A Fast Method for Correlated Updates of Proton PDFs and the Strong Coupling $\hat{I}{\pm }_s$

Abstract

We present an extended version of the \texttt{ePump} framework that enables the simultaneous profiling of proton parton distribution functions (PDFs) and the strong coupling $\hat{I}{\pm }_s$ using new experimental data. By promoting $\hat{I}{\pm }_s$ to a fit parameter within the Hessian updating formalism, the method performs coherent updates of $\{\text{PDFs},\hat{I}{\pm }_s\}$ while preserving parameter correlations and the full covariance structure. Validation studies based on CTEQ-TEA analyses with collider data demonstrate that the upgraded \texttt{ePump} accurately reproduces the shifts in PDFs, the preferred $\hat{I}{\pm }_s(m_Z)$, and the associated uncertainty reductions obtained in full global fits, including those inferred from Lagrange--Multiplier scans; small deviations arise only for data sets whose $\ddot{I}{‡}^2$ profiles exhibit nonlinear behavior. Applications to representative collider measurements illustrate the impact on the gluon distribution and on precision observables such as the Higgs boson production cross section via gluon fusion. This enhanced framework provides a fast and reliable tool for assessing the effects of new data on the global QCD parameter space, offering near-global-fit accuracy at a fraction of the computational cost.