Advertisement

Elements of a theory for multiparton interactions in QCD

  • Markus Diehl
  • Daniel Ostermeier
  • Andreas Schäfer
Open Access
Article

Abstract

We perform a detailed investigation of multiple hard interactions in hadron-hadron collisions. We discuss the space-time, spin and color structure of multiple interactions, classify different contributions according to their power behavior and provide several elements required for establishing all-order factorization. This also allows us to analyze the structure of Sudakov logarithms in double hard scattering. We show how multiparton distributions can be constrained by connecting them with generalized parton distributions and by calculating their behavior at large transverse parton momenta.

Keywords

Hadronic Colliders QCD 

References

  1. [1]
    P. Landshoff, J. Polkinghorne and D. Scott, Production of baryons with large transverse momentum, Phys. Rev. D 12 (1975) 3738 [INSPIRE].ADSGoogle Scholar
  2. [2]
    P. Landshoff and J. Polkinghorne, Calorimeter triggers for hard collisions, Phys. Rev. D 18 (1978) 3344 [INSPIRE].ADSGoogle Scholar
  3. [3]
    B. Humpert, Are there multi-quark interactions?, Phys. Lett. B 131 (1983) 461 [INSPIRE].ADSGoogle Scholar
  4. [4]
    B. Humpert and R. Odorico, Multiparton scattering and QCD radiation as sources of four jet events, Phys. Lett. B 154 (1985) 211 [INSPIRE].ADSGoogle Scholar
  5. [5]
    L. Ametller, N. Paver and D. Treleani, Possible signature of multiple parton interactions in collider four jet events, Phys. Lett. B 169 (1986) 289 [INSPIRE].ADSGoogle Scholar
  6. [6]
    M.L. Mangano, Four jet production at the Tevatron collider, Z. Phys. C 42 (1989) 331 [INSPIRE].Google Scholar
  7. [7]
    A. del Fabbro and D. Treleani, Double parton scatterings in b-quark pair production at the CERN LHC, Phys. Rev. D 66 (2002) 074012 [hep-ph/0207311].ADSGoogle Scholar
  8. [8]
    S. Domdey, H.-J. Pirner and U.A. Wiedemann, Testing the scale dependence of the scale factor σeff in double dijet production at the LHC, Eur. Phys. J. C 65 (2010) 153 [arXiv:0906.4335].ADSCrossRefGoogle Scholar
  9. [9]
    E.L. Berger, C.B. Jackson and G. Shaughnessy, Characteristics and estimates of double parton scattering at the Large Hadron Collider, Phys. Rev. D 81 (2010) 014014 [arXiv:0911.5348] [INSPIRE].ADSGoogle Scholar
  10. [10]
    M. Drees and T. Han, Signals for double parton scattering at the Fermilab Tevatron, Phys. Rev. Lett. 77 (1996) 4142 [hep-ph/9605430] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    C. Goebel, F. Halzen and D.M. Scott, Double Drell-Yan annihilations in hadron collisions: novel tests of the constituent picture, Phys. Rev. D 22 (1980) 2789.ADSGoogle Scholar
  12. [12]
    F. Halzen, P. Hoyer and W.J. Stirling, Evidence for multiple parton interactions from the observation of multi-muon events in Drell-Yan experiments, Phys. Lett. B 188 (1987) 375.ADSGoogle Scholar
  13. [13]
    C.H. Kom, A. Kulesza and W.J. Stirling, Prospects for observation of double parton scattering with four-muon final states at LHCb, Eur. Phys. J. C 71 (2011) 1802 [arXiv:1109.0309] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    C.H. Kom, A. Kulesza and W.J. Stirling, Pair production of J/ψ as a probe of double parton scattering at LHCb, Phys. Rev. Lett. 107 (2011) 082002 [arXiv:1105.4186] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    S.P. Baranov, A.M. Snigirev and N.P. Zotov, Double heavy meson production through double parton scattering in hadronic collisions, Phys. Lett. B 705 (2011) 116 [arXiv:1105.6276] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A. Novoselov, Double parton scattering as a source of quarkonia pairs in LHCb, arXiv:1106.2184.
