Radiative energy loss and radiative $p_T$-broadening of high-energy partons in QCD matter

In this talk, I shall give a review on radiative $p_T$-broadening and radiative energy loss of high-energy partons in QCD matter. The typical $p_T$^2 of high-energy partons receives a double logarithmic correction due to the recoiling effect of medium-induced gluon radiation. Such a double logarithmic term, averaged over the path length of the partons, can be taken as the radiative correction to the jet quenching parameter $\hat{q}$ and hence contributes to radiative energy loss. This has also been confirmed by detailed calculations of energy loss by radiating two gluons. Besides, I shall also report briefly on our recent understanding about the relation between such a double log inside QCD matter and the Sudakov double logs.