Effects of overlapping strings in pp collisions

  • Christian Bierlich
  • Gösta Gustafson
  • Leif Lönnblad
  • Andrey Tarasov
Open Access
Regular Article - Theoretical Physics


In models for hadron collisions based on string hadronization, the strings are usually treated as independent, allowing no interaction between the confined colour fields. In studies of nucleus collisions it has been suggested that strings close in space can fuse to form “colour ropes”. Such ropes are expected to give more strange particles and baryons, which also has been suggested as a signal for plasma formation. Overlapping strings can also be expected in pp collisions, where usually no phase transition is expected. In particular at the high LHC energies the expected density of strings is quite high. To investigate possible effects of rope formation, we present a model in which strings are allowed to combine into higher multiplets, giving rise to increased production of baryons and strangeness, or recombine into singlet structures and vanish. Also a crude model for strings recombining into junction structures is considered, again giving rise to increased baryon production. The models are implemented in the dipsy MC event generator, using Pythia8 for hadronization, and comparison to pp minimum bias data, reveals improvement in the description of identified particle spectra.


QCD Phenomenology Monte Carlo Simulations 


Open Access

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  1. [1]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    M. Bähr et al., HERWIG++ physics and manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    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].CrossRefADSGoogle Scholar
  4. [4]
    A. Białas 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
  5. [5]
    A.K. Kerman, T. Matsui and B. Svetitsky, Particle production in the central rapidity region of ultrarelativistic nuclear collisions, Phys. Rev. Lett. 56 (1986) 219 [INSPIRE].CrossRefADSGoogle Scholar
  6. [6]
    M. Gyulassy and A. Iwazaki, Quark and gluon pair production in SU(N) covariant constant fields, Phys. Lett. B 165 (1985) 157 [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    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].CrossRefADSGoogle Scholar
  8. [8]
    M. Braun and C. Pajares, A probabilistic model of interacting strings, Nucl. Phys. B 390 (1993) 542 [INSPIRE].CrossRefADSGoogle Scholar
  9. [9]
    M. Braun and C. Pajares, Cross-sections and multiplicities in hadron nucleus collisions with interacting color strings, Phys. Rev. D 47 (1993) 114 [INSPIRE].ADSGoogle Scholar
  10. [10]
    N.S. Amelin, M.A. Braun and C. Pajares, String fusion and particle production at high-energies: Monte Carlo string fusion model, Z. Phys. C 63 (1994) 507 [INSPIRE].ADSGoogle Scholar
  11. [11]
    N. Armesto, M.A. Braun, E.G. Ferreiro and C. Pajares, Strangeness enhancement and string fusion in nucleus-nucleus collisions, Phys. Lett. B 344 (1995) 301 [INSPIRE].CrossRefADSGoogle Scholar
  12. [12]
    K. Kajantie and T. Matsui, Decay of strong color electric field and thermalization in ultrarelativistic nucleus-nucleus collisions, Phys. Lett. B 164 (1985) 373 [INSPIRE].CrossRefADSGoogle Scholar
  13. [13]
    G. Gatoff, A.K. Kerman and T. Matsui, The flux tube model for ultrarelativistic heavy ion collisions: electrohydrodynamics of a quark gluon plasma, Phys. Rev. D 36 (1987) 114 [INSPIRE].ADSGoogle Scholar