  17. [17]
    R.M. Godbole, S. Gupta and J. Lindfors, Double parton scattering contribution to W + jets, Z. Phys. C 47 (1990) 69.Google Scholar
  18. [18]
    O. Éboli, F. Halzen and J.K. Mizukoshi, Associated production of weak bosons and jets by multiple parton interactions, Phys. Rev. D 57 (1998) 1730 [hep-ph/9710443] [INSPIRE].ADSGoogle Scholar
  19. [19]
    A. del Fabbro and D. Treleani, Double parton scattering background to Higgs boson production at the CERN LHC, Phys. Rev. D 61 (2000) 077502 [hep-ph/9911358] [INSPIRE].ADSGoogle Scholar
  20. [20]
    E. Cattaruzza, A.D. Fabbro and D. Treleani, Fractional momentum correlations in multiple production of W bosons and of \( b\overline b \) pairs in high energy pp collisions, Phys. Rev. D 72 (2005) 034022 [hep-ph/0507052] [INSPIRE].ADSGoogle Scholar
  21. [21]
    E. Maina, Multiple parton interactions, top-antitop and W + 4j production at the LHC, JHEP 04 (2009) 098 [arXiv:0904.2682].ADSCrossRefGoogle Scholar
  22. [22]
    E. Maina, Multiple parton interactions in Z + 4j, W ± W ± + 0/2j and W + W + 2j production at the LHC, JHEP 09 (2009) 081 [arXiv:0909.1586] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    E. Maina, Multiple parton interactions in Z + jets production at the LHC. A comparison of factorized and non-factorized double parton distribution functions, JHEP 01 (2011) 061 [arXiv:1010.5674] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    A. Kulesza and W.J. Stirling, Like-sign W boson production at the LHC as a probe of double parton scattering, Phys. Lett. B 475 (2000) 168 [hep-ph/9912232] [INSPIRE].ADSGoogle Scholar
  25. [25]
    J.R. Gaunt, C.-H. Kom, A. Kulesza and W.J. Stirling, Same-sign W pair production as a probe of double-parton scattering at the LHC, Eur. Phys. J. C 69 (2010) 53 [arXiv:1003.3953] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    E.L. Berger, C.B. Jackson, S. Quackenbush and G. Shaughnessy, Calculation of W \( b\overline b \) production via double parton scattering at the LHC, Phys. Rev. D 84 (2011) 074021 [arXiv:1107.3150] [INSPIRE].ADSGoogle Scholar
  27. [27]
    Axial Field Spectrometer collaboration, T. Akesson et al., Double parton scattering in pp collisions at \( \sqrt {\text{s}} = {63}GeV \), Z. Phys. C 34 (1987) 163 [INSPIRE].ADSGoogle Scholar
  28. [28]
    UA2 collaboration, J. Alitti et al., A study of multi-jet events at the CERN \( \overline p p \) collider and a search for double parton scattering, Phys. Lett. B 268 (1991) 145 [INSPIRE].ADSGoogle Scholar
  29. [29]
    CDF collaboration, F. Abe et al., Study of four jet events and evidence for double parton interactions in \( p\overline p \) collisions at \( \sqrt {\text{s}} = {1}.{8}TeV \), Phys. Rev. D 47 (1993) 4857 [INSPIRE].ADSGoogle Scholar
  30. [30]
    CDF collaboration, F. Abe et al., Measurement of double parton scattering in \( \overline p p \) collisions at \( \sqrt {\text{s}} = {1}.{8}TeV \), Phys. Rev. Lett. 79 (1997) 584 [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    CDF collaboration, F. Abe et al., Double parton scattering in \( \overline p p \) collisions at \( \sqrt {\text{s}} = {1}.{8}TeV \), Phys. Rev. D 56 (1997) 3811 [INSPIRE].ADSGoogle Scholar
  32. [32]
    D0 collaboration, V. Abazov et al., Double parton interactions in photon +3 jet events in pp-bar collisions \( \sqrt {\text{s}} = {1}.{96}TeV \), Phys. Rev. D 81 (2010) 052012 [arXiv:0912.5104] [INSPIRE].ADSGoogle Scholar
  33. [33]
    D0 collaboration, V.M. Abazov et al., Azimuthal decorrelations and multiple parton interactions in photon +2 jet and photon +3 jet events in pp collisions at \( \sqrt {\text{s}} = {1}.{96}TeV \), Phys. Rev. D 83 (2011) 052008 [arXiv:1101.1509] [INSPIRE].ADSGoogle Scholar
  34. [34]
    T. Sjöstrand and P.Z. Skands, Multiple interactions and the structure of beam remnants, JHEP 03 (2004) 053 [hep-ph/0402078] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    A. Buckley et al., General-purpose event generators for LHC physics, Phys. Rept. 504 (2011) 145 [arXiv:1101.2599] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S. Alekhin et al., HERA and the LHC: a workshop on the implications of HERA for LHC physics: proceedings part A, hep-ph/0601012 [INSPIRE].
