  This work presents a determination of the quark Collins-Soper kernel, which
relates transverse-momentum-dependent parton distributions (TMDs) at different
rapidity scales, using lattice Quantum Chromodynamics (QCD). This is the first
lattice QCD calculation of the kernel at quark masses corresponding to a
close-to-physical value of the pion mass, with next-to-next-leading logarithmic
matching to TMDs from the corresponding lattice-calculable distributions, and
includes a complete analysis of systematic uncertainties arising from operator
mixing. The kernel is extracted at transverse momentum scales
$240\,\text{MeV}\lesssim q_{T}\lesssim 1.6\,\text{GeV}$ with a precision
sufficient to begin to discriminate between different phenomenological models
in the non-perturbative region.