  14. [14]
    M.A. Braun, C. Pajares and J. Ranft, Fusion of strings versus percolation and the transition to the quark gluon plasma, Int. J. Mod. Phys. A 14 (1999) 2689 [hep-ph/9707363] [INSPIRE].CrossRefADSGoogle Scholar
  15. [15]
    E. Avsar, G. Gustafson and L. Lönnblad, Energy conservation and saturation in small-x evolution, JHEP 07 (2005) 062 [hep-ph/0503181] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    C. Flensburg, G. Gustafson and L. Lönnblad, Inclusive and exclusive observables from dipoles in high energy collisions, JHEP 08 (2011) 103 [arXiv:1103.4321] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    C. Merino, C. Pajares and J. Ranft, Effects of interaction of strings in the dual parton model, Phys. Lett. B 276 (1992) 168 [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    H.J. Möhring, J. Ranft, C. Merino and C. Pajares, String fusion in the dual parton model and the production of anti-hyperons in heavy ion collisions, Phys. Rev. D 47 (1993) 4142 [INSPIRE].ADSGoogle Scholar
  19. [19]
    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].CrossRefADSGoogle Scholar
  20. [20]
    M. Bleicher, W. Greiner, H. Stoecker and N. Xu, Strangeness enhancement from strong color fields at RHIC, Phys. Rev. C 62 (2000) 061901 [hep-ph/0007215] [INSPIRE].ADSGoogle Scholar
  21. [21]
    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].CrossRefADSGoogle Scholar
  22. [22]
    B. Andersson, G. Gustafson and B. Söderberg, A general model for jet fragmentation, Z. Phys. C 20 (1983) 317 [INSPIRE].ADSGoogle Scholar
  23. [23]
    B. Andersson and G. Gustafson, Semiclassical models for gluon jets and leptoproduction based on the massless relativistic string, Z. Phys. C 3 (1980) 223 [INSPIRE].ADSGoogle Scholar
  24. [24]
    B. Andersson, G. Gustafson, G. Ingelman and T. Sjöstrand, Parton fragmentation and string dynamics, Phys. Rept. 97 (1983) 31 [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    A. Buckley et al., General-purpose event generators for LHC physics, Phys. Rept. 504 (2011) 145 [arXiv:1101.2599] [INSPIRE].CrossRefADSGoogle Scholar
  26. [26]
    K. Hamacher and M. Weierstall, The next round of hadronic generator tuning heavily based on identified particle data, hep-ex/9511011 [INSPIRE].
  27. [27]
    T. Sjöstrand et al., An introduction to PYTHIA 8.2, arXiv:1410.3012 [INSPIRE].
  28. [28]
    A. Casher, H. Neuberger and S. Nussinov, Chromoelectric flux tube model of particle production, Phys. Rev. D 20 (1979) 179 [INSPIRE].ADSGoogle Scholar
  29. [29]
    B. Andersson, G. Gustafson and T. Sjöstrand, A three-dimensional model for quark and gluon jets, Z. Phys. C 6 (1980) 235 [INSPIRE].ADSGoogle Scholar
  30. [30]
    E.G. Gurvich, The quark anti-quark pair production mechanism in a quark jet, Phys. Lett. B 87 (1979) 386 [INSPIRE].CrossRefADSGoogle Scholar
  31. [31]
    N.K. Glendenning and T. Matsui, Creation of \( q\overline{q} \) pairs in a chromoelectric flux tube, Phys. Rev. D 28 (1983) 2890 [INSPIRE].ADSGoogle Scholar
  32. [32]
    J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].CrossRefADSzbMATHMathSciNetGoogle Scholar
  33. [33]
    E. Brezin and C. Itzykson, Pair production in vacuum by an alternating field, Phys. Rev. D 2 (1970) 1191 [INSPIRE].ADSGoogle Scholar
  34. [34]
    UA5 collaboration, G.J. Alner et al., Kaon production in \( \overline{p}p \) reactions at a center-of-mass energy of 540 GeV, Nucl. Phys. B 258 (1985) 505 [INSPIRE].ADSGoogle Scholar