  37. [37]
    S. Alekhin et al., HERA and the LHC: a workshop on the implications of HERA for LHC physics: proceedings part B, hep-ph/0601013 [INSPIRE].
  38. [38]
    Z. Ajaltouni et al., Proceedings of the workshop: HERA and the LHC workshop series on the implications of HERA for LHC physics, arXiv:0903.3861 [INSPIRE].
  39. [39]
    P. Bartalini and L. Fano, Multiple partonic interactions at the LHC. Proceedings, 1st international workshop MPI08, Perugia, Italy, October 27–31, 2008, arXiv:1003.4220 [INSPIRE].
  40. [40]
    P. Bartalini et al., Multi-parton interactions at the LHC, arXiv:1111.0469 [INSPIRE].
  41. [41]
    ATLAS collaboration, A measurement of hard double-partonic interactions in W → + 2 jet events, ATLAS-CONF-2011-160 (2011).
  42. [42]
    P. Bartalini and L. Fanò, Multiple parton interactions studies at CMS, arXiv:1103.6201 [INSPIRE].
  43. [43]
    A. Accardi and D. Treleani, Minijet transverse spectrum in high-energy hadron nucleus collisions, Phys. Rev. D 64 (2001) 116004 [hep-ph/0106306] [INSPIRE].ADSGoogle Scholar
  44. [44]
    M. Strikman and D. Treleani, Measuring double parton distributions in nucleons at proton nucleus colliders, Phys. Rev. Lett. 88 (2002) 031801 [hep-ph/0111468] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    E. Cattaruzza, A. Del Fabbro and D. Treleani, Heavy-quark production in proton-nucleus collision at the CERN LHC, Phys. Rev. D 70 (2004) 034022 [hep-ph/0404177] [INSPIRE].ADSGoogle Scholar
  46. [46]
    G. Calucci and D. Treleani, Disentangling correlations in multiple parton interactions, Phys. Rev. D 83 (2011) 016012 [arXiv:1009.5881] [INSPIRE].ADSGoogle Scholar
  47. [47]
    M. Strikman and W. Vogelsang, Multiple parton interactions and forward double pion production in pp and dA scattering, Phys. Rev. D 83 (2011) 034029 [arXiv:1009.6123] [INSPIRE].ADSGoogle Scholar
  48. [48]
    M. Diehl and A. Schäfer, Theoretical considerations on multiparton interactions in QCD, Phys. Lett. B 698 (2011) 389 [arXiv:1102.3081] [INSPIRE].ADSGoogle Scholar
  49. [49]
    J.C. Collins and D.E. Soper, Back-to-back jets in QCD, Nucl. Phys. B 193 (1981) 381 [Erratum ibid. B 213 (1983) 545] [INSPIRE].
