Unitarity dressing of the dynamical gluon mass scale
We examine how $s$-channel unitarization changes the dynamical gluon mass scale $m_g$ inferred from high-energy elastic $pp$ scattering. The Born input is the Reggeized Landshoff--Nachtmann exchange of two nonperturbative gluons in a color-singlet state. We fit the ATLAS and TOTEM forward data separately, using eikonal and $U$-matrix unitarizations with logarithmic and power-law running masses derived from Schwinger--Dyson analyses. At the common reference cut $|t|_{\rm max}=0.12~\GeV^2$, the Born fits give $m_g=297$--$427~\MeV$; the eikonal and $U$-matrix fits give $265$--$360~\MeV$ and $243$--$328~\MeV$, respectively. Unitarization changes the fitted values of the intercept parameter $ε$, $m_g$, and the exponential slope $a_1$ of the proton form factor together. Over $0.10\leq |t|_{\rm max}\leq0.14~\GeV^2$, the $U$-matrix parameters vary less with the cut, while the eikonal fits to TOTEM show a pronounced drift. Replacing the infrared continuation of the logarithmic effective charge by a Curci--Ferrari prescription changes $m_g$ by a mean absolute relative shift of $1.77\%$ over twenty comparisons, with a maximum of $2.17\%$. The inferred scale remains in the few-hundred-MeV region, but its fitted value depends on the nonperturbative input and on the unitarization prescription.