A local Monte Carlo framework for coherent QCD parton energy loss

  • Korinna Christine Zapp
  • Johanna Stachel
  • Urs Achim Wiedemann
Open Access


Monte Carlo (MC) simulations are the standard tool for describing jet-like multi-particle final states. To apply them to the simulation of medium-modified jets in heavy ion collisions, a probabilistic implementation of medium-induced quantum interference effects is needed. Here, we analyze in detail how the quantum interference effects included in the Baier-Dokshitzer-Mueller-Peigné-Schiff–Zakharov (BDMPS-Z) formalism of medium-induced gluon radiation can be implemented in a quantitatively controlled, local probabilistic parton cascade. The resulting MC algorithm is formulated in terms of elastic and inelastic mean free paths, and it is by construction insensitive to the IR and UV divergences of the total elastic and inelastic cross sections that serve as its basic building blocks in the incoherent limit. Interference effects are implemented by reweighting gluon production histories as a function of the number of scattering centers that act within the gluon formation time. Unlike existing implementations based on gluon formation time, we find generic arguments for why a quantitative implementation of quantum interference cannot amount to a mere dead-time requirement for subsequent gluon production. We validate the proposed MC algorithm by comparing MC simulations with parametric dependencies and analytical results of the BDMPS-Z formalism. In particular, we show that the MC algorithm interpolates correctly between analytically known limiting cases for totally coherent and incoherent gluon production, and that it accounts quantitatively for the medium-induced gluon energy distribution ωdI/dω and the resulting average parton energy loss. We also verify that the MC algorithm implements the transverse momentum broadening of the BDMPS-Z formalism. We finally discuss why the proposed MC algorithm provides a suitable starting point for going beyond the approximations of the BDMPS-Z formalism.


