Parton distribution functions beyond leading twist from lattice QCD: The $h_L(x)$ case

Abstract

We report the first-ever calculation of the isovector flavor combination of the chiral-odd twist-3 parton distribution $h_L(x)$ for the proton from lattice QCD. We employ gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3 fm and lattice spacing of 0.093 fm. The values of the quark masses lead to a pion mass of $260$ MeV. We use a source-sink time separation of 1.12 fm to control contamination from excited states. Our calculation is based on the quasi-distribution approach, with three values for the proton momentum: 0.83 GeV, 1.25 GeV, and 1.67 GeV. The lattice data are renormalized non-perturbatively using the RI${}^{\prime }$ scheme, and the final result for $h_L(x)$ is presented in the $\overline{\mathrm{MS}}$ scheme at the scale of 2 GeV. Furthermore, we compute in the same setup the transversity distribution, $h_1(x)$, which allows us, in particular, to compare $h_L(x)$ to its Wandzura-Wilczek approximation. We also combine results for the isovector and isoscalar flavor combinations to disentangle the individual quark contributions for $h_1(x)$ and $h_L(x)$, and address the Wandzura-Wilczek approximation in that case as well.

arXiv comment18 pages, 13 figures

References in corpus (91)

• Parton Physics on Euclidean Lattice
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Analytic Smearing of SU(3) Link Variables in Lattice QCD
• Universality of T-odd effects in single spin and azimuthal asymmetries
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Transverse momentum dependence in gluon distribution and fragmentation functions
• Large-Momentum Effective Theory
• Modelling quark distribution and fragmentation functions
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Nucleon Helicity and Transversity Parton Distributions from Lattice QCD
• Flavor Structure of the Nucleon Sea from Lattice QCD
• Extracting Parton Distribution Functions from Lattice QCD Calculations
• Novel quark smearing for hadrons with high momenta in lattice QCD
• Nucleon structure functions from lattice operator product expansion
• Exclusive processes in position space and the pion distribution amplitude
• A Lattice Calculation of Parton Distributions
• A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
• Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions
• One-Loop Matching for Parton Distributions: Non-Singlet Case
• A complete non-perturbative renormalization prescription for quasi-PDFs
• Parton distributions and lattice QCD calculations: toward 3D structure
• Perturbative Renormalization of quasi-PDFs
• On the Renormalizability of Quasi Parton Distribution Functions
• Renormalization in Large Momentum Effective Theory of Parton Physics
• Reconstruction of light-cone parton distribution functions from lattice QCD simulations at the physical point
• Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD
• Pion Valence Structure from Ioffe Time Pseudo-Distributions
• Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass
• Transversity parton distribution functions from lattice QCD
• Updated Lattice Results for Parton Distributions
• First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function
• Valence parton distribution function of pion from fine lattice
• Origin of single transverse-spin asymmetries in high-energy collisions
• Unpolarized and helicity generalized parton distributions of the proton within lattice QCD
• Non-perturbative renormalization of quark bilinear operators with Nf=2 (tmQCD) Wilson fermions and the tree-level improved gauge action
• Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
• Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
• Moments of Ioffe time parton distribution functions from non-local matrix elements
• Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
• Accessing gluon parton distributions in large momentum effective theory
• Parton Distribution Functions from Ioffe time pseudo-distributions
• One-loop evolution of parton pseudo-distribution functions on the lattice
• Operator Constraints for Twist-3 Functions and Lorentz Invariance Properties of Twist-3 Observables
• Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching
• Gluon quasidistribution function at one loop
• What can break the Wandzura--Wilczek relation?
• The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD
• Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions
• Self-Renormalization of Quasi-Light-Front Correlators on the Lattice
• Renormalization functions for Nf=2 and Nf=4 Twisted Mass fermions
• Quark masses using twisted mass fermion gauge ensembles
• Multiplicative renormalizability of quasi-parton operators
• Generalized Parton Distributions and Pseudo-Distributions
• Gluon Pseudo-Distributions at Short Distances: Forward Case
• Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations
• Confronting lattice parton distributions with global QCD analysis
• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• The chirally-odd twist-3 distribution e(x)
• Parton distribution functions of ${\Delta }^{+}$ on the lattice
• The role of the Euclidean signature in lattice calculations of quasi-distributions and other non-local matrix elements
• Parton distributions from lattice data: the nonsinglet case
• Lattice continuum-limit study of nucleon quasi-PDFs
• New insights on proton structure from lattice QCD: the twist-3 parton distribution function $g_T(x)$
• Next-to-next-to-leading order corrections to quark Quasi parton distribution functions
• Generalized quasi parton distributions in a diquark spectator model
• Neural-network analysis of Parton Distribution Functions from Ioffe-time pseudodistributions
• Gluon momentum fraction of the nucleon from lattice QCD
• Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike
• Flavor decomposition of the nucleon unpolarized, helicity and transversity parton distribution functions from lattice QCD simulations
• Violation of Sum Rules for Twist-3 Parton Distributions in QCD
• The role of zero-mode contributions in the matching for the twist-3 PDFs $e(x)$ and $h_L(x)$
• Flavor decomposition for the proton helicity parton distribution functions
• One-loop matching for the twist-3 parton distribution $g_T(x)$
• Measurements of $d_2^n$ and $A_1^n$: Probing the neutron spin structure
• The twist-three distribution $e^q(x,k_{\perp })$ in a light-front model
• Fundamental Properties of the Proton in Light-Front Zero Modes
• Exploring twist-2 GPDs through quasi-distributions in a diquark spectator model
• Parton physics from a heavy-quark operator product expansion: Formalism and Wilson coefficients
• On the twist-3 contribution to h_L in the instanton vacuum
• The nonperturbative origin of delta-function singularity in the chirally-odd twist-3 distribution function e(x)
• Twist-3 GPDs in Deeply-Virtual Compton Scattering
• Structure of the nucleon at leading and subleading twist in the covariant parton model
• Revealing Color Forces with Transverse Polarized Electron Scattering
• On the Possible Violation of Sum Rules for Higher-Twist Parton Distributions
• Singularities in Twist-3 Quark Distributions
• QCD factorization for twist-three axial-vector parton quasidistributions
• Connections between collinear and transverse-momentum-dependent polarized observables within the Collins-Soper-Sterman formalism
• Drell-Yan double-spin asymmetry A_{LT} in polarized p\bar{p} collisions: Wandzura-Wilczek contribution
• Renormalon Effects in Quasi Parton Distributions
• Twist-3 effect from the longitudinally polarized proton for $A_{LT}$ in hadron production from $pp$ collisions
• Chiral Perturbation for Large Momentum Effective Field Theory

Cited by in corpus (17)

• 50 Years of Quantum Chromodynamics
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks
• Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point
• Transversity GPDs of the proton from lattice QCD
• Moments of proton GPDs from the OPE of nonlocal quark bilinears up to NNLO
• Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics
• Continuum limit of parton distribution functions from the pseudo-distribution approach on the lattice
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Generalized parton distributions from the pseudo-distribution approach on the lattice
• Transverse structure of the proton beyond leading twist: A light-front Hamiltonian approach
• Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD
• Improved renormalization scheme for nonlocal operators
• Higher Twists
• Nucleon Structure from Basis Light-Front Quantization : Status and Prospects
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Parton distribution functions and QCD coupling constant from LHC and non-LHC data
• Quark-model relations among TMDs in the parton model