  50. [50]
    J. Collins, T. Rogers and A. Stasto, Fully unintegrated parton correlation functions and factorization in lowest-order hard scattering, Phys. Rev. D 77 (2008) 085009 [arXiv:0708.2833] [INSPIRE].ADSGoogle Scholar
  51. [51]
    J.C. Collins, The foundations of perturbative QCD, Cambridge University Press, Cambridge U.K. (2011).CrossRefGoogle Scholar
  52. [52]
    X.-D. Ji, J.-P. Ma and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71 (2005) 034005 [hep-ph/0404183] [INSPIRE].ADSGoogle Scholar
  53. [53]
    N. Paver and D. Treleani, Multi-quark scattering and large p T jet production in hadronic collisions, Nuovo Cim. A 70 (1982) 215 [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    M. Mekhfi, Multiparton processes: an application to double Drell-Yan, Phys. Rev. D 32 (1985) 2371 [INSPIRE].ADSGoogle Scholar
  55. [55]
    P. Landshoff and J. Polkinghorne, Models for hadronic and leptonic processes at high-energy, Phys. Rept. 5 (1972) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    M. Diehl and T. Gousset, Time ordering in off diagonal parton distributions, Phys. Lett. B 428 (1998) 359 [hep-ph/9801233] [INSPIRE].ADSGoogle Scholar
  57. [57]
    R. Jaffe, Parton distribution functions for twist four, Nucl. Phys. B 229 (1983) 205 [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    M. Hillery, R. O’Connell, M. Scully and E.P. Wigner, Distribution functions in physics: fundamentals, Phys. Rept. 106 (1984) 121 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  59. [59]
    A.V. Belitsky, X.-D. Ji and F. Yuan, Quark imaging in the proton via quantum phase space distributions, Phys. Rev. D 69 (2004) 074014 [hep-ph/0307383] [INSPIRE].ADSGoogle Scholar
  60. [60]
    B. Blok, Y. Dokshitzer, L. Frankfurt and M. Strikman, The four jet production at LHC and Tevatron in QCD, Phys. Rev. D 83 (2011) 071501 [arXiv:1009.2714] [INSPIRE].ADSGoogle Scholar
  61. [61]
    S.J. Brodsky and G.P. Lepage, Exclusive processes in quantum chromodynamics, in Perturbative quantum chromodynamics, A.H. Mueller ed., World Scientific, Singapore (1989).Google Scholar
  62. [62]
    M. Diehl, T. Feldmann, R. Jakob and P. Kroll, The overlap representation of skewed quark and gluon distributions, Nucl. Phys. B 596 (2001) 33 [Erratum ibid. B 605 (2001) 647] [hep-ph/0009255] [INSPIRE].
  63. [63]
    M. Diehl, Generalized parton distributions in impact parameter space, Eur. Phys. J. C 25 (2002) 223 [Erratum ibid. C 31 (2003) 277-278] [hep-ph/0205208] [INSPIRE].
  64. [64]
    H. Politzer, Power corrections at short distances, Nucl. Phys. B 172 (1980) 349 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  65. [65]
    D.E. Soper, The parton model and the Bethe-Salpeter wave function, Phys. Rev. D 15 (1977) 1141 [INSPIRE].ADSGoogle Scholar
  66. [66]
    M. Burkardt, Impact parameter space interpretation for generalized parton distributions, Int. J. Mod. Phys. A 18 (2003) 173 [hep-ph/0207047] [INSPIRE].ADSGoogle Scholar
  67. [67]
    G. Calucci and D. Treleani, Incoherence and multiple parton interactions, Phys. Rev. D 80 (2009) 054025 [arXiv:0907.4772] [INSPIRE].ADSGoogle Scholar
  68. [68]
    T. Sjöstrand and M. van Zijl, Multiple parton-parton interactions in an impact parameter picture, Phys. Lett. B 188 (1987) 149 [INSPIRE].ADSGoogle Scholar
  69. [69]
    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
  70. [70]
    L. Durand and P. Hong, QCD and rising total cross-sections, Phys. Rev. Lett. 58 (1987) 303 [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    L. Durand and H. Pi, Semihard QCD and high-energy pp and \( \overline p p \) scattering, Phys. Rev. D 40 (1989) 1436 [INSPIRE].ADSGoogle Scholar
  72. [72]
    L. Ametller and D. Treleani, Shadowing in semihard interactions, Int. J. Mod. Phys. A 3 (1988) 521 [INSPIRE].ADSGoogle Scholar
  73. [73]
    L. Frankfurt, M. Strikman and C. Weiss, Dijet production as a centrality trigger for pp collisions at CERN LHC, Phys. Rev. D 69 (2004) 114010 [hep-ph/0311231] [INSPIRE].ADSGoogle Scholar
  74. [74]
    G. Calucci and D. Treleani, Mini-jets and the two-body parton correlation, Phys. Rev. D 57 (1998) 503 [hep-ph/9707389] [INSPIRE].ADSGoogle Scholar
  75. [75]
    G. Calucci and D. Treleani, Proton structure in transverse space and the effective cross-section, Phys. Rev. D 60 (1999) 054023 [hep-ph/9902479] [INSPIRE].ADSGoogle Scholar
