Extending Soft-Collinear-Effective-Theory to describe hard jets in dense QCD media

An extension to the Soft-Collinear-Effective Theory (SCET) description of hard jets is motivated to include the leading contributions between the propagating partons within the jet with partons radiated from a dense extended medium. The resulting effective Lagrangian, containing both a leading and a power suppressed (in the hard scale $Q^2$) contribution, arises primarily from interactions between the hard collinear modes in the jet with Glauber modes from the medium. In this first attempt, the interactions between the hard jet and soft and collinear partonic modes have been ignored, in an effort to focus solely on the interactions with the Glauber modes. While the effect of such modes on vacuum cross sections are suppressed by powers of the hard scale compared to the terms from the SCET Lagrangian, such sub-leading contributions are enhanced by the extent of the medium and result in measurable corrections. The veracity of the derived Lagrangian is checked by direct comparison with known results from full QCD calculations of two physical observables: the transverse momentum broadening of hard jets in dense media and a reanalysis of the transverse momentum dependent parton distribution function (TMDPDF).