Abstract
We study the connection between radiative energy loss and radiative p ⊥- roadening of a high-energy quark or gluon passing through QCD matter. The generalized Baier-Dokshitzer-Mueller-Peigne-Schiff-Zakharov (BDMPS-Z) formalism is used to calculate energy loss due to multiple gluon emission. With L the length of the matter and l 0 the size of constituents of the matter we find a double logarithmic correction \( \propto { \ln}^2\frac{L}{l_0} \) to parton energy loss due to two-gluon emission. We also show that the radiative energy loss per unit length \( -\frac{dE}{dz}=\frac{\alpha_s{N}_c}{12}\left\langle {p}_{{}_{\perp}}^2\right\rangle \) by carrying out a resummation of the double logarithmic terms. Here, the transverse momentum broadening \( \left\langle {p}_{\perp}^2\right\rangle \) is obtained by resumming terms \( \propto {\alpha}_s{ \ln}^2\frac{L}{l_0} \) in ref. [11]. Our result agrees with that by the renormalization of \( \widehat{q} \) proposed in refs. [15, 16].
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Wu, B. Radiative energy loss and radiative p ⊥-broadening of high-energy partons in QCD matter. J. High Energ. Phys. 2014, 81 (2014). https://doi.org/10.1007/JHEP12(2014)081
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DOI: https://doi.org/10.1007/JHEP12(2014)081