Abstract
When an energetic parton propagates in a hot and dense QCD medium it loses energy by elastic scatterings or by medium-induced gluon radiation. The gluon radiation spectrum is suppressed at high frequency due to the LPM effect and encompasses two regimes that are known analytically: at high frequencies omega >{omega}_c=hat{q}{L}^2 , where hat{q} is the jet quenching transport coefficient and L the length of the medium, the spectrum is dominated by a single hard scattering, whereas the regime ω < ωc is dominated by multiple low momentum transfers. In this paper, we extend a recent approach (dubbed the Improved Opacity Expansion (IOE)), which allows an analytic (and systematic) treatment beyond the multiple soft scattering approximation, matching this result with the single hard emission spectrum. We calculate in particular the NNLO correction analytically and numerically and show that it is strongly suppressed compared to the NLO indicating a fast convergence of the IOE scheme and thus, we conclude that it is sufficient to truncate the series at NLO. We also propose a prescription to compare the GW and the HTL potentials and relate their parameters for future phenomenological works.
Highlights
Free path, tf ≡ ω/k⊥2 ∼ mfp which is assumed to be much smaller than the medium length L, and the gluon is emitted incoherently by individual scattering centers
The gluon radiation spectrum is suppressed at high frequency due to the LPM effect and encompasses two regimes that are known analytically: at high frequencies ω > ωc = qL2, where qis the jet quenching transport coefficient and L the length of the medium, the spectrum is dominated by a single hard scattering, whereas the regime ω < ωc is dominated by multiple low momentum transfers
We calculate in particular the NNLO correction analytically and numerically and show that it is strongly suppressed compared to the NLO indicating a fast convergence of the IOE scheme and we conclude that it is sufficient to truncate the series at NLO
Summary
The general form for the integrated medium-induced gluon spectrum off a high energy parton (in color representation R) is given by [14, 20]. Where ω is the gluon frequency (assumed to be much softer than the emitting parton E ω) and the second term inside the brackets subtracts the vacuum like contributions. The Green’s functions K and K0 are solutions to a 2-dimensional Schrodinger equation in the transverse plane, and obey. Where v(x) is the potential defined by the in-medium (elastic) scattering cross section. K0 obeys a similar equation with v = 0
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