Towards the phenomenological implications of the Physical Scheme in PDF fits

TL;DR

This paper explores the implications of the Physical Scheme for parton distribution function (PDF) extractions, emphasizing modifications to the $ ext{MS}$ scheme, presenting analytic NLO coefficient functions, and highlighting the importance for future high-precision collider experiments.

Contribution

It introduces a new Physical Scheme for PDFs that incorporates intrinsic heavy-quark effects and provides analytic NLO DIS coefficient functions, enhancing the accuracy of PDF extractions.

Findings

Modified splitting functions and $ ext{α}_s$ running in the Physical Scheme.

Analytic formulas for NLO DIS coefficient functions.

Results for the $F_2$ charm structure function.

Abstract

We describe the impact on PDF extractions of the 'Physical Scheme', a heavy-quark mass scheme that accounts for the effects of intrinsic heavy-quarks and provides a way to smoothly transition over the heavy-quark thresholds. The modifications made to the conventional $\overline{\text{MS}}$ scheme splitting functions and $\alpha_s$ running will be emphasised, collectively giving rise to a new Physical Scheme PDF evolution. We also present the analytic formulae for the DIS coefficient functions at NLO in the Physical Scheme and show results for the $F_2$ charm DIS structure function. Motivated by the upcoming statistics from the High-Luminosity LHC, embodying the next phase of the precision physics era at the LHC, as well as in time from the Electron-Ion collider, we end by highlighting the need to quantify the effect of these corrections on PDF extractions over a wide range of momentum fractions $x$ and scales $Q^2$ and propose the use of $\texttt{xFitter}$ for doing so.