Towards the phenomenological implications of the Physical Scheme in PDF fits

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.