Evidence for Strange-Quark Contributions to the Nucleon’s Form Factors at $Q^2=0.108(\mathrm{GeV}/c{)}^2$

We report on a measurement of the parity violating asymmetry in the elastic scattering of polarized electrons off unpolarized protons with the A4 apparatus at MAMI in Mainz at a four momentum transfer value of $Q^2=0.108(\mathrm{GeV}/c{)}^2$ and at a forward electron scattering angle of $30°<{\theta }_e<40°$. The measured asymmetry is $A_{LR}(\overrightarrow{e}p)=[-1.36\pm 0.29(\mathrm{stat})\pm 0.13(\mathrm{syst})]\times {10}^{-6}$. The expectation from the standard model assuming no strangeness contribution to the vector current is $A_0=(-2.06\pm 0.14)\times {10}^{-6}$. We have improved the statistical accuracy by a factor of 3 as compared to our previous measurements at a higher $Q^2$. We have extracted the strangeness contribution to the electromagnetic form factors from our data to be $G_E^s+0.106G_M^s=0.071\pm 0.036$ at $Q^2=0.108(\mathrm{GeV}/c{)}^2$. We again find the value for $G_E^s+0.106G_M^s$ to be positive, this time at an improved significance level of two $\sigma$.

Figure 1

Extracted physics asymmetries for $Q^2=0.108(\mathrm{GeV}/c{)}^2$ with respect to the state of the $\lambda /2$-wave plate. The flip of sign can be observed well. The dashed lines represent the global fit to all data with $\lambda /2$-wave plate sign flip taken into account.

Figure 2

Difference between the measured parity violating asymmetry in electron proton scattering $A_{LR}(\overrightarrow{e}p)$ and the asymmetry $A_0$ without vector strangeness contribution from the standard model for the SAMPLE experiment at backward angles, and the HAPPEX and the two A4 results at forward angles. We have taken the published asymmetry values from the SAMPLE and HAPPEX results and recalculated $A_0$ according to Eqs. (1, 3), taking for SAMPLE the mean values of the kinematical variables. The new experimental result at $Q^2=0.108(\mathrm{GeV}/c{)}^2$ presented here is the most accurate measurement.

Figure 3

The solid lines represent our result on $G_E^s+0.106G_M^s$ as extracted from our new data presented here. The shaded region represents in all cases the one-$\sigma$ uncertainty with statistical and systematic and theory error added in quadrature. The dashed lines represent the result on $G_M^s$ from the SAMPLE experiment [5]. The dotted lines represent the result of a recent lattice gauge theory calculation for ${\mu }_s$ [17]. The black squares represent different model calculations, and the numbers denote the references.