Nonperturbative strange-quark sea from lattice QCD, light-front holography, and meson-baryon fluctuation models

We demonstrate that a nonzero strangeness contribution to the spacelike electromagnetic form factor of the nucleon is evidence for a strange-antistrange asymmetry in the nucleon’s light-front wave function, thus implying different nonperturbative contributions to the strange and antistrange quark distribution functions. A recent lattice QCD calculation of the nucleon strange quark form factor predicts that the strange quark distribution is more centralized in coordinate space than the antistrange quark distribution, and thus the strange quark distribution is more spread out in light-front momentum space. We show that the lattice prediction implies that the difference between the strange and antistrange parton distribution functions, $s(x)-\overline{s}(x)$, is negative at small-$x$ and positive at large-$x$. We also evaluate the strange quark form factor and $s(x)-\overline{s}(x)$ using a baryon-meson fluctuation model and a novel nonperturbative model based on light-front holographic QCD. This procedure leads to a Veneziano-like expression of the form factor, which depends exclusively on the twist of the hadron and the properties of the Regge trajectory of the vector meson which couples to the quark current in the hadron. The holographic structure of the model allows us to introduce unambiguously quark masses in the form factors and quark distributions preserving the hard scattering counting rule at large-$Q^2$ and the inclusive counting rule at large-$x$. Quark masses modify the Regge intercept which governs the small-$x$ behavior of quark distributions, therefore modifying their small-$x$ singular behavior. Both nonperturbative approaches provide descriptions of the strange-antistrange asymmetry and intrinsic strangeness in the nucleon consistent with the lattice QCD result.

Figure 1

Nonzero form factor $F_1(Q^2)$ (right panel) from asymmetric sea quark and antiquark distributions in transverse LF coordinate space (left panel). The dashed-dotted curves (blue) represent the quark, the dashed curves (red) represent the antiquark, and the continuous curves (black) represent $q-\overline{q}$. The quark/antiquark number is normalized to 1 in this figure.

Figure 2

Predictions for $F_1^s(Q^2)$ from the fluctuation model, LFHQCD, and lattice QCD [5, 7]. The predictions of the fluctuation model use the LFWFs from Refs. [51, 52].

Figure 3

Fits to the lattice QCD data of $F_1^s(Q^2)$ using the fluctuation model and LFHQCD.

Figure 4

Asymmetric strange-antistrange $x[s(x)-\overline{s}(x)]$ distribution. In the upper panel, the fit results from the fluctuation model and LFHQCD are compared. In the middle panel, the global fits are presented by central curves and standard deviation bands. In the lower panel, the global fits are presented by a hundred Monte Carlo replicas. The global fits are at $\mu =1\mathrm{GeV}$: NNPDF3.0 (gray) [16], MMHT2014 (green) [17], JR14 (cyan) [18].

Figure 5

Chew-Frautschi plot for the leading $\rho$ and $\omega$ (gray dashed) and $\varphi$ (red continuous) trajectories in LFHQCD. At values $t=M^2$ where $\alpha (t)$ is an integer, there is a hadron with mass squared $M^2$ and spin $J=\alpha (M^2)$. The $\rho$ and $\omega$ intercepts are fixed by the pion mass from the relation $\mathrm{\Delta }{M}_{\rho }^2=\mathrm{\Delta }{M}_{\omega }^2=M_{{\pi }^{\pm }}^2$ and the mass scale $\lambda$ is fixed by the best fit to the slopes of both trajectories: This fixes the intercept of the $\varphi$ trajectory. We find $\sqrt{\lambda }=0.534\mathrm{GeV}$, ${\alpha }_{\rho }(0)={\alpha }_{\omega }(0)=\frac{1}{2}-\frac{\mathrm{\Delta }{M}_{\pi }^2}{4\lambda }=0.483$ and ${\alpha }_{\varphi }(0)=0.01$. Solid triangles represent the $\omega$ trajectory. The data is from Ref. [54].

Figure 6

Effect of $\varphi -\omega$ mixing in $F_1^s(Q^2)$ and the $s(x)-\overline{s}(x)$ asymmetry. The effect of the mixing is negligible even for 10% mixing, i.e., for $\eta =0.1$.

Figure 7

The distributions $xs(x)$ (continuous curves) and $x\overline{s}(x)$ (dashed curves) correspond to the minimum intrinsic strange probability $I_s=0.2N_s$ with $N_s=0.047$, $\sqrt{\lambda }=0.534\mathrm{GeV}$, and $M_{\varphi }^2=1.96\lambda$. The results with massless quarks are included for comparison.

Figure 8

Light-front holographic results for the asymmetric strange and antistrange quark distributions in transverse coordinate space corresponding to the minimum possible intrinsic strange probability.