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Journal of High Energy Physics

, 2017:140 | Cite as

Thermodynamical string fragmentation

  • Nadine Fischer
  • Torbjörn Sjöstrand
Open Access
Regular Article - Theoretical Physics

Abstract

The observation of heavy-ion-like behaviour in pp collisions at the LHC suggests that more physics mechanisms are at play than traditionally assumed. The introduction e.g. of quark-gluon plasma or colour rope formation can describe several of the observations, but as of yet there is no established paradigm. In this article we study a few possible modifications to the Pythia event generator, which describes a wealth of data but fails for a number of recent observations. Firstly, we present a new model for generating the transverse momentum of hadrons during the string fragmentation process, inspired by thermodynamics, where heavier hadrons naturally are suppressed in rate but obtain a higher average transverse momentum. Secondly, close-packing of strings is taken into account by making the temperature or string tension environment-dependent. Thirdly, a simple model for hadron rescattering is added. The effect of these modifications is studied, individually and taken together, and compared with data mainly from the LHC. While some improvements can be noted, it turns out to be nontrivial to obtain effects as big as required, and further work is called for.

Keywords

Phenomenological Models QCD Phenomenology 

Notes

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.

References

  1. [1]
    G.P. Salam, QCD Theory Overview — Towards Precision at LHC, (2016), https://indico.cern.ch/event/442390/contributions/1095992/.
  2. [2]
    B. Andersson, G. Gustafson, G. Ingelman and T. Sjöstrand, Parton Fragmentation and String Dynamics, Phys. Rept. 97 (1983) 31 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    R.D. Field and S. Wolfram, A QCD Model for e + e Annihilation, Nucl. Phys. B 213 (1983) 65 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    T.D. Gottschalk, An Improved Description of Hadronization in the QCD Cluster Model for e + e Annihilation, Nucl. Phys. B 239 (1984) 349 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    B.R. Webber, A QCD Model for Jet Fragmentation Including Soft Gluon Interference, Nucl. Phys. B 238 (1984) 492 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    A. Ortiz Velasquez, P. Christiansen, E. Cuautle Flores, I. Maldonado Cervantes and G. Paić, Color Reconnection and Flowlike Patterns in pp Collisions, Phys. Rev. Lett. 111 (2013) 042001 [arXiv:1303.6326] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    CMS collaboration, Observation of Long-Range Near-Side Angular Correlations in Proton-Proton Collisions at the LHC, JHEP 09 (2010) 091 [arXiv:1009.4122] [INSPIRE].
  8. [8]
    ATLAS collaboration, Observation of Long-Range Elliptic Azimuthal Anisotropies in \( \sqrt{s}=13 \) and 2.76 TeV pp Collisions with the ATLAS Detector, Phys. Rev. Lett. 116 (2016) 172301 [arXiv:1509.04776] [INSPIRE].
  9. [9]
    CMS collaboration, Evidence for collectivity in pp collisions at the LHC, Phys. Lett. B 765 (2017)193 [arXiv:1606.06198] [INSPIRE].
  10. [10]
    ALICE collaboration, Multiplicity-dependent enhancement of strange and multi-strange hadron production in proton-proton collisions at \( \sqrt{s}=7 \) TeV, arXiv:1606.07424 [INSPIRE].
  11. [11]
    E. Cuautle and G. Paić, The energy density representation of the strangeness enhancement from p+p to Pb+Pb, arXiv:1608.02101 [INSPIRE].
  12. [12]
