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We study radiative $p_{\perp}$-broadening of high energy quarks passingthrough hot and cold QCD matter. With $L$ the length of the matter and $l_{0}$the size of constituents of the matter we find $\avg{p_{\perp}^{2}}$ has bothdouble logarithmic terms, $\ln^{2}(L/l_{0})$, and single logarithmic terms,$\ln(L/l_{0})$, coming from gluon radiation induced by the matter. We use a(slight) extension of a formalism developed by B. Zakharov for studying energyloss, a formalism which, for much of our calculation, reduces to a simpledipole scattering analysis. We estimate the radiative contribution to be asizable correction to the nonradiative value of $\avg{p_{\perp}^{2}}$. We alsocarry out a resummation of the double logarithmic terms that we find, and webriefly discuss running coupling effects which appear here in a rather unusualway.

Radiative pT-broadening of high-energy quarks and gluons in QCD matter