Transverse momentum broadening in semi-inclusive deep inelastic scattering at next-to-leading order

Within the framework of higher-twist collinear factorization, transverse momentum broadening for the final hadrons in semi-inclusive deeply inelastic $e+A$ collisions is studied at the next-to-leading order (NLO) in perturbative QCD. Through explicit calculations of real and virtual corrections at twist-4, the transverse-momentum-weighted differential cross section due to double scattering is shown to factorize at NLO and can be expressed as a convolution of twist-4 nuclear parton correlation functions, the usual twist-2 fragmentation functions and hard parts which are finite and free of any divergences. A QCD evolution equation is also derived for the renormalized twist-4 quark-gluon correlation function which can be applied to future phenomenological studies of transverse momentum broadening and jet quenching at NLO.