  35. [35]
    H1 collaboration, F.D. Aaron et al., Strangeness production at low Q 2 in deep-inelastic ep scattering at HERA, Eur. Phys. J. C 61 (2009) 185 [arXiv:0810.4036] [INSPIRE].ADSGoogle Scholar
  36. [36]
    CMS collaboration, Strange particle production in pp collisions at \( \sqrt{s} \) = 0.9 and 7 TeV, JHEP 05 (2011) 064 [arXiv:1102.4282] [INSPIRE].Google Scholar
  37. [37]
    J. Ambjørn, P. Olesen and C. Peterson, Stochastic confinement and dimensional reduction. 2. Three-dimensional SU(2) lattice gauge theory, Nucl. Phys. B 240 (1984) 533 [INSPIRE].CrossRefADSGoogle Scholar
  38. [38]
    G.S. Bali, Casimir scaling of SU(3) static potentials, Phys. Rev. D 62 (2000) 114503 [hep-lat/0006022] [INSPIRE].ADSGoogle Scholar
  39. [39]
    A.H. Mueller, Soft gluons in the infinite-momentum wave function and the BFKL pomeron, Nucl. Phys. B 415 (1994) 373 [INSPIRE].CrossRefADSGoogle Scholar
  40. [40]
    A.H. Mueller and B. Patel, Single and double BFKL pomeron exchange and a dipole picture of high-energy hard processes, Nucl. Phys. B 425 (1994) 471 [hep-ph/9403256] [INSPIRE].CrossRefADSGoogle Scholar
  41. [41]
    A.H. Mueller, Unitarity and the BFKL pomeron, Nucl. Phys. B 437 (1995) 107 [hep-ph/9408245] [INSPIRE].CrossRefADSGoogle Scholar
  42. [42]
    L.D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D 49 (1994) 2233 [hep-ph/9309289] [INSPIRE].ADSGoogle Scholar
  43. [43]
    L.D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49 (1994) 3352 [hep-ph/9311205] [INSPIRE].ADSGoogle Scholar
  44. [44]
    C. Flensburg, G. Gustafson, L. Lönnblad and A. Ster, Correlations in double parton distributions at small x, JHEP 06 (2011) 066 [arXiv:1103.4320] [INSPIRE].CrossRefADSGoogle Scholar
  45. [45]
    C. Flensburg and G. Gustafson, Fluctuations, saturation and diffractive excitation in high energy collisions, JHEP 10 (2010) 014 [arXiv:1004.5502] [INSPIRE].CrossRefADSGoogle Scholar
  46. [46]
    C. Flensburg, G. Gustafson and L. Lönnblad, Exclusive final states in diffractive excitation, JHEP 12 (2012) 115 [arXiv:1210.2407] [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    C. Flensburg, Correlations and fluctuations in the initial state of high energy heavy ion collisions, arXiv:1108.4862 [INSPIRE].
  48. [48]
    C. Flensburg, Heavy ion inital states from DIPSY, Prog. Theor. Phys. Suppl. 193 (2012) 172 [INSPIRE].CrossRefADSGoogle Scholar
  49. [49]
    K.G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].ADSGoogle Scholar
  50. [50]
    B. Andersson and G. Gustafson, Why are vector mesons suppressed in jet fragmentation?, Lund Preprint LU-TP-82-5 (1982) [INSPIRE].
  51. [51]
    B. Andersson, G. Gustafson and T. Sjöstrand, A model for baryon production in quark and gluon jets, Nucl. Phys. B 197 (1982) 45 [INSPIRE].CrossRefADSGoogle Scholar
  52. [52]
    B. Andersson, G. Gustafson and T. Sjöstrand, Baryon production in jet fragmentation and γ-decay, Phys. Scripta 32 (1985) 574 [INSPIRE].CrossRefADSGoogle Scholar
  53. [53]
    S. Jeon and R. Venugopalan, Random walks of partons in SU(N c) and classical representations of color charges in QCD at small x, Phys. Rev. D 70 (2004) 105012 [hep-ph/0406169] [INSPIRE].ADSGoogle Scholar
  54. [54]
    K. Johnson, The M.I.T. bag model, Acta Phys. Polon. B 6 (1975) 865 [INSPIRE].Google Scholar
  55. [55]
    K. Johnson and C.B. Thorn, String-like solutions of the bag model, Phys. Rev. D 13 (1976) 1934 [INSPIRE].ADSGoogle Scholar