  76. [76]
    A. Del Fabbro and D. Treleani, Scale factor in double parton collisions and parton densities in transverse space, Phys. Rev. D 63 (2001) 057901 [hep-ph/0005273] [INSPIRE].ADSGoogle Scholar
  77. [77]
    T. Rogers and M. Strikman, Multiple hard partonic collisions with correlations in proton-proton scattering, Phys. Rev. D 81 (2010) 016013 [arXiv:0908.0251] [INSPIRE].ADSGoogle Scholar
  78. [78]
    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].ADSCrossRefGoogle Scholar
  79. [79]
    J.P. Ralston and D.E. Soper, Production of dimuons from high-energy polarized proton proton collisions, Nucl. Phys. B 152 (1979) 109 [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    R. Tangerman and P. Mulders, Intrinsic transverse momentum and the polarized Drell-Yan process, Phys. Rev. D 51 (1995) 3357 [hep-ph/9403227] [INSPIRE].ADSGoogle Scholar
  81. [81]
    R. Jaffe and A. Manohar, Nuclear gluonometry, Phys. Lett. B 223 (1989) 218 [INSPIRE].ADSGoogle Scholar
  82. [82]
    A.V. Belitsky and D. Mueller, Off forward gluonometry, Phys. Lett. B 486 (2000) 369 [hep-ph/0005028] [INSPIRE].ADSGoogle Scholar
  83. [83]
    P. Mulders and J. Rodrigues, Transverse momentum dependence in gluon distribution and fragmentation functions, Phys. Rev. D 63 (2001) 094021 [hep-ph/0009343] [INSPIRE].ADSGoogle Scholar
  84. [84]
    P.M. Nadolsky, C. Balázs, E.L. Berger and C.-P. Yuan, Gluon-gluon contributions to the production of continuum diphoton pairs at hadron colliders, Phys. Rev. D 76 (2007) 013008 [hep-ph/0702003] [INSPIRE].ADSGoogle Scholar
  85. [85]
    S. Catani and M. Grazzini, QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B 845 (2011) 297 [arXiv:1011.3918] [INSPIRE].ADSCrossRefGoogle Scholar
  86. [86]
    D. Boer, S.J. Brodsky, P.J. Mulders and C. Pisano, Direct probes of linearly polarized gluons inside unpolarized hadrons, Phys. Rev. Lett. 106 (2011) 132001 [arXiv:1011.4225] [INSPIRE].ADSCrossRefGoogle Scholar
  87. [87]
    J.-W. Qiu, M. Schlegel and W. Vogelsang, Probing gluonic spin-orbit correlations in photon pair production, Phys. Rev. Lett. 107 (2011) 062001 [arXiv:1103.3861] [INSPIRE].ADSCrossRefGoogle Scholar
  88. [88]
    D. Boer, W.J. den Dunnen, C. Pisano, M. Schlegel and W. Vogelsang, Linearly polarized gluons and the Higgs transverse momentum distribution, Phys. Rev. Lett. 108 (2012) 032002 [arXiv:1109.1444] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    J. Collins and T. Rogers, The gluon distribution function and factorization in Feynman gauge, Phys. Rev. D 78 (2008) 054012 [arXiv:0805.1752] [INSPIRE].ADSGoogle Scholar
  90. [90]
    M. Mekhfi, Correlations in color and spin in multiparton processes, Phys. Rev. D 32 (1985) 2380 [INSPIRE].ADSGoogle Scholar
  91. [91]
    A. MacFarlane, A. Sudbery and P. Weisz, On Gell-Manns gamma matrices, d tensors and f tensors, octets and parametrizations of SU(3), Commun. Math. Phys. 11 (1968) 77 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  92. [92]
    R. Ragazzon and D. Treleani, Multiparton interactions and production of mini-jets in high-energy hadronic collisions, Phys. Rev. D 53 (1996) 55 [hep-ph/9508286] [INSPIRE].ADSGoogle Scholar
  93. [93]
    M. Braun and D. Treleani, The double parton distributions in the hard Pomeron model, Eur. Phys. J. C 18 (2001) 511 [hep-ph/0005078] [INSPIRE].ADSCrossRefGoogle Scholar
  94. [94]
    J. Bartels, M. Salvadore and G. Vacca, AGK cutting rules and multiple scattering in hadronic collisions, Eur. Phys. J. C 42 (2005) 53 [hep-ph/0503049] [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    E. Levin and J. Miller, Two parton shower background for associate W Higgs production, Eur. Phys. J. C 61 (2009) 1 [arXiv:0803.0646] [INSPIRE].ADSCrossRefGoogle Scholar
  96. [96]
    J. Bartels and M. Ryskin, Recombination within multi-chain contributions in pp scattering, arXiv:1105.1638 [INSPIRE].
  97. [97]
    J. Bartels, L. Lipatov and G. Vacca, A new odderon solution in perturbative QCD, Phys. Lett. B 477 (2000) 178 [hep-ph/9912423] [INSPIRE].ADSGoogle Scholar
  98. [98]
    R. Janik and J. Wosiek, Solution of the odderon problem, Phys. Rev. Lett. 82 (1999) 1092 [hep-th/9802100] [INSPIRE].ADSCrossRefGoogle Scholar
  99. [99]
    B. Blok, Y. Dokshitser, L. Frankfurt and M. Strikman, pQCD physics of multiparton interactions, arXiv:1106.5533 [INSPIRE].
