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

We re-analyze the data of the elastic electron proton scattering to look for model-independent evidence of the two-photon-exchange (TPE) effect. In contrast to previous analyses, TPE effect is parametrized in forms which are free of kinematical-singularity, in addition to being consistent with the constraint derived from crossing symmetry and the charge conjugation. Moreover, we fix the value of $R=G_E/G_M$ as determined from the data of the polarization transfer experiment. 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 $G_{E}$. It also 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 effect. More precise data at extreme angles will be crucial for a model-independent extraction of the TPE effect.