Abstract
We study the gluon cascade generated via successive medium-induced branchings by an energetic parton propagating through a dense QCD medium. We focus on the high-energy regime where the energy E of the leading particle is much larger than the characteristic medium scale \( {\omega}_c=\widehat{q}{L}^2/2 \), with q the jet quenching parameter and L the distance travelled through the medium. In this regime the leading particle loses only a small fraction ∼ α s (ω c /E) of its energy and can be treated as a steady source of radiation for gluons with energies ω ≤ ω c . For this effective problem with a source, we obtain exact analytic solutions for the gluon spectrum and the energy flux. These solutions exhibit wave turbulence: the basic physical process is a continuing fragmentation which is ‘quasi-democratic’ (i.e. quasi-local in energy) and which provides an energy transfer from the source to the medium at a rate (the energy flux ℱ ) which is quasi-independent of ω. The locality of the branching process implies a spectrum of the Kolmogorov-Obukhov type, i.e. a power-law spectrum which is a fixed point of the branching process and whose strength is proportional to the energy flux: \( D\left(\omega \right)\sim \mathrm{\mathcal{F}}/\sqrt{\omega } \) for ω ≪ ω c . Via this turbulent flow, the gluon cascade loses towards the medium an energy ΔE ∼ α 2 s ω c , which is independent of the initial energy E of the leading particle and of the details of the thermalization mechanism at the low-energy end of the cascade. This energy is carried away by very soft gluons, which propagate at very large angles with respect to the jet axis. Our predictions for the value of ΔE and for its angular distribution appear to agree quite well, qualitatively and even semi-quantitatively, with the phenomenology of di-jet asymmetry in nucleus-nucleus collisions at the LHC.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at \( \sqrt{s_{NN}} \) = 2.77 TeV with the ATLAS detector at the LHC, Phys. Rev. Lett. 105 (2010) 252303 [arXiv:1011.6182] [INSPIRE].
CMS collaboration, Observation and studies of jet quenching in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV, Phys. Rev. C 84 (2011) 024906 [arXiv:1102.1957] [INSPIRE].
CMS collaboration, Jet momentum dependence of jet quenching in PbPb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Lett. B 712 (2012) 176 [arXiv:1202.5022] [INSPIRE].
ATLAS collaboration, Measurement of the jet radius and transverse momentum dependence of inclusive jet suppression in lead-lead collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV with the ATLAS detector, Phys. Lett. B 719 (2013) 220 [arXiv:1208.1967] [INSPIRE].
CMS collaboration, Modification of jet shapes in PbPb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Lett. B 730 (2014) 243 [arXiv:1310.0878] [INSPIRE].
CMS collaboration, Measurement of jet fragmentation in PbPb and pp collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Rev. C 90 (2014) 024908 [arXiv:1406.0932] [INSPIRE].
ATLAS collaboration, Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV with the ATLAS detector, Phys. Lett. B 739 (2014) 320 [arXiv:1406.2979] [INSPIRE].
CMS collaboration, Measurement of momentum flow relative to the dijet system in PbPb and pp collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, CMS-PAS-HIN-14-010 (2014.
Y. Mehtar-Tani, C.A. Salgado and K. Tywoniuk, Anti-angular ordering of gluon radiation in QCD media, Phys. Rev. Lett. 106 (2011) 122002 [arXiv:1009.2965] [INSPIRE].
Y. Mehtar-Tani, C.A. Salgado and K. Tywoniuk, Jets in QCD media: from color coherence to decoherence, Phys. Lett. B 707 (2012) 156 [arXiv:1102.4317] [INSPIRE].
J. Casalderrey-Solana, J.G. Milhano and U.A. Wiedemann, Jet quenching via jet collimation, J. Phys. G 38 (2011) 035006 [arXiv:1012.0745] [INSPIRE].
G.-Y. Qin and B. Müller, Explanation of di-jet asymmetry in Pb+Pb collisions at the Large Hadron Collider, Phys. Rev. Lett. 106 (2011) 162302 [Erratum ibid. 108 (2012) 189904] [arXiv:1012.5280] [INSPIRE].
J. Casalderrey-Solana and E. Iancu, Interference effects in medium-induced gluon radiation, JHEP 08 (2011) 015 [arXiv:1105.1760] [INSPIRE].
J.-P. Blaizot, F. Dominguez, E. Iancu and Y. Mehtar-Tani, Medium-induced gluon branching, JHEP 01 (2013) 143 [arXiv:1209.4585] [INSPIRE].
J. Casalderrey-Solana, Y. Mehtar-Tani, C.A. Salgado and K. Tywoniuk, New picture of jet quenching dictated by color coherence, Phys. Lett. B 725 (2013) 357 [arXiv:1210.7765] [INSPIRE].
