Constraining nucleon strangeness

Determining the nonperturbative $s\overline{s}$ content of the nucleon has attracted considerable interest and has been the subject of numerous experimental searches. These measurements used a variety of reactions, and place important limits on the vector form factors observed in parity-violating (PV) elastic scattering and the parton distributions determined by deep inelastic scattering (DIS). In spite of this progress, attempts to relate information obtained from elastic and DIS experiments have been sparse. To ameliorate this situation, we develop an interpolating model using light-front wave functions capable of computing both DIS and elastic observables. This framework is used to show that existing knowledge of DIS places significant restrictions on our wave functions. The result is that the predicted effects of nucleon strangeness on elastic observables are much smaller than those tolerated by direct fits to PV elastic scattering data alone. Using our model, we find $-0.024\le {\mu }_s\le 0.035$ and $-0.137\le {\rho }_s^D\le 0.081$ for the strange contributions to the nucleon magnetic moment and charge radius. The model we develop also independently predicts the nucleon's strange spin content $\Delta s$ and scalar density $\langle N\left|\overline{s}s\right|N\rangle$, and for these we find agreement with previous determinations.

Figure 1

(a) We plot predictions for $s\left(x\right)$ (solid curves) and $\overline{s}\left(x\right)$ (dashed lines) using the model wave functions G1 (thick lines) and G2 (thin lines) defined by the numerical values of Table 1 in Eq. (21). (b) The integrands of the sum rule ${\int }_0^{1}dx[s\left(x\right)-\overline{s}\left(x\right)]=0$ (solid) and of $x{S}^{-}$ (dot-dashed) as given by Eq. (1). In this case, results computed with G1 and G2 are given by thick and thin lines, respectively.

Figure 2

A comparison of the systematic LFWF uncertainty between the Gaussian models G1 and G2 against Rosenbluth-separated measurements for $G_E^{s\overline{s}}\left(Q^2\right)$ (a) and $G_M^{s\overline{s}}\left(Q^2\right)$ (b). The inner bands represent the constraints due to CTEQ6.5S, while the outer bands correspond to ad hoc ranges for $x{S}^{\pm }$ produced by doubling the ranges of Eq. (23) so as to be more comparable to the experimental uncertainties of the elastic data.

Figure 3

An extension of the curves evaluated in Fig. 2 to the quantity $G_E^{s\overline{s}}\left(Q^2\right)+\eta G_M^{s\overline{s}}\left(Q^2\right)$ determined at forward kinematics. The bands about $G_E^{s\overline{s}}\left(Q^2\right)+\eta G_M^{s\overline{s}}\left(Q^2\right)$ are as described for Fig. 2.