  100. [100]
    P. Hägler, Hadron structure from lattice quantum chromodynamics, Phys. Rept. 490 (2010) 49 [arXiv:0912.5483] [INSPIRE].ADSCrossRefGoogle Scholar
  101. [101]
    H1 collaboration, A. Aktas et al., Elastic J/ψ production at HERA, Eur. Phys. J. C 46 (2006) 585 [hep-ex/0510016] [INSPIRE].ADSGoogle Scholar
  102. [102]
    ZEUS collaboration, S. Chekanov et al., Exclusive photoproduction of J/ψ mesons at HERA, Eur. Phys. J. C 24 (2002) 345 [hep-ex/0201043] [INSPIRE].CrossRefGoogle Scholar
  103. [103]
    M. Diehl and W. Kugler, Some numerical studies of the evolution of generalized parton distributions, Phys. Lett. B 660 (2008) 202 [arXiv:0711.2184] [INSPIRE].ADSGoogle Scholar
  104. [104]
    L. Frankfurt, M. Strikman and C. Weiss, Transverse nucleon structure and diagnostics of hard parton-parton processes at LHC, Phys. Rev. D 83 (2011) 054012 [arXiv:1009.2559] [INSPIRE].ADSGoogle Scholar
  105. [105]
    R. Corke and T. Sjöstrand, Multiparton interactions with an x-dependent proton size, JHEP 05 (2011) 009 [arXiv:1101.5953] [INSPIRE].ADSCrossRefGoogle Scholar
  106. [106]
    L. Frankfurt, M. Strikman and C. Weiss, 3D parton imaging of the nucleon in high-energy pp and pA collisions, Ann. Phys. 13 (2004) 665 [hep-ph/0410307] [INSPIRE].MATHCrossRefGoogle Scholar
  107. [107]
    G.F. Sterman, Mass divergences in annihilation processes. 1. Origin and nature of divergences in cut vacuum polarization diagrams, Phys. Rev. D 17 (1978) 2773 [INSPIRE].ADSGoogle Scholar
  108. [108]
    S.B. Libby and G.F. Sterman, Mass divergences in two particle inelastic scattering, Phys. Rev. D 18 (1978) 4737 [INSPIRE].ADSGoogle Scholar
  109. [109]
    S. Coleman and R. Norton, Singularities in the physical region, Nuovo Cim. 38 (1965) 438 [INSPIRE].CrossRefGoogle Scholar
  110. [110]
    N. Paver and D. Treleani, Multiple parton processes in the TeV region, Z. Phys. C 28 (1985) 187 [INSPIRE].ADSGoogle Scholar
  111. [111]
    R. Corke and T. Sjöstrand, Multiparton interactions and rescattering, JHEP 01 (2010) 035 [arXiv:0911.1909] [INSPIRE].ADSCrossRefGoogle Scholar
  112. [112]
    T.C. Rogers and P.J. Mulders, No generalized TMD-factorization in hadro-production of high transverse momentum hadrons, Phys. Rev. D 81 (2010) 094006 [arXiv:1001.2977] [INSPIRE].ADSGoogle Scholar
  113. [113]
    J.C. Collins and A. Metz, Universality of soft and collinear factors in hard-scattering factorization, Phys. Rev. Lett. 93 (2004) 252001 [hep-ph/0408249] [INSPIRE].ADSCrossRefGoogle Scholar
  114. [114]
    A.V. Belitsky, X. Ji and F. Yuan, Final state interactions and gauge invariant parton distributions, Nucl. Phys. B 656 (2003) 165 [hep-ph/0208038] [INSPIRE].ADSCrossRefGoogle Scholar
  115. [115]
    D. Boer, P. Mulders and F. Pijlman, Universality of T odd effects in single spin and azimuthal asymmetries, Nucl. Phys. B 667 (2003) 201 [hep-ph/0303034] [INSPIRE].ADSCrossRefGoogle Scholar
  116. [116]
    S. Aybat and T.C. Rogers, TMD parton distribution and fragmentation functions with QCD evolution, Phys. Rev. D 83 (2011) 114042 [arXiv:1101.5057] [INSPIRE].ADSGoogle Scholar
  117. [117]
