Improved opacity expansion at NNLO for medium induced gluon radiation

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 $$ \omega >{\omega}_c=\hat{q}{L}^2 $$ ω > ω c = q ̂ L 2 , where $$ \hat{q} $$ 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.

Improved opacity expansion for medium-induced parton splitting

“…For T = 0.4 GeV and g = 1.94 (so that α s ≈ 0.3) we findq 0 (t) = 1.83 GeV 2 /fm and m D = 0.9 GeV. For the remaining part of the paper, we identify µ = m D , see also [26] for a more precise matching.…”

“…Since the procedure in principle encodes the full information about the power-law behavior of Coulomb interactions, we also introduce an interpolation to the Bethe-Heitler regime of very soft gluon emissions, i.e. t f L, which is especially relevant for dilute media, mfp L. The description of this regime is achieved through a prescription of the matching scale that removes the possibility for multiple scattering, see also [26] for a discussion of the matching scale. Our result for the spectrum of medium-induced splittings is therefore valid for arbitrary energies and medium sizes, interpolating between three regimes: 1) Bethe-Heitler (t f < mfp ), 2) LPM ( mfp < t f < L) and 3) single, hard scattering (L < t f ).…”

“…It is worth pointing out that in the regime ω ω BH that corresponds to Q 2 sub µ 2 the dependence on the matching scale in of higher order and thus is weak. This is the leading logarithm dominated regime that was analyzed in detail up to NNLO in [26] in the improved opacity expansion scheme where the matching scale between the LPM and the UV regimes was precisely pinned down. However, at the BH scale, power corrections become sizable.…”

Medium-induced fragmentation and equilibration of highly energetic partons

“…Starting with the original calculations of the rates for medium-induced radiation [12][13][14][15][16] and more recent refinements [17][18][19][20][21][22][23], there have been several theoretical studies tackling the description of the jet evolution in QCD medium, based on (semi-)analytic approaches [24][25][26], effective kinetic descriptions [27][28][29][30][31][32] as well as sophisticated Monte Carlo simulations [33][34][35][36][37][38][39][40] some of which even include a fully coupled jet-medium evolution. Although, all of these approaches provide a solid description of experimental measurements in their respective range of applicability, a general challenge in the description of in-medium jet evolution is to devise a consistent simultaneous description of the near-thermal soft and hard constituents of the jet.…”

A modified in-medium evolution equation with color coherence

“…See[25][26][27][28][29] for recent efforts 2. See the discussion on the multiple soft emission region conducted in[9,11].…”