QCD Phenomenology 


  1. [1]
    STAR collaboration, J. Adams et al., Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757 (2005) 102 [nucl-ex/0501009] [SPIRES].ADSCrossRefGoogle Scholar
  2. [2]
    PHENIX collaboration, K. Adcox et al., Formation of dense partonic matter in relativistic nucleus nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration, Nucl. Phys. A 757 (2005) 184 [nucl-ex/0410003] [SPIRES].ADSGoogle Scholar
  3. [3]
    CERES/NA45 collaboration, G. Agakichiev et al., Semi-hard scattering unraveled from collective dynamics by two-pion correlations in 158-A-GeV/c Pb + Au collisions, Phys. Rev. Lett. 92 (2004) 032301 [nucl-ex/0303014] [SPIRES].ADSCrossRefGoogle Scholar
  4. [4]
    D.G. d’Enterria, Indications of suppressed high p T hadron production in nucleus nucleus collisions at CERN-SPS, Phys. Lett. B 596 (2004) 32 [nucl-ex/0403055] [SPIRES].ADSGoogle Scholar
  5. [5]
    STAR collaboration, M. Płoskoń, Inclusive cross section and correlations of fully reconstructed jets in 200 GeV Au + Au and p + p collisions, Nucl. Phys. A 830 (2009) 255c–258c [arXiv:0908.1799] [SPIRES].ADSGoogle Scholar
  6. [6]
    STAR collaboration, E. Bruna, Measurements of jet structure and fragmentation from full jet reconstruction in heavy ion collisions at RHIC, Nucl. Phys. A 830 (2009) 267c–270c [arXiv:0907.4788] [SPIRES].ADSGoogle Scholar
  7. [7]
    PHENIX collaboration, Y.-S. Lai, Probing medium-induced energy loss with direct jet reconstruction in p + p and Cu + Cu collisions at PHENIX, Nucl. Phys. A 830 (2009) 251c–254c [arXiv:0907.4725] [SPIRES].ADSGoogle Scholar
  8. [8]
    ALICE collaboration, K. Aamodt et al., Suppression of Charged Particle Production at Large Transverse Momentum in Central Pb-Pb Collisions at \( \sqrt {{{s_{NN}}}} = 2.76 \)276 TeV, Phys. Lett. B 696 (2011) 30 [arXiv:1012.1004] [SPIRES].ADSGoogle Scholar
  9. [9]
    ATLAS collaboration, G. Aad et al., Observation of a Centrality-Dependent Dijet Asymmetry in Lead-Lead Collisions at \( \sqrt {{{S_{NN}}}} = 2.76 \) TeV with the ATLAS Detector at the LHC, Phys. Rev. Lett. 105 (2010) 252303 [arXiv:1011.6182] [SPIRES].ADSCrossRefGoogle Scholar
  10. [10]
    CMS collaboration, S. Chatrchyan et al., Observation and studies of jet quenching in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV, arXiv:1102.1957 [SPIRES].
  11. [11]
    J. Casalderrey-Solana, J.G. Milhano and U.A. Wiedemann, Jet Quenching via Jet Collimation, J. Phys. G 38 (2011) 035006 [arXiv:1012.0745] [SPIRES].ADSGoogle Scholar
  12. [12]
    U.A. Wiedemann, Jet Quenching in Heavy Ion Collisions, arXiv:0908.2306 [SPIRES].
  13. [13]
    J. Casalderrey-Solana and C.A. Salgado, Introductory lectures on jet quenching in heavy ion collisions, Acta Phys. Polon. B 38 (2007) 3731 [arXiv:0712.3443] [SPIRES].ADSGoogle Scholar
  14. [14]
    A. Majumder and M. Van Leeuwen, The theory and phenomenology of perturbative QCD based jet quenching, arXiv:1002.2206 [SPIRES].
  15. [15]
    P. Jacobs and X.-N. Wang, Matter in extremis: Ultrarelativistic nuclear collisions at RHIC, Prog. Part. Nucl. Phys. 54 (2005) 443 [hep-ph/0405125] [SPIRES].ADSCrossRefGoogle Scholar
  16. [16]
    M. Gyulassy, I. Vitev, X.-N. Wang and B.-W. Zhang, Jet quenching and radiative energy loss in dense nuclear matter, nucl-th/0302077 [SPIRES].
  17. [17]
    M. Cacciari, J. Rojo, G.P. Salam and G. Soyez, Jet Reconstruction in Heavy Ion Collisions, Eur. Phys. J. C 71 (2011) 1539 [arXiv:1010.1759] [SPIRES].ADSGoogle Scholar
  18. [18]
    M. Gyulassy and X.-N. Wang, HIJING 1.0: A Monte Carlo program for parton and particle production in high-energy hadronic and nuclear collisions, Comput. Phys. Commun. 83 (1994) 307 [nucl-th/9502021] [SPIRES].ADSCrossRefGoogle Scholar
  19. [19]
    W.-T. Deng, X.-N. Wang and R. Xu, Hadron production in p + p, p + Pb and Pb + Pb collisions with the HIJING 2.0 model at energies available at the CERN Large Hadron Collider, Phys. Rev. C 83 (2011) 014915 [arXiv:1008.1841] [SPIRES].ADSGoogle Scholar
  20. [20]
    N. Armesto, L. Cunqueiro and C.A. Salgado, Q-PYTHIA: a medium-modified implementation of final state radiation, Eur. Phys. J. C 63 (2009) 679 [arXiv:0907.1014] [SPIRES]. ADSCrossRefGoogle Scholar
  21. [21]
    N. Armesto, G. Corcella, L. Cunqueiro and C.A. Salgado, Angular-ordered parton showers with medium-modified splitting functions, JHEP 11 (2009) 122 [arXiv:0909.5118][SPIRES].ADSCrossRefGoogle Scholar
  22. [22]
    I.P. Lokhtin and A.M. Snigirev, A model of jet quenching in ultrarelativistic heavy ion collisions and high-p T hadron spectra at RHIC, Eur. Phys. J. C 45 (2006) 211 [hep-ph/0506189] [SPIRES].ADSCrossRefGoogle Scholar
  23. [23]
