Is there model-independent evidence of the two-photon-exchange effect in the electron-proton elastic scattering cross section?

The data of the elastic electron proton scattering is analyzed to search for model-independent evidence of the two-photon-exchange (TPE) effect. In our analysis, the value of $R=G_E/G_M$ is fixed as determined from the polarization transfer experiment and the TPE contribution parametrized in forms which are consistent with the constraint derived from crossing symmetry, charge conjugation, and model calculation results. In contrast to the previous analyses we find that, at high $Q^2 \geq 2 GeV^2$ values, the contribution of the TPE effect to the slope of $\sigma_R$ vs. $\epsilon$ is large and comparable with that arising from $G_{E}$, and behaves quasi-linearly in the region of current data, namely, in the range of $0.2 < \epsilon < 0.95$. Hence the fact that current elastic $ep$ cross section data show little nonlinearity with respect to $\epsilon$ can not be used to exclude the presence of the TPE effects. More precise data at extreme angles will be very helpful for model-independent extraction of the TPE effect.