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

We analyze the data of the elastic electron proton scattering to look for model-independent evidence of the two-photon-exchange (TPE) effect. We fix the value of $R=G_E/G_M$ as determined from the data of the polarization transfer experiment and parametrize the TPE contribution in forms which are consistent with the constraint derived from crossing symmetry and the charge conjugation. 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 the current elastic $ep$ cross section data shows 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 crucial for a model-independent extraction of the TPE effects.