  In the framework of large-momentum effective theory at one-loop matching
accuracy, we perform a lattice calculation of the Collins-Soper kernel which
governs the rapidity evolution of transverse-momentum-dependent (TMD)
distributions. We first obtain the quasi TMD wave functions at three different
meson momenta on a lattice with valence clover quarks on a dynamical HISQ sea
and lattice spacing $a=0.12$~fm from MILC, and renormalize the pertinent linear
divergences using Wilson loops. Through one-loop matching to the light-cone
wave functions, we determine the Collins-Soper kernel with transverse
separation up to 0.6~fm. We study the systematic uncertainties from operator
mixing and scale dependence, as well as the impact from higher power
corrections. Our results potentially allow for a determination of the soft
function and other transverse-momentum dependent quantities at one-loop
accuracy.