    P. Braun-Munzinger and J. Stachel, The quest for the quark-gluon plasma, Nature 448 (2007) 302 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    T. Pierog, I. Karpenko, J.M. Katzy, E. Yatsenko and K. Werner, EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider, Phys. Rev. C 92 (2015) 034906 [arXiv:1306.0121] [INSPIRE].ADSGoogle Scholar
  14. [14]
    T.S. Biro, H.B. Nielsen and J. Knoll, Color Rope Model for Extreme Relativistic Heavy Ion Collisions, Nucl. Phys. B 245 (1984) 449 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A. Bialas and W. Czyz, Chromoelectric Flux Tubes and the Transverse Momentum Distribution in High-energy Nucleus-nucleus Collisions, Phys. Rev. D 31 (1985) 198 [INSPIRE].ADSGoogle Scholar
  16. [16]
    B. Andersson and P.A. Henning, On the dynamics of a color rope: The fragmentation of interacting strings and the longitudinal distributions, Nucl. Phys. B 355 (1991) 82 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    C. Bierlich, G. Gustafson, L. Lönnblad and A. Tarasov, Effects of Overlapping Strings in pp Collisions, JHEP 03 (2015) 148 [arXiv:1412.6259] [INSPIRE].CrossRefGoogle Scholar
  18. [18]
    P. Capiluppi, G. Giacomelli, A.M. Rossi, G. Vannini and A. Bussiere, Transverse momentum dependence in proton proton inclusive reactions at very high-energies, Nucl. Phys. B 70 (1974) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3 (1965) 147 [INSPIRE].Google Scholar
  20. [20]
    R. Hagedorn, Remarks on the thermodynamical model of strong interactions, Nucl. Phys. B 24 (1970) 93 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    R. Hagedorn, Multiplicities, p T Distributions and the Expected Hadronquark-gluon Phase Transition, Riv. Nuovo Cim. 6N10 (1983) 1 [INSPIRE].
  22. [22]
    S. Barshay and Y.A. Chao, Longitudinal mass, inclusive transverse-momentum distributions, proton proton elastic diffraction slopes and the total cross-section, Phys. Lett. B 38 (1972) 225 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    C. Tsallis, Possible Generalization of Boltzmann-Gibbs Statistics, J. Statist. Phys. 52 (1988) 479 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    J. Cleymans, On the Use of the Tsallis Distribution at LHC Energies, arXiv:1609.02289 [INSPIRE].
  25. [25]
    A.A. Bylinkin and A.A. Rostovtsev, Parametrization of the shape of hadron-production spectra in high-energy particle interactions, Phys. Atom. Nucl. 75 (2012) 999 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    T. Sjöstrand and M. van Zijl, A Multiple Interaction Model for the Event Structure in Hadron Collisions, Phys. Rev. D 36 (1987) 2019 [INSPIRE].ADSGoogle Scholar
  27. [27]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
  28. [28]
    T. Sjöstrand et al., An Introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
  29. [29]
    X. Artru and G. Mennessier, String model and multiproduction, Nucl. Phys. B 70 (1974) 93 [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    B. Andersson, G. Gustafson and B. Soderberg, A Probability Measure on Parton and String States, Nucl. Phys. B 264 (1986) 29 [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
  32. [32]
    B. Andersson, G. Gustafson and T. Sjöstrand, How to Find the Gluon Jets in e + e Annihilation, Phys. Lett. B 94 (1980) 211 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    JADE collaboration, W. Bartel et al., Experimental study of jets in electron-positron annihilation, Phys. Lett. B 101 (1981) 129 [INSPIRE].
  34. [34]
    T. Sjöstrand, Jet Fragmentation of Nearby Partons, Nucl. Phys. B 248 (1984) 469 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    T. Sjöstrand and P.Z. Skands, Baryon number violation and string topologies, Nucl. Phys. B 659 (2003) 243 [hep-ph/0212264] [INSPIRE].
  36. [36]