  56. [56]
    C. Semay, About the Casimir scaling hypothesis, Eur. Phys. J. A 22 (2004) 353 [hep-ph/0409105] [INSPIRE].CrossRefADSGoogle Scholar
  57. [57]
    M. Cardoso, N. Cardoso and P. Bicudo, Lattice QCD computation of the colour fields for the static hybrid quark-gluon-antiquark system and microscopic study of the Casimir scaling, Phys. Rev. D 81 (2010) 034504 [arXiv:0912.3181] [INSPIRE].ADSGoogle Scholar
  58. [58]
    P. Cea, L. Cosmai, F. Cuteri and A. Papa, Flux tubes in the SU(3) vacuum: London penetration depth and coherence length, Phys. Rev. D 89 (2014) 094505 [arXiv:1404.1172] [INSPIRE].ADSGoogle Scholar
  59. [59]
    E. Avsar, G. Gustafson and L. Lönnblad, Small-x dipole evolution beyond the large-N c limit, JHEP 01 (2007) 012 [hep-ph/0610157] [INSPIRE].ADSGoogle Scholar
  60. [60]
    E. Avsar, G. Gustafson and L. Lönnblad, Diifractive excitation in DIS and pp collisions, JHEP 12 (2007) 012 [arXiv:0709.1368] [INSPIRE].ADSGoogle Scholar
  61. [61]
    E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The pomeranchuk singularity in nonabelian gauge theories, Sov. Phys. JETP 45 (1977) 199 [INSPIRE].ADSMathSciNetGoogle Scholar
  62. [62]
    I.I. Balitsky and L.N. Lipatov, The pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [INSPIRE].Google Scholar
  63. [63]
    G. Gustafson, Dual description of a confined color field, Phys. Lett. B 175 (1986) 453 [INSPIRE].CrossRefADSGoogle Scholar
  64. [64]
    G. Gustafson and U. Pettersson, Dipole formulation of QCD cascades, Nucl. Phys. B 306 (1988) 746 [INSPIRE].CrossRefADSGoogle Scholar
  65. [65]
    L. Lönnblad, ARIADNE version 4: a program for simulation of QCD cascades implementing the color dipole model, Comput. Phys. Commun. 71 (1992) 15 [INSPIRE].CrossRefADSGoogle Scholar
  66. [66]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  67. [67]
    L. Lönnblad, Reconnecting colored dipoles, Z. Phys. C 70 (1996) 107 [INSPIRE].Google Scholar
  68. [68]
    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
  69. [69]
    G. Gustafson, U. Pettersson and P.M. Zerwas, Jet final states in WW pair production and color screening in the QCD vacuum, Phys. Lett. B 209 (1988) 90 [INSPIRE].CrossRefADSGoogle Scholar
  70. [70]
    T. Sjöstrand and V.A. Khoze, Does the W mass reconstruction survive QCD effects?, Phys. Rev. Lett. 72 (1994) 28 [hep-ph/9310276] [INSPIRE].CrossRefADSGoogle Scholar
  71. [71]
    A. Edin, G. Ingelman and J. Rathsman, Soft color interactions as the origin of rapidity gaps in DIS, Phys. Lett. B 366 (1996) 371 [hep-ph/9508386] [INSPIRE].CrossRefADSGoogle Scholar
  72. [72]
    R. Enberg, G. Ingelman and N. Timneanu, Soft color interactions and diffractive hard scattering at the Tevatron, Phys. Rev. D 64 (2001) 114015 [hep-ph/0106246] [INSPIRE].ADSGoogle Scholar
  73. [73]
    B. Andersson, G. Gustafson and B. Söderberg, A probability measure on parton and string states, Nucl. Phys. B 264 (1986) 29 [INSPIRE].CrossRefADSGoogle Scholar
  74. [74]
    B. Andersson, P. Dahlkvist and G. Gustafson, An infrared stable multiplicity measure on QCD parton states, Phys. Lett. B 214 (1988) 604 [INSPIRE].CrossRefADSGoogle Scholar
  75. [75]
    L. Lönnblad, ThePEG, PYTHIA7, HERWIG++ and Ariadne, Nucl. Instrum. Meth. A 559 (2006) 246 [INSPIRE].CrossRefADSGoogle Scholar
  76. [76]
    A. Karneyeu, L. Mijovic, S. Prestel and P.Z. Skands, MCPLOTS: a particle physics resource based on volunteer computing, Eur. Phys. J. C 74 (2014) 2714 [arXiv:1306.3436] [INSPIRE].CrossRefADSGoogle Scholar
