New insights on proton structure from lattice QCD: the twist-3 parton distribution function $g_T(x)$

Abstract

In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function $g_T(x)$ for the proton from lattice QCD. We use an ensemble of 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, lattice spacing of 0.093~fm, and reproduces a pion mass of $260$ MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV, and 1.67 GeV. We use a source-sink separation of 1.12~fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the matching equation within Large Momentum Effective Theory, which is applied to the lattice data in order to obtain $g_T$. The final distribution is presented in the $\overline{\mathrm{MS}}$ scheme at a scale of 2 GeV. We also calculate the helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for $g_T$. We find that the approximation works well for a broad range of $x$. This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD and can provide essential insights into the structure of hadrons.

arXiv comment10 pages, 6 figures, version accepted for publication

References in corpus (60)

• 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
• Chirally improving Wilson fermions - I. O(a) improvement
• A first unbiased global determination of polarized PDFs and their uncertainties
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• First simultaneous extraction of spin-dependent parton distributions and fragmentation functions from a global QCD analysis
• 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
• 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
• Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass
• Pion Valence Structure from Ioffe Time Pseudo-Distributions
• 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
• Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
• Simulating twisted mass fermions at physical light, strange and charm quark masses
• 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
• Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass
• Gluon quasidistribution function at one loop
• Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching
• What can break the Wandzura--Wilczek relation?
• Complete Matching for Quasi-distribution Functions in Large Momentum Effective Theory
• Renormalization functions for Nf=2 and Nf=4 Twisted Mass fermions
• Multiplicative renormalizability of quasi-parton operators
• Generalized Parton Distributions and Pseudo-Distributions
• Gluon Pseudo-Distributions at Short Distances: Forward Case
• 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
• Gluon momentum fraction of the nucleon from lattice QCD
• Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike
• 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
• Fundamental Properties of the Proton in Light-Front Zero Modes
• Exploring twist-2 GPDs through quasi-distributions in a diquark spectator model
• Revealing Color Forces with Transverse Polarized Electron Scattering
• $K\to \pi$ matrix elements of the chromomagnetic operator on the lattice

Cited by in corpus (34)

• Large-Momentum Effective Theory
• Parton distributions and lattice QCD calculations: toward 3D structure
• Unpolarized and helicity generalized parton distributions of the proton within lattice QCD
• A Hybrid Renormalization Scheme for Quasi Light-Front Correlations in Large-Momentum Effective Theory
• Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD
• Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point
• Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• Transversity GPDs of the proton from lattice QCD
• Lattice continuum-limit study of nucleon quasi-PDFs
• Flavor decomposition for the proton helicity parton distribution functions
• First Glimpse into the Kaon Gluon Parton Distribution Using Lattice QCD
• Parton distribution functions beyond leading twist from lattice QCD: The $h_L(x)$ case
• The Mellin moments $⟨x⟩$ and $⟨x^2⟩$ for the pion and kaon from lattice QCD
• Pion Valence-Quark Generalized Parton Distribution at Physical Pion Mass
• QCD factorization for twist-three axial-vector parton quasidistributions
• Gluon Parton Distribution of the Nucleon from 2+1+1-Flavor Lattice QCD in the Physical-Continuum Limit
• One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions
• Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon
• Generalized parton distributions from the pseudo-distribution approach on the lattice
• QCD factorization for chiral-odd parton quasi- and pseudo-distributions
• Transverse structure of the proton beyond leading twist: A light-front Hamiltonian approach
• Chiral Perturbation for Large Momentum Effective Field Theory
• Burkhardt-Cottingham-type sum rules for light-cone and quasi-PDFs
• Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD
• On the odderon mechanism for transverse single spin asymmetry in the Wandzura-Wilczek approximation
• Nucleon Structure from Basis Light-Front Quantization : Status and Prospects
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
• Hadron spin structure from lattice QCD
• Light-cone PDFs and GPDs from Lattice QCD
• One-loop Matching Factors for Singlet Quasi-Parton Distribution Functions in the Hybrid-Ratio Scheme
• Towards High-Precision Parton Distributions From Lattice QCD via Distillation