    B. Andersson, G. Gustafson and T. Sjöstrand, On Soft Gluon Emission and the Transverse Momentum Properties of Final State Particles, Z. Phys. C 12 (1982) 49 [INSPIRE].ADSGoogle Scholar
  37. [37]
    F.E. Close, An Introduction to Quarks and Partons, Academic Press, London (1979).Google Scholar
  38. [38]
    B. Andersson, G. Gustafson and T. Sjöstrand, A Model for Baryon Production in Quark and Gluon Jets, Nucl. Phys. B 197 (1982) 45 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    B. Andersson, G. Gustafson and T. Sjöstrand, Baryon Production in Jet Fragmentation and Y Decay, Phys. Scripta 32 (1985) 574 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    S. Platzer and S. Gieseke, Dipole Showers and Automated NLO Matching in HERWIG++, Eur. Phys. J. C 72 (2012) 2187 [arXiv:1109.6256] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    P. Richardson and D. Winn, Investigation of Monte Carlo Uncertainties on Higgs Boson searches using Jet Substructure, Eur. Phys. J. C 72 (2012) 2178 [arXiv:1207.0380] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    S. Chun and C. Buchanan, A Simple plausible path from QCD to successful prediction of e + e hadronization data, Phys. Rept. 292 (1998) 239 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    S. Abachi, C. Buchanan, A. Chien, S. Chun and B. Hartfiel, UCLA space-time area law model: A persuasive foundation for hadronization, Eur. Phys. J. C 49 (2007) 569 [hep-ph/0612103] [INSPIRE].
  44. [44]
    A. Buckley et al., Rivet user manual, Comput. Phys. Commun. 184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    STAR collaboration, B.I. Abelev et al., Systematic Measurements of Identified Particle Spectra in pp, d + Au and Au+Au Collisions from STAR, Phys. Rev. C 79 (2009) 034909 [arXiv:0808.2041] [INSPIRE].
  46. [46]
    ALICE collaboration, Production of Σ(1385)± and Ξ(1530)0 in proton-proton collisions at \( \sqrt{s}=7 \) TeV, Eur. Phys. J. C 75 (2015) 1 [arXiv:1406.3206] [INSPIRE].
  47. [47]
    ATLAS collaboration, Charged-particle multiplicities in pp interactions measured with the ATLAS detector at the LHC, New J. Phys. 13 (2011) 053033 [arXiv:1012.5104] [INSPIRE].
  48. [48]
    ALICE collaboration, Strangeness production as a function of charged particle multiplicity in proton-proton collisions, Nucl. Phys. A 956 (2016) 777 [arXiv:1604.06736] [INSPIRE].
  49. [49]
    CMS collaboration, Charged particle transverse momentum spectra in pp collisions at \( \sqrt{s}=0.9 \) and 7 TeV, JHEP 08 (2011) 086 [arXiv:1104.3547] [INSPIRE].
  50. [50]
    ALICE collaboration, Pseudorapidity and transverse-momentum distributions of charged particles in proton-proton collisions at \( \sqrt{s}=13 \) TeV, Phys. Lett. B 753 (2016) 319 [arXiv:1509.08734] [INSPIRE].
  51. [51]
    ALICE collaboration, Measurement of pion, kaon and proton production in proton-proton collisions at \( \sqrt{s}=7 \) TeV, Eur. Phys. J. C 75 (2015) 226 [arXiv:1504.00024] [INSPIRE].
  52. [52]
    CMS collaboration, Strange Particle Production in pp Collisions at \( \sqrt{s}=0.9 \) and 7 TeV, JHEP 05 (2011) 064 [arXiv:1102.4282] [INSPIRE].
  53. [53]
    UA1 collaboration, C. Albajar et al., A Study of the General Characteristics of \( p\overline{p} \) Collisions at \( \sqrt{s}=0.2 \) TeV to 0.9 TeV, Nucl. Phys. B 335 (1990) 261 [INSPIRE].
  54. [54]
    T. Sjöstrand and V.A. Khoze, On color rearrangement in hadronic W+ W- events, Z. Phys. C 62 (1994) 281 [hep-ph/9310242] [INSPIRE].
  55. [55]
    J.R. Christiansen and P.Z. Skands, String Formation Beyond Leading Colour, JHEP 08 (2015) 003 [arXiv:1505.01681] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn and V.F. Weisskopf, A New Extended Model of Hadrons, Phys. Rev. D 9 (1974) 3471 [INSPIRE].ADSMathSciNetGoogle Scholar