J.-P. Blaizot, E. Iancu and Y. Mehtar-Tani, Medium-induced QCD cascade: democratic branching and wave turbulence, Phys. Rev. Lett. 111 (2013) 052001 [arXiv:1301.6102] [INSPIRE].
J.-P. Blaizot, F. Dominguez, E. Iancu and Y. Mehtar-Tani, Probabilistic picture for medium-induced jet evolution, JHEP 06 (2014) 075 [arXiv:1311.5823] [INSPIRE].
E. Iancu, Di-jet asymmetry and wave turbulence, arXiv:1404.4566 [INSPIRE].
A. Kurkela and U.A. Wiedemann, Picturing perturbative parton cascades in QCD matter, Phys. Lett. B 740 (2015) 172 [arXiv:1407.0293] [INSPIRE].
J.-P. Blaizot, Y. Mehtar-Tani and M.A.C. Torres, Angular structure of the in-medium QCD cascade, arXiv:1407.0326 [INSPIRE].
L. Apolinário, N. Armesto, J.G. Milhano and C.A. Salgado, Medium-induced gluon radiation and colour decoherence beyond the soft approximation, JHEP 02 (2015) 119 [arXiv:1407.0599] [INSPIRE].
R. Baier, A.H. Mueller, D. Schiff and D.T. Son, ‘Bottom up’ thermalization in heavy ion collisions, Phys. Lett. B 502 (2001) 51 [hep-ph/0009237] [INSPIRE].
S. Jeon and G.D. Moore, Energy loss of leading partons in a thermal QCD medium, Phys. Rev. C 71 (2005) 034901 [hep-ph/0309332] [INSPIRE].
B. Schenke, C. Gale and S. Jeon, MARTINI: an event generator for relativistic heavy-ion collisions, Phys. Rev. C 80 (2009) 054913 [arXiv:0909.2037] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma, Nucl. Phys. B 483 (1997) 291 [hep-ph/9607355] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss and p T broadening of high-energy partons in nuclei, Nucl. Phys. B 484 (1997) 265 [hep-ph/9608322] [INSPIRE].
B.G. Zakharov, Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD, JETP Lett. 63 (1996) 952 [hep-ph/9607440] [INSPIRE].
B.G. Zakharov, Radiative energy loss of high-energy quarks in finite size nuclear matter and quark-gluon plasma, JETP Lett. 65 (1997) 615 [hep-ph/9704255] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller and D. Schiff, Medium induced radiative energy loss: equivalence between the BDMPS and Zakharov formalisms, Nucl. Phys. B 531 (1998) 403 [hep-ph/9804212] [INSPIRE].
V. Zakharov, V. Lvov and G. Falkovich, Kolmogorov spectra of turbulence, volume 1, Springer, Germany (1992).
S. Nazarenko, Wave turbulence, Springer, Germany (2011).
A. Kurkela and G.D. Moore, Thermalization in weakly coupled nonabelian plasmas, JHEP 12 (2011) 044 [arXiv:1107.5050] [INSPIRE].
T. Liou, A.H. Mueller and B. Wu, Radiative p ⊥ -broadening of high-energy quarks and gluons in QCD matter, Nucl. Phys. A 916 (2013) 102 [arXiv:1304.7677] [INSPIRE].
E. Iancu, The non-linear evolution of jet quenching, JHEP 1410 (2014) 95 [arXiv:1403.1996] [INSPIRE].
J.-P. Blaizot and Y. Mehtar-Tani, Renormalization of the jet-quenching parameter, Nucl. Phys. A 929 (2014) 202 [arXiv:1403.2323] [INSPIRE].
E. Iancu and D.N. Triantafyllopoulos, Running coupling effects in the evolution of jet quenching, Phys. Rev. D 90 (2014) 074002 [arXiv:1405.3525] [INSPIRE].
B. Wu, Radiative energy loss and radiative p ⊥ -broadening of high-energy partons in QCD matter, JHEP 12 (2014) 081 [arXiv:1408.5459] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller and D. Schiff, Quenching of hadron spectra in media, JHEP 09 (2001) 033 [hep-ph/0106347] [INSPIRE].
JET collaboration, K.M. Burke et al., Extracting the jet transport coefficient from jet quenching in high-energy heavy-ion collisions, Phys. Rev. C 90 (2014) 014909 [arXiv:1312.5003] [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1409.2010
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Fister, L., Iancu, E. Medium-induced jet evolution: wave turbulence and energy loss. J. High Energ. Phys. 2015, 82 (2015). https://doi.org/10.1007/JHEP03(2015)082
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2015)082