    I.P. Lokhtin et al., Heavy ion event generator HYDJET++ (HYDrodynamics plus JETs), Comput. Phys. Commun. 180 (2009) 779 [arXiv:0809.2708] [SPIRES].ADSCrossRefGoogle Scholar
  24. [24]
    T. Renk, Parton shower evolution in a 3−D hydrodynamical medium, Phys. Rev. C 78 (2008) 034908 [arXiv:0806.0305] [SPIRES].ADSGoogle Scholar
  25. [25]
    T. Renk, A comparison study of medium-modified QCD shower evolution scenarios, Phys. Rev. C 79 (2009) 054906 [arXiv:0901.2818] [SPIRES].ADSGoogle Scholar
  26. [26]
    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] [SPIRES].ADSGoogle Scholar
  27. [27]
    K. Zapp, G. Ingelman, J. Rathsman, J. Stachel and U.A. Wiedemann, A Monte Carlo Model for ’Jet Quenching’, Eur. Phys. J. C 60 (2009) 617 [arXiv:0804.3568] [SPIRES].ADSCrossRefGoogle Scholar
  28. [28]
    K.C. Zapp, Monte Carlo simulations of jet quenching in heavy ion collisions, Nucl. Phys. A 855 (2011) 60 [arXiv:1012.0177] [SPIRES].ADSGoogle Scholar
  29. [29]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [SPIRES].ADSzbMATHCrossRefGoogle Scholar
  30. [30]
    M. Bahr et al., HERWIG++ Physics and Manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [SPIRES].ADSCrossRefGoogle Scholar
  31. [31]
    T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [SPIRES].ADSCrossRefGoogle Scholar
  32. [32]
    R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigné 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] [SPIRES].ADSCrossRefGoogle Scholar
  33. [33]
    R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigné 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] [SPIRES].ADSCrossRefGoogle Scholar
  34. [34]
    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] [SPIRES].ADSCrossRefGoogle Scholar
  35. [35]
    B.G. Zakharov, Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD, JETP Lett. 63 (1996) 952 [hep-ph/9607440] [SPIRES].ADSCrossRefGoogle Scholar
  36. [36]
    U.A. Wiedemann, Gluon radiation off hard quarks in a nuclear environment: Opacity expansion, Nucl. Phys. B 588 (2000) 303 [hep-ph/0005129] [SPIRES].ADSCrossRefGoogle Scholar
  37. [37]
    M. Gyulassy, P. Levai and I. Vitev, Reaction operator approach to non-Abelian energy loss, Nucl. Phys. B 594 (2001) 371 [nucl-th/0006010] [SPIRES].ADSCrossRefGoogle Scholar
  38. [38]
    X.-N. Wang and X.-f. Guo, Multiple parton scattering in nuclei: Parton energy loss, Nucl. Phys. A 696 (2001) 788 [hep-ph/0102230] [SPIRES].ADSGoogle Scholar
  39. [39]
    P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon and Gluon Emission in Relativistic Plasmas, JHEP 06 (2002) 030 [hep-ph/0204343] [SPIRES].ADSCrossRefGoogle Scholar
  40. [40]
    Y. Mehtar-Tani, C.A. Salgado and K. Tywoniuk, Antiangular Ordering of Gluon Radiation in QCD Media, Phys. Rev. Lett. 106 (2011) 122002 [arXiv:1009.2965] [SPIRES].ADSCrossRefGoogle Scholar
  41. [41]
    Y. Mehtar-Tani, C.A. Salgado and K. Tywoniuk, Jets in QCD media: from color coherence to decoherence, arXiv:1102.4317 [SPIRES].
  42. [42]
    K. Zapp, J. Stachel and U.A. Wiedemann, A local Monte Carlo implementation of the non-abelian Landau-Pomerantschuk-Migdal effect, Phys. Rev. Lett. 103 (2009) 152302 [arXiv:0812.3888] [SPIRES].ADSCrossRefGoogle Scholar
  43. [43]
    M. Gyulassy and X.-n. Wang, Multiple collisions and induced gluon Bremsstrahlung in QCD, Nucl. Phys. B 420 (1994) 583 [nucl-th/9306003] [SPIRES].ADSCrossRefGoogle Scholar
  44. [44]
    X.-N. Wang, M. Gyulassy and M. Plumer, The LPM effect in QCD and radiative energy loss in a quark gluon plasma, Phys. Rev. D 51 (1995) 3436 [hep-ph/9408344] [SPIRES].ADSGoogle Scholar
  45. [45]
    J.F. Gunion and G. Bertsch, Hadronization by color Bremsstrahlung, Phys. Rev. D 25 (1982) 746 [SPIRES].ADSGoogle Scholar
  46. [46]
    R. Baier, Y.L. Dokshitzer, A.H. Mueller and D. Schiff, On the angular dependence of the radiative gluon spectrum, Phys. Rev. C 64 (2001) 057902 [hep-ph/0105062] [SPIRES].ADSGoogle Scholar
  47. [47]
    C.A. Salgado and U.A. Wiedemann, Medium modification of jet shapes and jet multiplicities, Phys. Rev. Lett. 93 (2004) 042301 [hep-ph/0310079] [SPIRES].ADSCrossRefGoogle Scholar
  48. [48]
    C.A. Salgado and U.A. Wiedemann, Calculating quenching weights, Phys. Rev. D 68 (2003) 014008 [hep-ph/0302184] [SPIRES].ADSGoogle Scholar

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© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Korinna Christine Zapp
    • 1
  • Johanna Stachel
    • 2
  • Urs Achim Wiedemann
    • 3
  1. 1.Institute for Particle Physics PhenomenologyDurham UniversityDurhamU.K.
  2. 2.Physikalisches InstitutUniversität HeidelbergHeidelbergGermany
  3. 3.Department of PhysicsCERN, Theory UnitGeneva 23Switzerland

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