Collins-Soper kernel for TMD evolution from lattice QCD
Phiala E. Shanahan, Michael L. Wagman, Yong Zhao
Abstract
The Collins-Soper kernel relates transverse momentum-dependent parton distribution functions (TMDPDFs) at different energy scales. For small parton transverse momentum ${q}_{T}\ensuremath{\sim}{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$, this kernel is nonperturbative 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 $250\text{ }\text{ }\mathrm{MeV}<{q}_{T}<2\text{ }\text{ }\mathrm{GeV}$, and an analysis of the remaining systematic uncertainties is undertaken.