Improved opacity expansion for medium-induced parton splitting
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Springer
Received: November Revised: May Accepted: June Published: June
22, 29, 10, 30,
2019 2020 2020 2020
Yacine Mehtar-Tania and Konrad Tywoniukb a
Physics Department, Brookhaven National Laboratory, Upton, NY 11973, U.S.A. b Department of Physics and Technology, University of Bergen, 5007 Bergen, Norway
E-mail: [email protected], [email protected] Abstract: We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This provides the tools to go beyond the leading logarithmic approximation and compare to the full numerical solution to the corresponding Schr¨ odinger equation across a wide range of gluon frequencies. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed. Keywords: Heavy Ion Phenomenology, Jets ArXiv ePrint: 1910.02032
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)187
JHEP06(2020)187
Improved opacity expansion for medium-induced parton splitting
Contents 1
2 Spectrum of medium-induced gluons
2
3 Expanding around the harmonic oscillator 3.1 Leading order: the harmonic oscillator approximation 3.2 Next-to-leading order correction to the harmonic oscillator
5 6 7
4 Numerics
10
5 Conclusions
12
1
Introduction
Measurements of significant modifications of hard probes observables, in particular jets, in heavy ion collisions as compared to proton-proton collisions at RHIC and LHC have firmly established the prominent role of final-state interactions in the dense nuclear medium created in heavy-ion collisions. For large systems, radiative processes are the main mechanism responsible for the observed quenching effects [1] (for recent reviews see [2, 3]). Therefore a precise description of these processes is essential for a quantitative understanding of the mechanisms driving in-medium jet modification and probing non-equilibrium dynamics of the quark-gluon plasma (QGP). For energetic particles propagating close to the light-cone through a QCD medium, the problem reduces to describing the (non-relativistic) dynamics in the transverse plane perpendicular to the direction of propagation. A formalism for dealing with multiple scattering in a QCD medium was developed by Baier-Dokshitzer-Mueller-Peign´e-Schiff [4, 5] and Zakharov [6, 7], usually referred to as the BDMPS-Z formalism.1 This resummation [9] can also be cast as an expansion in medium opacity [10–13].2 The regime of strong interactions can be approximated by diffusive broadening of the transverse momentum, governed by the diff
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