Emergence of resummation scales in the evolution of the QCD strong coupling and PDFs

The QCD strong coupling and the parton distribution functions (PDFs) of the proton are fundamental ingredients for phenomenology at high-energy facilities such as the Large Hadron Collider (LHC). It is therefore of crucial importance to estimate any theoretical uncertainties associated to them. Both the coupling and the PDFs obey their own renormalisation-group equations (RGEs) whose solution determines their scale evolution. Although the kernels that govern these RGEs have been computed to very high perturbative precision, they are not exactly known. In this contribution, we outline a procedure that allows us to assess the uncertainty on the evolution of the coupling and the PDFs due to our imperfect knowledge of their respective evolution kernels. Inspired by transverse-momentum and threshold resummation, we introduce additional scales, that we dub resummation scales, that can be varied to estimate the uncertainty on the evolution at any scale. As a test case, we consider the deep-inelastic-scattering structure function 𝐹2 in a region relevant for the extraction of PDFs. We study the effect of varying these resummation scales and compare it to the usual renormalisation and factorisation scale variations.