  In the present investigation we study the leading and subleading high-energy
behavior of hadron-hadron total cross sections using a best-fit analysis of
hadronic scattering data. The parametrization used for the hadron-hadron total
cross sections at high energy is inspired by recent results obtained by
Giordano and Meggiolaro (2014) using a nonperturbative approach in the
framework of QCD and it reads $\sigma_\text{tot} \sim B\ln^2 s + C\ln s\ln\ln
s$. Both $B$ and $C$ are obtained by means of best-fits to data for
proton-proton and antiproton-proton scattering, including recent data obtained
at the LHC, and also to data for other meson-baryon and baryon-baryon
scattering processes. The results are compared to the theoretical predictions
existing in the literature. In particular, following the above-mentioned
nonperturbative QCD approach, we also consider fits where the parameters $B$
and $C$ are set to $B = \kappa B_\text{th}$ and $C = \kappa C_\text{th}$, where
$B_\text{th}$ and $C_\text{th}$ are universal quantities related to the QCD
stable spectrum, while $\kappa$ (treated as an extra free parameter) is related
to the asymptotic value of the ratio $\sigma_\text{el}/\sigma_\text{tot}$.
Different possible scenarios are then considered and compared.
