Unified framework for generalized and transverse-momentum dependent parton distributions within a 3Q light-cone picture of the nucleon

Article

Abstract

We present a systematic study of generalized transverse-momentum dependent parton distributions (GTMDs). By taking specific limits or projections, these GTMDs yield various transverse-momentum dependent and generalized parton distributions, thus providing a unified framework to simultaneously model different observables. We present such simultaneous modeling by considering a light-cone wave function overlap representation of the GTMDs. We construct the different quark-quark correlation functions from the 3-quark Fock components within both the light-front constituent quark model and the chiral quark-soliton model. We provide a comparison with available data and make predictions for different observables.

Keywords

Deep Inelastic Scattering Phenomenological Models QCD 

References

  1. [1]
    S. Meissner, A. Metz, M. Schlegel and K. Goeke, Generalized parton correlation functions for a spin-0 hadron, JHEP 08 (2008) 038 [arXiv:0805.3165] [SPIRES].CrossRefGoogle Scholar
  2. [2]
    S. Meissner, A. Metz and M. Schlegel, Generalized parton correlation functions for a spin-1/2 hadron, JHEP 08 (2009) 056 [arXiv:0906.5323] [SPIRES].ADSCrossRefGoogle Scholar
  3. [3]
    X.-d. Ji, Viewing the proton through ’color’-filters, Phys. Rev. Lett. 91 (2003) 062001 [hep-ph/0304037] [SPIRES].ADSCrossRefGoogle Scholar
  4. [4]
    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] [SPIRES].ADSGoogle Scholar
  5. [5]
    A.V. Belitsky and A.V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rept. 418 (2005) 1 [hep-ph/0504030] [SPIRES].ADSCrossRefGoogle Scholar
  6. [6]
    D.E. Soper, The parton model and the Bethe-Salpeter wave function, Phys. Rev. D 15 (1977) 1141 [SPIRES].ADSGoogle Scholar
  7. [7]
    M. Burkardt, Impact parameter dependent parton distributions and off-forward parton distributions for ζ → 0, Phys. Rev. D 62 (2000) 071503 [Erratum ibid. D 66 (2002) 119903] [hep-ph/0005108] [SPIRES].ADSGoogle Scholar
  8. [8]
    M. Burkardt, Impact parameter space interpretation for generalized parton distributions, Int. J. Mod. Phys. A 18 (2003) 173 [hep-ph/0207047] [SPIRES].ADSGoogle Scholar
  9. [9]
    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] [SPIRES].ADSCrossRefGoogle Scholar
  10. [10]
    S.J. Brodsky, M. Diehl and D.S. Hwang, Light-cone wavefunction representation of deeply virtual Compton scattering, Nucl. Phys. B 596 (2001) 99 [hep-ph/0009254] [SPIRES].ADSCrossRefGoogle Scholar
  11. [11]
    M. Diehl, T. Feldmann, R. Jakob and P. Kroll, Skewed parton distributions in real and virtual Compton scattering, Phys. Lett. B 460 (1999) 204 [hep-ph/9903268] [SPIRES].ADSGoogle Scholar
  12. [12]
    S. Boffi and B. Pasquini, Generalized parton distributions and the structure of the nucleon, Riv. Nuovo Cim. 30 (2007) 387 [arXiv:0711.2625] [SPIRES].ADSGoogle Scholar
  13. [13]
    S. Boffi, B. Pasquini and M. Traini, Linking generalized parton distributions to constituent quark models, Nucl. Phys. B 649 (2003) 243 [hep-ph/0207340] [SPIRES].ADSCrossRefGoogle Scholar
  14. [14]
    S. Boffi, B. Pasquini and M. Traini, Helicity-dependent generalized parton distributions in constituent quark models, Nucl. Phys. B 680 (2004) 147 [hep-ph/0311016] [SPIRES].ADSCrossRefGoogle Scholar