    J.C. Collins, What exactly is a parton density?, Acta Phys. Polon. B 34 (2003) 3103 [hep-ph/0304122] [INSPIRE].ADSGoogle Scholar
  118. [118]
    A. Bacchetta, D. Boer, M. Diehl and P.J. Mulders, Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum, JHEP 08 (2008) 023 [arXiv:0803.0227] [INSPIRE].ADSCrossRefGoogle Scholar
  119. [119]
    J.C. Collins, D.E. Soper and G.F. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].ADSCrossRefGoogle Scholar
  120. [120]
    A. Idilbi, X.-d. Ji, J.-P. Ma and F. Yuan, Collins-Soper equation for the energy evolution of transverse-momentum and spin dependent parton distributions, Phys. Rev. D 70 (2004) 074021 [hep-ph/0406302] [INSPIRE].ADSGoogle Scholar
  121. [121]
    S. Descotes-Genon and C.T. Sachrajda, Sudakov effects in Bπlν(l) form-factors, Nucl. Phys. B 625 (2002) 239 [hep-ph/0109260] [INSPIRE].ADSCrossRefGoogle Scholar
  122. [122]
    M. Mekhfi and X. Artru, Sudakov suppression of color correlations in multiparton scattering, Phys. Rev. D 37 (1988) 2618 [INSPIRE].ADSGoogle Scholar
  123. [123]
    J.C. Collins, Leading twist single transverse-spin asymmetries: Drell-Yan and deep inelastic scattering, Phys. Lett. B 536 (2002) 43 [hep-ph/0204004] [INSPIRE].ADSGoogle Scholar
  124. [124]
    P. Hägler, B. Musch, J. Negele and A. Schäfer, Intrinsic quark transverse momentum in the nucleon from lattice QCD, Europhys. Lett. 88 (2009) 61001 [arXiv:0908.1283] [INSPIRE].ADSCrossRefGoogle Scholar
  125. [125]
    B.U. Musch, P. Hägler, J.W. Negele and A. Schäfer, Exploring quark transverse momentum distributions with lattice QCD, Phys. Rev. D 83 (2011) 094507 [arXiv:1011.1213] [INSPIRE].ADSGoogle Scholar
  126. [126]
    C. Alexandrou and G. Koutsou, A study of hadron deformation in lattice QCD, Phys. Rev. D 78 (2008) 094506 [arXiv:0809.2056] [INSPIRE].ADSGoogle Scholar
  127. [127]
    D. Mueller, D. Robaschik, B. Geyer, F. Dittes and J. Hořejši, Wave functions, evolution equations and evolution kernels from light ray operators of QCD, Fortsch. Phys. 42 (1994) 101 [hep-ph/9812448] [INSPIRE].ADSCrossRefGoogle Scholar
  128. [128]
    X.-D. Ji, Gauge invariant decomposition of nucleon spin and its spin-off, Phys. Rev. Lett. 78 (1997) 610 [hep-ph/9603249] [INSPIRE].ADSCrossRefGoogle Scholar
  129. [129]
    A. Radyushkin, Nonforward parton distributions, Phys. Rev. D 56 (1997) 5524 [hep-ph/9704207] [INSPIRE].ADSGoogle Scholar
  130. [130]
    K. Goeke, M.V. Polyakov and M. Vanderhaeghen, Hard exclusive reactions and the structure of hadrons, Prog. Part. Nucl. Phys. 47 (2001) 401 [hep-ph/0106012] [INSPIRE].ADSCrossRefGoogle Scholar
  131. [131]
    M. Diehl, Generalized parton distributions, Phys. Rept. 388 (2003) 41 [hep-ph/0307382] [INSPIRE].ADSCrossRefGoogle Scholar
  132. [132]
    A. Belitsky and A. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rept. 418 (2005) 1 [hep-ph/0504030] [INSPIRE].ADSCrossRefGoogle Scholar
  133. [133]
    S. Meissner, A. Metz and M. Schlegel, Generalized parton correlation functions for a spin-1/2 hadron, JHEP 08 (2009) 056 [arXiv:0906.5323] [INSPIRE].ADSCrossRefGoogle Scholar
  134. [134]
    D. Soper, Infinite-momentum helicity states, Phys. Rev. D 5 (1972) 1956 [INSPIRE].ADSGoogle Scholar
  135. [135]
