  We develop a new formalism to describe the inclusive production of small
radius jets in heavy-ion collisions, which is consistent with jet calculations
in the simpler proton-proton system. Only at next-to-leading order (NLO) and
beyond, the jet radius parameter $R$ and the jet algorithm dependence of the
jet cross section can be studied and a meaningful comparison to experimental
measurements is possible. We are able to consistently achieve NLO accuracy by
making use of the recently developed semi-inclusive jet functions within Soft
Collinear Effective Theory (SCET). In addition, single logarithms of the jet
size parameter $\alpha_s^n\ln^n R$ are resummed to next-to-leading logarithmic
(NLL$_R$) accuracy. The medium modified semi-inclusive jet functions are
obtained within the framework of SCET with Glauber gluons that describe the
interaction of jets with the medium. We present numerical results for the
suppression of inclusive jet cross sections in heavy ion collisions at the LHC
and the formalism developed here can be extended directly to corresponding jet
substructure observables.
