Semiparametric Estimation of Physics Parameters and Parton Distribution Functions

Abstract

The simultaneous determination of Parton Distribution Functions (PDFs) and fundamental physical parameters, e.g. the strong coupling constant $α_s$, the mass of the top quark $m_t$, or Wilson coefficients of an Effective Field Theory operators, is essential for the high-precision physics programme of the Large Hadron Collider. Yet, simultaneous global fits face significant methodological and computational challenges, rooted in the fundamental tension between estimating a finite-dimensional parameter and an infinite-dimensional function. In this paper, we address this problem by introducing a semiparametric estimation framework. The key advantage of our approach is that it avoids the need to refit the PDFs in the presence of either modified SM parameters or BSM contributions. Starting from standard, decoupled estimates of the PDFs and physics parameters, the method computes a bias correction a posteriori via the efficient influence function, yielding a debiased one-step estimator of the finite-dimensional parameter along with uncertainties with valid frequentist coverage. This correction rigorously accounts for the interplay between PDF and physics parameters without requiring a computationally expensive joint fit. As a proof of concept, we apply the method to two toy scenarios preparatory to a realistic global fit: the extraction of a dimension-six SMEFT Wilson coefficient from Deep Inelastic Scattering (DIS) pseudo-data based on BCDMS measurements, isolating the non-singlet PDF combination $T_3$, and to the determination of the proton total valence $V$ from combined HERA measurements. Our results demonstrate that the one-step estimator successfully removes the bias inherent in a preliminary, decoupled estimate and achieves confidence intervals with correct nominal coverage, offering a statistically rigorous and computationally efficient alternative to full simultaneous PDF fits.