  57. [57]
    H. Sorge, H. Stoecker and W. Greiner, Poincaré Invariant Hamiltonian Dynamics: Modeling Multi-Hadronic Interactions in a Phase Space Approach, Annals Phys. 192 (1989) 266 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  58. [58]
    H. Sorge, M. Berenguer, H. Stoecker and W. Greiner, Color rope formation and strange baryon production in ultrarelativistic heavy ion collisions, Phys. Lett. B 289 (1992) 6 [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    S.A. Bass et al., Microscopic models for ultrarelativistic heavy ion collisions, Prog. Part. Nucl. Phys. 41 (1998) 255 [nucl-th/9803035] [INSPIRE].
  60. [60]
    M. Bleicher et al., Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model, J. Phys. G 25 (1999) 1859 [hep-ph/9909407] [INSPIRE].
  61. [61]
    S. Soff et al., Enhanced strange particle yields - signal of a phase of massless particles?, J. Phys. G 27 (2001) 449 [nucl-th/0010103] [INSPIRE].
  62. [62]
    S. Soff, J. Randrup, H. Stoecker and N. Xu, Effects of strong color fields on baryon dynamics, Phys. Lett. B 551 (2003) 115 [nucl-th/0209093] [INSPIRE].
  63. [63]
    B. Zhang, C.M. Ko, B.-A. Li and Z.-w. Lin, A multiphase transport model for nuclear collisions at RHIC, Phys. Rev. C 61 (2000) 067901 [nucl-th/9907017] [INSPIRE].
  64. [64]
    Z.-W. Lin, C.M. Ko, B.-A. Li, B. Zhang and S. Pal, A multi-phase transport model for relativistic heavy ion collisions, Phys. Rev. C 72 (2005) 064901 [nucl-th/0411110] [INSPIRE].
  65. [65]
    Z.-w. Lin, S. Pal, C.M. Ko, B.-A. Li and B. Zhang, Charged particle rapidity distributions at relativistic energies, Phys. Rev. C 64 (2001) 011902 [nucl-th/0011059] [INSPIRE].
  66. [66]
    N.S. Amelin, M.A. Braun and C. Pajares, Multiple production in the Monte Carlo string fusion model, Phys. Lett. B 306 (1993) 312 [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    N.S. Amelin, N. Armesto, C. Pajares and D. Sousa, Monte Carlo model for nuclear collisions from SPS to LHC energies, Eur. Phys. J. C 22 (2001) 149 [hep-ph/0103060] [INSPIRE].
  68. [68]
    M.A. Braun and C. Pajares, Particle production in nuclear collisions and string interactions, Phys. Lett. B 287 (1992) 154 [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    M.A. Braun and C. Pajares, Implications of percolation of color strings on multiplicities, correlations and the transverse momentum, Eur. Phys. J. C 16 (2000) 349 [hep-ph/9907332] [INSPIRE].
  70. [70]
    M.A. Braun and C. Pajares, Transverse momentum distributions and their forward backward correlations in the percolating color string approach, Phys. Rev. Lett. 85 (2000) 4864 [hep-ph/0007201] [INSPIRE].
  71. [71]
    C. Pajares, String and parton percolation, Eur. Phys. J. C 43 (2005) 9 [hep-ph/0501125] [INSPIRE].
  72. [72]
    Particle Data Group collaboration, C. Amsler et al., Review of Particle Physics, Phys. Lett. B 667 (2008) 1 [INSPIRE].
  73. [73]
    British-Scandinavian collaboration, B. Alper et al., Production Spectra of π ± , K ± , ρ ± at Large Angles in Proton Proton Collisions in the CERN Intersecting Storage Rings, Nucl. Phys. B 100 (1975) 237 [INSPIRE].
  74. [74]
    British-Scandinavian-MIT collaboration, K. Guettler et al., Inclusive Production of Low-Momentum Charged Pions at x = 0 at the CERN Intersecting Storage Rings, Phys. Lett. B 64 (1976) 111 [INSPIRE].
  75. [75]
    G. Giacomelli and M. Jacob, Physics at the CERN ISR, Phys. Rept. 55 (1979) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, fourth edition, Academic Press, London (1980).zbMATHGoogle Scholar
  77. [77]
    M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical tables, Dover Publications, New York (1965).zbMATHGoogle Scholar
