Drell--Yan lepton pair production at low invariant masses: transverse-momentum resummation and non-perturbative effects in QCD

We consider the transverse-momentum ($q_T$) distribution of Drell-Yan lepton pairs produced with invariant masses ($M$) from low values up to the $Z$-boson peak ($4\le M\le 116$~GeV). We present perturbative predictions obtained by consistently combining the resummation of logarithmically enhanced QCD corrections at small $q_T$ ($q_T\ll M$) up to next-to-next-to-next-to-next-to-leading logarithmic accuracy with the available fixed-order calculations at next-to-next-to-leading order (i.e. $\mathcal{O}({\alpha }_S^3)$) valid at large $q_T$. For very low $q_T$ ($q_T\sim {\mathrm{\Lambda }}_{\mathrm{Q}\mathrm{C}\mathrm{D}}$), non-perturbative (NP) QCD effects become dominant and have been included through a NP form factor with a small number of free-parameters. We compare our results with multiple experimental datasets from hadron colliders, finding excellent agreement between theory and data. By fitting the NP parameters, we achieve a precise extraction of the NP form factor and the so-called Collins-Soper kernel.