Flavor Structure of the Nucleon Sea from Lattice QCD

Abstract

We present the first direct lattice calculation of the isovector sea-quark parton distributions using the formalism developed recently by one of the authors. We use $N_f=2+1+1$ HISQ lattice gauge ensembles (generated by MILC Collaboration) and clover valence fermions with pion mass 310 MeV. We are able to obtain the qualitative features of the nucleon sea flavor structure even at this large pion mass: We observe violation of the Gottfried sum rule, indicating $\overline{d}(x) > \overline{u}(x)$; the helicity distribution obeys $Δ\overline{u}(x) > Δ\overline{d}(x)$, which is consistent with the STAR data at large and small leptonic pseudorapidity.

Figures (3)

• Figure 1: The isovector quark quasi-distribution $\tilde{u}(x)-\tilde{d}(x)$ as defined in Eq. \ref{['eq:quark-dist']} computed on a lattice with the nucleon momentum $P_z$ (in units of $2\pi /L$) $=$ 1 (red), 2 (green), 3 (cyan).
• Figure 2: The physical quark distribution $u(x)-d(x)$ extracted from Fig. \ref{['fig:quasi']} after making $M_N^n/P_z^n$ corrections and one-loop corrections. The red, green and cyan bands correspond to $P_z \in \{1,2,3\}\frac{2\pi}{L}$. The two higher-momentum distributions are now almost identical.
• Figure 3: The unpolarized isovector quark distribution $u(x)-d(x)$ computed on the lattice after extrapolation in $P_{z}$ is shown as the purple band, compared with the global analyses by MSTW Martin:2009iq (brown dotted line), and CTEQ-JLab (CJ12, green dashed line) Owens:2012bv with medium nuclear correction near $(1.3\text{ GeV})^{2}$. The negative $x$ region is the sea quark distribution with $\overline{q}(x)=-q(-x)$. The lattice uncertainty band in the plot reflects the 68% C.L. The global fit uncertainty is not shown in the figure.