  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.
