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jet quenching phenomenology based on perturbative qcd and energy loss calculations has been quite successful in describing data from rhic and lhc heavy ion collisions , see @xcite and the references therein .
typically , such calculations incorporate scattering of highly energetic quarks and gluons produced in the medium off of the qgp quasiparticles . the resulting energy loss and the steepness of the production cross section of quarks and gluons combine together and lead to the phenomenon of jet quenching .    in order to go beyond the approximations used in energy loss calculations
we take the effective theory point of view , without assuming that the emitted partons are soft .
a good start for an effective theory for jet propagation in the medium is soft - collinear effective theory ( scet ) @xcite . in this effective theory
all hard modes are integrated out and only quark and gluons with momenta collinear to the directions of interest and ultrasoft gluons are present . in order to adapt scet for proper description of jets in the medium
, the elastic scattering of energetic quarks and gluons off of the medium sources has to be included .
this elastic scattering is mediated by transverse @xmath2channel gluons , which are traditionally called glauber gluons .
inclusion of this mode leads to an effective theory , which we call @xmath0 , which stands for soft collinear effective theory with glauber gluons .
this effective theory has been developed in a series of papers @xcite .
also , note that it has been shown in ref .
@xcite that in order to consistently describe drell - yan process in effective theory one needs to go beyond scet and use in fact , @xmath0 and include the potential scattering of spectators off each other .    in this talk
we overview main results obtained in ref .
@xcite for medium - induced splitting kernels . in the framework of @xmath0 we present all splitting kernels keeping the full emitted parton energy fraction @xmath1 dependence , which is consistent with the power counting of our effective theory .
the momentum of the @xmath2channel gluon mode that mediates the elastic scattering of jets off of the qgp quasiparticles can vary from @xmath3 for static source to @xmath4 for soft source @xcite .
we refer to gluons with momentum scaling of both of these modes as glauber gluons , even though traditionally under this name the former mode is understood .
both modes are off - shell and from effective theory point of view the role of these modes is to provide interaction with the potential created by the source .
thus , the appropriate treatment for such interaction would be a term in the lagrangian coupled with background vector potential .
this has been done in ref .
@xcite for a collinear quark field and extended in ref .
@xcite for a collinear gluon field interacting with external vector potential .
the details of this extra term in the lagrangian that needs to be added to scet depend on the gauge fixing condition and the underlying assumption on the momentum scaling of the source field that produces the elastic scattering .
different gauges and different choices of scaling for the source have been considered in ref .
@xcite . assuming static quark center with momentum scaling of hqet field , i.e. @xmath5 for the source and a particularly simple gauge choice , where glauber gluons are quantized in the covariant gauge and collinear gluons are quantized in the light - cone gauge , which we call the hybrid gauge ,
we get the following effective lagrangian of @xmath0@xcite : @xmath6 the first term in the second line describes elastic scattering of a collinear quark field off of the scattering center and the second term describes elastic scattering of a collinear gluon field off of the scattering center in the medium .
note that different collinear sectors with momenta @xmath7 and @xmath8 separated in the transverse direction are coupled through this term .
with the effective lagrangian of @xmath0 at hand , it is a straightforward task to calculate the medium - induced splitting kernels .
we consider an initial quark or gluon with momentum @xmath9 splitting into two partons with momenta @xmath7 and @xmath10 , where the splitting energy fraction is defined as @xmath11 .
we use the following momentum assignment to partons in the splitting : @xmath12 , i.e. for example when we refer to @xmath13 splitting we have in mind that a quark with momentum @xmath9 splits into a quark with momentum @xmath7 and a gluon with momentum @xmath10 .
we thus have four possible splittings : @xmath13 , @xmath14 , @xmath15 and @xmath16 .
the final partons are taken to be on - shell : @xmath17 .
the light - cone vector @xmath18 is aligned with the initial parton , so that by definition @xmath19 and thus @xmath20 .
the diagrams in the medium that need to be evaluated are presented in figure [ fig1 ] .
the result of applying the feynman rules of @xmath0 and evaluating single and double born diagrams along with longitudinal integrals can be expressed through four transverse momenta which we define as : @xmath21 after a straightforward though lengthy calculation we obtain the following result for arbitrary medium - induced splitting@xcite : @xmath22 where @xmath23 is the elastic scattering cross section of the parton in the medium and as suggested by notation the phases @xmath24 are independent of the splittings .
they are equal to :    [ fig2 ]    @xmath25    the coefficients @xmath26 and the scattering lengths @xmath27 in fact depend on the splitting .
the scattering lengths are equal to the gluon scattering length @xmath28 for splittings @xmath13 and @xmath29 and the quark scattering length @xmath30 for the splittings @xmath15 and @xmath16 .
the coefficients @xmath31 for the @xmath13 splitting are equal to : @xmath32 and for three remaining splittings they all have been calculated and can easily be extracted from ref .
the vacuum splitting functions @xmath33 are well known @xcite and we do not present them here for brevity .
the numerical evaluation of splitting intensity @xmath34 for the splitting @xmath13 is shown in figure [ fig2 ] . for details on implementation of nuclear recoil and phase space cuts
@xcite .    in the process of deriving the medium - induced splitting kernels in ref .
@xcite we have shown explicitly that they are gauge invariant and that they factorize from the hard scattering process that creates the jet .
this is described in detail in ref .
@xcite for @xmath13 splitting and works similarly for the remaining splittings .
using @xmath0 , several theoretical advances were achieved , relevant for jet quenching phenomenology .
we proved the gauge invariance and factorization of the medium - induced splitting kernels . on the quantitative level we calculated the medium - splitting kernels beyond the small@xmath35 approximation which is inherent to energy loss calculations . with these improved results for @xmath13 and @xmath14 splittings , as well as
two additional splittings @xmath15 and @xmath16 , which only appear at finite @xmath1 order , we have all ingredients to present improved theoretical predictions for jet production at rhic and lhc @xcite .
these results will be presented elsewhere .
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using the framework of soft - collinear effective theory with glauber gluons ( @xmath0 ) , we evaluate medium - induced splitting kernels . because of the power counting of the effective theory , our results are valid for arbitrary , not necessarily small values of the energy fraction @xmath1 taken by the emitted parton . in this framework 
 we prove the factorization from the hard process and gauge invariance of the splitting kernels , we also show how nuclear recoil and the phase space cuts can be implemented into the phenomenology .