High-energy gluon bremsstrahlung in a finite medium: harmonic oscillator versus single scattering approximation - Nuclear TheoryReport as inadecuate




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Abstract: A particle produced in a hard collision can lose energy throughbremsstrahlung. It has long been of interest to calculate the effect onbremsstrahlung if the particle is produced inside a finite-size QCD medium suchas a quark-gluon plasma. For the case of very high-energy particles travelingthrough the background of a weakly-coupled quark-gluon plasma, it is known howto reduce this problem to an equivalent problem in non-relativistictwo-dimensional quantum mechanics. Analytic solutions, however, have alwaysresorted to further approximations. One is a harmonic oscillator approximationto the corresponding quantum mechanics problem, which is appropriate forsufficiently thick media. Another is to formally treat the particle as havingonly a single significant scattering from the plasma known as the N=1 term ofthe opacity expansion, which is appropriate for sufficiently thin media. In abroad range of intermediate cases, these two very different approximations givesurprisingly similar but slightly differing results if one works to leadinglogarithmic order in the particle energy, and there has been confusion aboutthe range of validity of each approximation. In this paper, I sort out indetail the parametric range of validity of these two approximations at leadinglogarithmic order. For simplicity, I study the problem for small alpha s andlarge logarithms but alpha s log << 1.



Author: Peter Arnold

Source: https://arxiv.org/







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