Jet Definition and Transverse-Momentum-Dependent Factorization in Semi-Inclusive Deep-Inelastic Scattering

Using the colour dipole picture of Deep Inelastic Scattering (DIS) and the Colour Glass Condensate effective theory, we study semi-inclusive jet production in DIS at small $x$ in the limit where the photon virtuality $Q^2$ is much larger than the transverse momentum squared $P_\perp^2$ of the produced jet. In this limit, the cross-section is dominated by aligned jet configurations, that is, quark-antiquark pairs in which one of the fermions -- the would-be struck quark in the Breit frame -- carries most of the longitudinal momentum of the virtual photon. We show that physically meaningful jet definitions in DIS are such that the effective axis of the jet sourced by the struck quark is controlled by its virtuality rather than by its transverse momentum. For such jet definitions, we show that the next-to-leading order (NLO) cross-section admits factorisation in terms of the (sea) quark transverse momentum dependent (TMD) distribution, which in turn satisfies a universal Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Sudakov evolution.