Inferring the Matching Scale in Glueball Effective Field Theory from Scattering Data

We investigate low-energy glueball--glueball scattering within aneffective field theory framework, with particular emphasis on the roleof the matching scale separating short- and long-distance dynamics.Rather than treating the matching scale as a purely technical parameter,we promote it to an inference variable constrained by scattering data. Using posterior predictive consistency as a diagnostic, we perform asystematic scan of the matching scale and identify a preferredintermediate region that yields stable and consistent predictions forlow-energy effective couplings.This region remains robust under variations of the short-distanceregulator, indicating that it reflects intrinsic dynamics rather thanregulator artifacts. Interpreting the preferred matching scale as an effective screeningmass, we extract a characteristic screening length$\ell_{\rm scr}\simeq 0.18\text{--}0.22~\mathrm{fm}$.Remarkably, this scale lies within a Polyakov-loop--inspired,center-symmetry--motivated range, suggesting a qualitative link betweenzero-temperature glueball scattering and confinement-driven screeningphysics.Our results demonstrate that glueball scattering data can be used notonly to constrain effective couplings, but also to infer physicallymeaningful matching scales encoding nonperturbative screening effects.