M. J. Menon, P. V. R. G. Silva
A forward amplitude analysis on $pp$ and $\bar{p}p$ elastic scattering above 5 GeV is presented. The dataset includes the five recent high-precision TOTEM measurements of the $pp$ total cross section at 7 and 8 TeV. Following previous works, the leading high-energy contribution for the total cross section is parametrized as $\ln^{\gamma}(s/s_h)$, where $s$ is the c.m. energy squared, $\gamma$ and $s_h$ are free \textit{real} fit parameters. Using singly-subtracted derivative dispersion relations the total cross section ($\sigma_{tot}$) and the rho parameter ($\rho$) are analytically connected. Different fit procedures are considered, including individual fits to $\sigma_{tot}$ data, global fits to $\sigma_{tot}$ and $\rho$ data, constrained and unconstrained data reductions. The results favor a rise of the total cross section at the LHC energy region faster than the log-squared bound by Froissart and Martin, namely $\gamma$ greater than 2. A critical discussion on the correlation, practical role and physical implications of the parameters $\gamma$ and $s_h$, including a physically meaningful representation for $s_h$, is presented. The discussion comprises the 2002 prediction by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton total cross section at the highest energies are also presented.
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http://arxiv.org/abs/1212.5096
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