Strange Quark Contribution to the Vector and Axial Form Factors of the Nucleon: Combined Analysis of G0, HAPPEx, and Brookhaven E734 Data

The strange quark contribution to the vector and axial form factors of the nucleon has been determined for momentum transfers in the range $0.45<Q^2<1.0$ GeV${}^2$. The results are obtained via a combined analysis of forward-scattering, parity-violating elastic $\vec{e}p$ asymmetry data from the G0 and HAPPEx experiments at Jefferson Lab, and elastic $\nu p$ and $\bar{\nu} p$ scattering data from Experiment 734 at Brookhaven National Laboratory. The parity-violating asymmetries measured in elastic $\vec{e}p$ scattering at forward angles establish a relationship between the strange vector form factors $G_E^s$ and $G_M^s$, with little sensitivity to the strange axial form factor $G_A^s$. On the other hand, elastic neutrino scattering at low $Q^2$ is dominated by the axial form factor, with some significant sensitivity to the vector form factors as well. Combination of the two data sets allows the simultaneous extraction of $G_E^s$, $G_M^s$, and $G_A^s$ over a significant range of $Q^2$ for the very first time. The $Q^2$-dependence of the strange axial form factor suggests that the strange quark contribution to the proton spin, $\mathrm{\Delta }s$, is negative.