  77. [77]
    STAR collaboration, J. Adams et al., Identified hadron spectra at large transverse momentum in p + p and d + Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 200 GeV, Phys. Lett. B 637 (2006) 161 [nucl-ex/0601033] [INSPIRE].ADSGoogle Scholar
  78. [78]
    K. Werner, B. Guiot, I. Karpenko and T. Pierog, A unified description of the reaction dynamics from pp to pA to AA collisions, Nucl. Phys. A 931 (2014) 83 [arXiv:1411.1048] [INSPIRE].CrossRefADSGoogle Scholar
  79. [79]
    N. Armesto et al., Heavy ion collisions at the LHClast call for predictions, J. Phys. G 35 (2008) 054001 [arXiv:0711.0974] [INSPIRE].CrossRefGoogle Scholar
  80. [80]
    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].CrossRefADSGoogle Scholar
  81. [81]
    ALICE collaboration, Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 2.76 TeV, Phys. Lett. B 736 (2014) 196 [arXiv:1401.1250] [INSPIRE].ADSGoogle Scholar
  82. [82]
    R. Engel and J. Ranft, Hadronic photon-photon interactions at high-energies, Phys. Rev. D 54 (1996) 4244 [hep-ph/9509373] [INSPIRE].ADSGoogle Scholar
  83. [83]
    J.M. Butterworth, J.R. Forshaw and M.H. Seymour, Multiparton interactions in photoproduction at HERA, Z. Phys. C 72 (1996) 637 [hep-ph/9601371] [INSPIRE].ADSGoogle Scholar
  84. [84]
    V.S. Fadin and L.N. Lipatov, BFKL pomeron in the next-to-leading approximation, Phys. Lett. B 429 (1998) 127 [hep-ph/9802290] [INSPIRE].CrossRefADSGoogle Scholar
  85. [85]
    M. Ciafaloni and G. Camici, Energy scale(s) and next-to-leading BFKL equation, Phys. Lett. B 430 (1998) 349 [hep-ph/9803389] [INSPIRE].CrossRefADSGoogle Scholar
  86. [86]
    G.P. Salam, An introduction to leading and next-to-leading BFKL, Acta Phys. Polon. B 30 (1999) 3679 [hep-ph/9910492] [INSPIRE].ADSGoogle Scholar
  87. [87]
    J. Kwiecinski, A.D. Martin and P.J. Sutton, Constraints on gluon evolution at small x, Z. Phys. C 71 (1996) 585 [hep-ph/9602320] [INSPIRE].ADSGoogle Scholar
  88. [88]
    B. Andersson, G. Gustafson and J. Samuelsson, The linked dipole chain model for DIS, Nucl. Phys. B 467 (1996) 443 [INSPIRE].CrossRefADSGoogle Scholar
  89. [89]
    I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].CrossRefADSGoogle Scholar
  90. [90]
    Y.V. Kovchegov, Small-x F 2 structure function of a nucleus including multiple pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [INSPIRE].ADSGoogle Scholar
  91. [91]
    A. Buckley et al., Rivet user manual, Comput. Phys. Commun. 184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].CrossRefADSGoogle Scholar
  92. [92]
    A. Buckley, H. Hoeth, H. Lacker, H. Schulz and J.E. von Seggern, Systematic event generator tuning for the LHC, Eur. Phys. J. C 65 (2010) 331 [arXiv:0907.2973] [INSPIRE].CrossRefADSGoogle Scholar
  93. [93]
    DELPHI collaboration, P. Abreu et al., Tuning and test of fragmentation models based on identified particles and precision event shape data, Z. Phys. C 73 (1996) 11 [INSPIRE].Google Scholar
  94. [94]
    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].CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Christian Bierlich
    • 1
  • Gösta Gustafson
    • 1
  • Leif Lönnblad
    • 1
  • Andrey Tarasov
    • 2
  1. 1.Dept. of Astronomy and Theoretical PhysicsLund UniversityLundSweden
  2. 2.Theory CenterJefferson LabNewport NewsU.S.A.

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