    X. Ji, J.-W. Qiu, W. Vogelsang and F. Yuan, A unified picture for single transverse-spin asymmetries in hard processes, Phys. Rev. Lett. 97 (2006) 082002 [hep-ph/0602239] [INSPIRE].ADSCrossRefGoogle Scholar
  136. [136]
    X. Ji, J.-w. Qiu, W. Vogelsang and F. Yuan, Single transverse-spin asymmetry in Drell-Yan production at large and moderate transverse momentum, Phys. Rev. D 73 (2006) 094017 [hep-ph/0604023] [INSPIRE].ADSGoogle Scholar
  137. [137]
    X. Ji, J.-W. Qiu, W. Vogelsang and F. Yuan, Single-transverse spin asymmetry in semi-inclusive deep inelastic scattering, Phys. Lett. B 638 (2006) 178 [hep-ph/0604128] [INSPIRE].ADSGoogle Scholar
  138. [138]
    Y. Koike, W. Vogelsang and F. Yuan, On the relation between mechanisms for single-transverse-spin asymmetries, Phys. Lett. B 659 (2008) 878 [arXiv:0711.0636] [INSPIRE].ADSGoogle Scholar
  139. [139]
    A. Bukhvostov, G. Frolov, L. Lipatov and E. Kuraev, Evolution equations for quasi-partonic operators, Nucl. Phys. B 258 (1985) 601 [INSPIRE].ADSCrossRefGoogle Scholar
  140. [140]
    L.N. Lipatov, private communication (2012).Google Scholar
  141. [141]
    J. Bartels, Unitarity corrections to the Lipatov Pomeron and the four gluon operator in deep inelastic scattering in QCD, Z. Phys. C 60 (1993) 471 [INSPIRE].ADSGoogle Scholar
  142. [142]
    M. Cacciari, G.P. Salam and S. Sapeta, On the characterisation of the underlying event, JHEP 04 (2010) 065 [arXiv:0912.4926] [INSPIRE].ADSCrossRefGoogle Scholar
  143. [143]
    J.R. Gaunt and W. Stirling, Double parton scattering singularity in one-loop integrals, JHEP 06 (2011) 048 [arXiv:1103.1888] [INSPIRE].ADSCrossRefGoogle Scholar
  144. [144]
    M. Ryskin and A. Snigirev, A fresh look at double parton scattering, Phys. Rev. D 83 (2011) 114047 [arXiv:1103.3495] [INSPIRE].ADSGoogle Scholar
  145. [145]
    R. Kirschner, Generalized Lipatov-Altarelli-Parisi equations and jet calculus rules, Phys. Lett. B 84 (1979) 266 [INSPIRE].ADSGoogle Scholar
  146. [146]
    V. Shelest, A. Snigirev and G. Zinovev, The multiparton distribution equations in QCD, Phys. Lett. B 113 (1982) 325 [INSPIRE].ADSGoogle Scholar
  147. [147]
    A. Snigirev, Double parton distributions in the leading logarithm approximation of perturbative QCD, Phys. Rev. D 68 (2003) 114012 [hep-ph/0304172] [INSPIRE].ADSGoogle Scholar
  148. [148]
    J.R. Gaunt and W. Stirling, Double parton distributions incorporating perturbative QCD evolution and momentum and quark number sum rules, JHEP 03 (2010) 005 [arXiv:0910.4347] [INSPIRE].ADSCrossRefGoogle Scholar
  149. [149]
    G. Bozzi, S. Catani, D. de Florian and M. Grazzini, Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC, Nucl. Phys. B 737 (2006) 73 [hep-ph/0508068] [INSPIRE].ADSCrossRefGoogle Scholar
  150. [150]
    J. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
  151. [151]
    D. Binosi and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Markus Diehl
    • 1
  • Daniel Ostermeier
    • 2
  • Andreas Schäfer
    • 2
  1. 1.Deutsches Elektronen-Synchroton DESYHamburgGermany
  2. 2.Institut für Theoretische PhysikUniversität RegensburgRegensburgGermany

Personalised recommendations