Unitarity dressing of the dynamical gluon mass scale

Abstract

We study the effect of $s$-channel unitarity on the dynamical gluon mass scale, $m_g$, extracted from high-energy elastic $pp$ scattering. The elementary input is a Reggeized Landshoff--Nachtmann two-gluon exchange, in which the soft Pomeron is represented by a color-singlet pair of dynamically massive gluons. At Born level, the logarithmic and power-law mass solutions give $m_g=299$--$422~\MeV$, in the usual phenomenological range. When the same input is embedded in the eikonal and $U$-matrix schemes, the preferred values move to $m_g=749$--$1101~\MeV$. The enhancement, by a factor close to $2.5$, is stable against the ATLAS--TOTEM data choice, the running of the gluon mass, and the unitarization prescription. We trace this shift to the nonlinear mapping between the elementary two-gluon kernel and the physical impact-parameter profile. The scale inferred from elastic scattering is therefore a unitarity-dressed infrared scale, fixed jointly by the nonperturbative gluon propagator and by multiple-exchange dynamics.