Determination of the strange form factors of the nucleon from $\nu p$, $\bar{\nu} p$, and parity-violating $\vec{e}p$ elastic scattering

A new method of obtaining the strange form factors of the nucleon is presented, in which forward-angle parity-violating $\vec{e}p$ elastic scattering data is combined with $\nu p$ and $\bar{\nu} p$ elastic scattering data. The axial form factor in electron-nucleon scattering is complicated by the presence of electro-weak radiative corrections that in principle need to be calculated or separately measured, but this axial form factor is suppressed at forward angles. The neutrino data has no such complication. Hence the use of forward-angle parity-violating $\vec{e}p$ data with $\nu p$ and $\bar{\nu} p$ data allows the extraction of all three strange form factors: electric, magnetic and axial ($G_E^s$, $G_M^s$, and $G_A^s$). In this letter, $\nu p$ and $\bar{\nu} p$ data from the Brookhaven E734 experiment are combined with the Jefferson Lab HAPPEX $\vec{e}p$ data to obtain two distinct solutions for the strange form factors at $Q^2$ = 0.5 GeV$^2$. More generally, combining the neutrino elastic scattering data from E734 with the existing and upcoming $\vec{e}p$ data will yield the strange form factors of the nucleon for $Q^2$ of 0.45-1.05 GeV$^2$. Measurement of $G_A^s$ is crucial to the determination of the strange quark contribution to the nucleon spin, $\Delta s$.