[Paper Review] Selected results on hadron structure using state-of-the-art lattice QCD simulations

Constantia Alexandrou|arXiv (Cornell University)|Dec 12, 2015

Quantum Chromodynamics and Particle Interactions25 references3 citations

TL;DR

This paper presents state-of-the-art lattice QCD simulations at or near physical quark masses to compute key hadron structure observables, including nucleon charges, spin decomposition, and parton distribution functions. It reports the first inclusion of disconnected quark loop contributions at the physical point, significantly improving agreement with experimental data for the nucleon spin and axial charges.

ABSTRACT

We review progress on hadron structure using lattice QCD simulations at or near to physical values of the QCD parameters. In particular, we discuss recent results on hadron masses, the nucleon charges, spin, gluon and quark unpolarized moments, the axial charge of hyperons, and the pion unpolarized moment.

Motivation & Objective

• To compute benchmark hadron structure observables using lattice QCD at or near physical values of the QCD parameters.
• To reduce systematic uncertainties by eliminating chiral extrapolations through simulations at physical pion mass.
• To include disconnected quark loop contributions in matrix elements, which were previously an uncontrolled approximation.
• To explore new techniques for computing parton distribution functions via the quasi-PDF approach.
• To provide precise results for nucleon spin decomposition and axial charges, enabling comparison with experimental data.

Proposed method

• Use of large-volume lattice QCD ensembles with physical pion mass, small lattice spacing (<0.1 fm), and multiple volumes to control finite-volume and cut-off effects.
• Employment of various fermion discretizations including twisted mass, clover-improved, domain wall, and staggered fermions to ensure consistency across methods.
• Application of smearing techniques to interpolating fields to enhance overlap with the ground state and improve signal-to-noise ratios.
• Computation of three-point functions for matrix elements, including both connected and disconnected quark contractions.
• Use of the quasi-PDF method to compute parton distribution functions via matrix elements of quark bilinears with a Wilson line, followed by perturbative matching to the physical PDF.
• Implementation of the $ar{\rm MS}$ renormalization scheme at $\mu = 2$ GeV to match lattice results to physical observables.

Experimental results

Research questions

• RQ1 What are the values of the nucleon spin and its decomposition into quark and gluon contributions at the physical point?
• RQ2 How do disconnected quark contractions affect the axial charge and spin structure of the nucleon?
• RQ3 Can the quasi-PDF approach in lattice QCD accurately reproduce the physical parton distribution functions for the nucleon?
• RQ4 What is the impact of including disconnected quark loops on the precision of hadron matrix elements at physical quark masses?
• RQ5 To what extent do finite-volume and cut-off effects affect the extraction of hadron structure observables in current simulations?

Key findings

• The nucleon mass shows negligible finite-volume and cut-off effects for $a \lesssim 0.1$ fm and $m_\pi L \gtrsim 3$.
• The gluon unpolarized moment in the nucleon is found to be $\langle x \rangle_g = 0.282(39)$ in $\overline{\rm MS}$ at $\mu = 2$ GeV for the physical ensemble.
• The nucleon spin decomposition yields $J^{u+d} = 0.273(22)$, with $\frac{1}{2}\Delta\Sigma^{u+d} = 0.229(20)$, and $\frac{1}{2}\Delta\Sigma^{u+d+s} = 0.211(21)$, including disconnected quark loops for the first time at the physical point.
• The axial charge of the nucleon is computed with high precision, showing improved agreement with experiment after including disconnected contributions.
• First results for the isovector parton distribution function $q^{u-d}(x)$ are obtained using the quasi-PDF method on $N_f=2+1+1$ twisted mass fermions with $m_\pi = 373$ MeV.
• The renormalization procedure for the quasi-PDF is implemented with perturbative matching, and divergences are handled via principal value prescriptions, with remaining UV divergences translated into a scale $\mu$.