Quark Contributions to Nucleon Momentum and Spin from Domain Wall fermion calculations

TL;DR

The paper investigates how light quarks share nucleon momentum and spin using fully dynamical domain-wall fermion lattice QCD with $N_f=2+1$. By computing nucleon matrix elements of the quark energy-momentum tensor, it examines the $n=2$ generalized form factors $A_{20}$, $B_{20}$, and $C_{20}$ to extract $ angle x angle$ and the Ji sum rule $J_q= frac12[A_{20}(0)+B_{20}(0)]$, across isovector and isoscalar channels with pion masses $m_\pi$ in the $300$--$400$ MeV range and $a=0.084$ fm. The results indicate opposite spin and orbital angular momenta for $u$ and $d$ quarks (with $|J^d| obreak\ll obreak|J^u|$) and a relatively small variation of the $n=2$ GFFs with $m_\pi$, though the isovector $ angle x angle^{u-d}$ overshoots phenomenology on chiral extrapolation while the isoscalar $ angle x angle^{u+d}$ agrees within uncertainties and without disconnected contractions. Renormalization is performed nonperturbatively in RI$^ extprime$-MOM, with results converted to $ar{ ext{MS}}$ at 2 GeV and cross-validated against perturbative running, lending robustness to the extracted moments and spin decompositions. Overall, the work corroborates prior mixed-action findings and highlights the importance of lighter pions and excited-state control for precise nucleon structure predictions from lattice QCD.

Abstract

We report contributions to the nucleon spin and momentum from light quarks calculated using dynamical domain wall fermions with pion masses down to 300 MeV and fine lattice spacing a=0.084 fm. Albeit without disconnected diagrams, we observe that spin and orbital angular momenta of both u and d quarks are opposite, almost canceling in the case of the d quark, which agrees with previous calculations using a mixed quark action. We also present the full momentum dependence of n=2 generalized form factors showing little variation with the pion mass.

Figures (5)

• Figure 1: html:<A name="ref-fig:renorm-rank2">html:</A> LAB: fig:renorm-rank2 RI/MOM renormalization constant divided by 3-loop perturbative running (scale-independent). The extracted values must be multiplied with factors $Z_A/Z_{\mathcal{A}}$ and $(Z^{\overline{\text{MS}}}_{\mathcal{O}} / Z^{\text{RI}^\prime}_{\mathcal{O}})_{2\text{ GeV}}$ to get the final renormalization constants.
• Figure 2: html:<A name="ref-figs:ABC-vs-Q2">html:</A> LAB: figs:ABC-vs-Q2 (Color online) Isovector (left) and isoscalar (right) $n=2$ Generalized form factors (GFF) of the proton from domain wall calculations.
• Figure 3: html:<A name="ref-fig:chiral-extrap-isovec">html:</A> LAB: fig:chiral-extrap-isovec (Color online) Chiral extrapolations of isovector GFFs $A_{20}$, $B_{20}$, $C_{20}$ (left) and their derivatives $d/dQ^2$ (right) at $Q^2=0$. The ChPT predictions are taken from Ref. Dorati:2007bk.
• Figure 4: html:<A name="ref-fig:momfrac">html:</A> LAB: fig:momfrac (Color online) Isovector (left) and isoscalar (right) quark momentum fraction in the proton compared to calculations in Ref. Pleiter:2011gwAoki:2010xg.
• Figure 5: html:<A name="ref-fig:quark-spin-oam">html:</A> LAB: fig:quark-spin-oam (Color online) Left: $u$ and $d$ quark contributions to the nucleon spin from the domain wall and hybrid action calculations. Right: $u$ and $d$ quark spin and orbital momentum from the domain wall calculations.