Muon-Proton Deep Elastic Scattering

We have measured muon-proton elastic scattering in the range $0.6<\mathrm{}{q}^2<3.2\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. We compared these data with the corresponding elastic electron-proton cross sections by forming the ratio $r\left(q^2\right)=\frac{G^2(\mu -p)}{G^2\mathrm{}(e-p)\mathrm{}}$, where $G\left(q^2\right)=\frac{G_M\left(q^2\right)}{\mu }$ is the form factor of the proton. By fitting $r\left(q^2\right)=N{(1+\frac{q^2}{{\Lambda }^2})}^{-2\mathrm{}}$ we find $N=1.043\mathrm{}\pm 0.080$ and ${\Lambda }^{-2\mathrm{}}=+0.064\mathrm{}\pm 0.038$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{-2\mathrm{}}$. Combining our data with those of two previous $\mu -p$ elastic scattering experiments yields ${\Lambda }^{-2\mathrm{}}=+0.051\mathrm{}\pm 0.024$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{-2\mathrm{}}$ which is a much weaker limit on muon-electron universality than that obtained from $\mu -p$ inelastic scattering.