Can New Physics hide in the proton PDFs?

A major recent breakthrough in global fits of the structure of the proton has been the inclusion of a significant amount of precise LHC measurements. While this data provides important constraints, especially on the poorly-know gluon and anti-quark PDFs, it is crucial to avoid any contamination from potential beyond the Standard Model (BSM) effects that could be present in the high energy or transverse momentum tails of the fitted experimental distributions. This problem is particularly acute for LHC data from Runs II and III, as well as for the future High-Luminosity Run, where many PDF-sensitive observables will reach the few TeV region. In this talk, I present a first quantitative study aiming to study whether or not New Physics effects can be reabsorbed into the fitted PDFs, as well as the possibility of setting up a global QCD fit to simultaneously constrain the proton structure and New Physics dynamics.