flavor lattice QCD
• Unpolarized proton PDF at NNLO from lattice QCD with physical quark masses
• Quark-gluon vertex from Nf=2 lattice QCD
• Stochastic method with low mode substitution for nucleon isovector matrix elements
• Charting the coming synergy between lattice QCD and high-energy phenomenology
• Moments of nucleon isovector structure functions in $2+1+1$-flavor QCD
• Chiral perturbation theory and nucleon-pion-state contaminations in lattice QCD
• Parton Distribution Function from the Hadronic Tensor on the Lattice
• Nucleon-pion-state contribution in lattice calculations of moments of parton distribution functions
• Double parton distributions in the pion from lattice QCD
• Hadron Structure from Lattice QCD
• Nucleon Momentum Fraction, Helicity and Transversity from 2+1-flavor Lattice QCD
• A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac operator in lattice QCD
• Parton distribution functions from Lattice QCD
• Heavy Quark Entropy shift: From the Hadron Resonance Gas to Power Corrections
• Measurements of Non-Singlet Moments of the Nucleon Structure Functions and Comparison to Predictions from Lattice QCD for $Q^2=4$ $\mathrm{Ge}{\mathrm{V}}^2$
• Finite Volume corrections to $<x{>}_{u\pm d}$