  78. [78]
    J. Dias de Deus and C. Pajares, Percolation of color sources and critical temperature, Phys. Lett. B 642 (2006) 455 [hep-ph/0607101] [INSPIRE].
  79. [79]
    M. Gyulassy and L. McLerran, New forms of QCD matter discovered at RHIC, Nucl. Phys. A 750 (2005) 30 [nucl-th/0405013] [INSPIRE].
  80. [80]
    U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Ann. Rev. Nucl. Part. Sci. 63 (2013) 123 [arXiv:1301.2826] [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    G. Roland, K. Safarik and P. Steinberg, Heavy-ion collisions at the LHC, Prog. Part. Nucl. Phys. 77 (2014) 70 [INSPIRE].ADSCrossRefGoogle Scholar
  82. [82]
    R.D. Field and R.P. Feynman, A Parametrization of the Properties of Quark Jets, Nucl. Phys. B 136 (1978) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  83. [83]
    CMS collaboration, Transverse-momentum and pseudorapidity distributions of charged hadrons in pp collisions at \( \sqrt{s}=7 \) TeV, Phys. Rev. Lett. 105 (2010) 022002 [arXiv:1005.3299] [INSPIRE].
  84. [84]
    SLD collaboration, K. Abe et al., Production of π + , π , K + , K , p and \( \overline{p} \) in light (uds), c and b jets from Z 0 decays, Phys. Rev. D 69 (2004) 072003 [hep-ex/0310017] [INSPIRE].
  85. [85]
    ALEPH collaboration, R. Barate et al., Studies of quantum chromodynamics with the ALEPH detector, Phys. Rept. 294 (1998) 1 [INSPIRE].
  86. [86]
    STAR collaboration, J. Adams et al., Distributions of charged hadrons associated with high transverse momentum particles in pp and Au + Au collisions at \( \sqrt{s_{\;N\;N}}=200 \) GeV, Phys. Rev. Lett. 95 (2005) 152301 [nucl-ex/0501016] [INSPIRE].
  87. [87]
    STAR collaboration, B.I. Abelev et al., Long range rapidity correlations and jet production in high energy nuclear collisions, Phys. Rev. C 80 (2009) 064912 [arXiv:0909.0191] [INSPIRE].
  88. [88]
    PHOBOS collaboration, B. Alver et al., High transverse momentum triggered correlations over a large pseudorapidity acceptance in Au+Au collisions at \( \sqrt{s_{\;N\;N}}=200 \) GeV, Phys. Rev. Lett. 104 (2010) 062301 [arXiv:0903.2811] [INSPIRE].
  89. [89]
    CMS collaboration, Long-range and short-range dihadron angular correlations in central PbPb collisions at a nucleon-nucleon center of mass energy of 2.76 TeV, JHEP 07 (2011) 076 [arXiv:1105.2438] [INSPIRE].
  90. [90]
    J.-Y. Ollitrault, Anisotropy as a signature of transverse collective flow, Phys. Rev. D 46 (1992) 229 [INSPIRE].
  91. [91]
    S. Voloshin and Y. Zhang, Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions, Z. Phys. C 70 (1996) 665 [hep-ph/9407282] [INSPIRE].
  92. [92]
    Y. Akiba et al., The Hot QCD White Paper: Exploring the Phases of QCD at RHIC and the LHC, arXiv:1502.02730 [INSPIRE].
  93. [93]
    W. Li, Observation of a ‘Ridge’ correlation structure in high multiplicity proton-proton collisions: A brief review, Mod. Phys. Lett. A 27 (2012) 1230018 [arXiv:1206.0148] [INSPIRE].ADSCrossRefGoogle Scholar
  94. [94]
    K. Werner, I. Karpenko and T. Pierog, The ‘Ridge’ in Proton-Proton Scattering at 7 TeV, Phys. Rev. Lett. 106 (2011) 122004 [arXiv:1011.0375] [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    C. Bierlich, G. Gustafson and L. Lönnblad, A shoving model for collectivity in hadronic collisions, arXiv:1612.05132 [INSPIRE].

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© The Author(s) 2017

Authors and Affiliations

  1. 1.Theoretical Particle Physics, Department of Astronomy and Theoretical PhysicsLund UniversityLundSweden
  2. 2.School of Physics and AstronomyMonash UniversityClaytonAustralia

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