Collins-Soper Kernel for TMD Evolution from Lattice QCD

The Collins-Soper kernel relates transverse momentum-dependent parton distribution functions (TMDPDFs) at different energy scales. For small parton transverse momentum $q_T\sim {\mathrm{\Lambda }}_{\text{QCD}}$, this kernel is non-perturbative and can only be determined with controlled uncertainties through experiment or first-principles calculations. This work presents the first exploratory determination of the Collins-Soper kernel using the lattice formulation of Quantum Chromodynamics. In a quenched calculation, the $N_f=0$ kernel is determined at scales in the range 250 MeV $<q_T<2$ GeV, and an analysis of the remaining systematic uncertainties is undertaken.