Flavor structure of the nucleon sea from lattice QCD

We present the first direct lattice calculation of the isovector sea-quark distributions in the nucleon within the framework of the large-momentum effective field theory proposed recently. We use $N_f=2+1+1$ highly improved staggered quarks lattice gauge ensembles (generated by the MILC Collaboration) and clover valence fermions with pion mass 310 MeV. We establish the convergence of the result as the nucleon momentum increases within the uncertainty of the calculation. Although the lattice systematics are not yet fully under control, we obtain some qualitative features of the flavor structure of the nucleon sea: $\overline{d}(x)>\overline{u}(x)$ leading to the violation of the Gottfried sum rule, $\mathrm{\Delta }\overline{u}(x)>\mathrm{\Delta }\overline{d}(x)$ as indicated by the STAR data at large and small leptonic pseudorapidity.

Figure 1

The isovector quark quasidistribution $\tilde{u}(x)-\tilde{d}(x)$ as defined in Eq. (1) computed on a lattice with the nucleon momentum $P_z$ $(\text{in}\text{units}\text{of}2\pi /L)$ $=1$ (red), 2 (green), 3 (cyan). The $P_z$ $=1(3)$ curve has the lowest(highest) value among the curves at $x$ $=0.4$.

Figure 2

The physical quark distribution $u(x)-d(x)$ extracted from Fig. 1 after making $M_N^n/P_z^n$ corrections and one-loop corrections. The red, green, and cyan bands correspond to $P_z$ (in units of $2\pi /L$) $=1$ (red), 2 (green), 3 (cyan). The $P_z$ $=1(3)$ curve has the highest(lowest) value among the curves at $x$ $=0.6$. 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 [16] (brown dotted line), and CTEQ-JLab (CJ12, green dashed line) [17] with medium nuclear correction near $(1.3\mathrm{GeV}{)}^2$. 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.