  15. [15]
    B. Pasquini, M. Pincetti and S. Boffi, Chiral-odd generalized parton distributions in constituent quark models, Phys. Rev. D 72 (2005) 094029 [hep-ph/0510376] [SPIRES].ADSGoogle Scholar
  16. [16]
    D. Diakonov and V.Y. Petrov, Chiral condensate in the instanton vacuum, Phys. Lett. B 147 (1984) 351 [SPIRES].ADSGoogle Scholar
  17. [17]
    D. Diakonov and V.Y. Petrov, A theory of light quarks in the instanton vacuum, Nucl. Phys. B 272 (1986) 457 [SPIRES].ADSCrossRefGoogle Scholar
  18. [18]
    D. Diakonov and V.Y. Petrov, Chiral theory of nucleons, JETP Lett. 43 (1986) 75 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 57] [SPIRES].ADSGoogle Scholar
  19. [19]
    D. Diakonov, V.Y. Petrov and P.V. Pobylitsa, A chiral theory of nucleons, Nucl. Phys. B 306 (1988) 809 [SPIRES].ADSCrossRefGoogle Scholar
  20. [20]
    V.Y. Petrov and M.V. Polyakov, Light cone nucleon wave function in the quark soliton model, hep-ph/0307077 [SPIRES].
  21. [21]
    D. Diakonov and V. Petrov, Estimate of the+ width in the relativistic mean field approximation, Phys. Rev. D 72 (2005) 074009 [hep-ph/0505201] [SPIRES].ADSGoogle Scholar
  22. [22]
    C. Lorcé, Improvement of the+ width estimation method on the light cone, Phys. Rev. D 74 (2006) 054019 [hep-ph/0603231] [SPIRES].ADSGoogle Scholar
  23. [23]
    C. Lorcé, Baryon vector and axial content up to the 7Q component, Phys. Rev. D 78 (2008) 034001 [arXiv:0708.3139] [SPIRES].ADSGoogle Scholar
  24. [24]
    C. Lorcé, Tensor charges of light baryons in the infinite momentum frame, Phys. Rev. D 79 (2009) 074027 [arXiv:0708.4168] [SPIRES].ADSGoogle Scholar
  25. [25]
    H.J. Melosh, Quarks: currents and constituents, Phys. Rev. D 9 (1974) 1095 [SPIRES].ADSGoogle Scholar
  26. [26]
    J.B. Kogut and D.E. Soper, Quantum electrodynamics in the infinite momentum frame, Phys. Rev. D 1 (1970) 2901 [SPIRES].ADSGoogle Scholar
  27. [27]
    B. Pasquini, S. Cazzaniga and S. Boffi, Transverse momentum dependent parton distributions in a light-cone quark model, Phys. Rev. D 78 (2008) 034025 [arXiv:0806.2298] [SPIRES].ADSGoogle Scholar
  28. [28]
    H. Avakian, A.V. Efremov, P. Schweitzer and F. Yuan, The transverse momentum dependent distribution functions in the bag model, Phys. Rev. D 81 (2010) 074035 [arXiv:1001.5467] [SPIRES].ADSGoogle Scholar
  29. [29]
    H. Avakian, A.V. Efremov, P. Schweitzer and F. Yuan, Transverse momentum dependent distribution function \( h_{1T}^\bot \) and the single spin asymmetry \( A_{UT}^{\sin \left( {3\phi - {\phi_S}} \right)} \), Phys. Rev. D 78 (2008) 114024 [arXiv:0805.3355] [SPIRES].ADSGoogle Scholar
  30. [30]
    B. Pasquini and C. Lorcé, Modeling the transverse momentum dependent parton distributions, arXiv:1008.0945 [SPIRES].
  31. [31]
    B.U. Musch, P. Hägler, J.W. Negele and A. Schäfer, Exploring quark transverse momentum distributions with lattice QCD, arXiv:1011.1213 [SPIRES].
  32. [32]
    P. Hägler, B.U. Musch, J.W. Negele and A. Schäfer, Intrinsic quark transverse momentum in the nucleon from lattice QCD, EuroPhys. Lett. 88 (2009) 61001 [arXiv:0908.1283] [SPIRES].ADSCrossRefGoogle Scholar
  33. [33]
    M. Wakamatsu, Transverse momentum distributions of quarks in the nucleon from the chiral quark soliton model, Phys. Rev. D 79 (2009) 094028 [arXiv:0903.1886] [SPIRES].ADSGoogle Scholar
  34. [34]
    M. Diehl and P. Hägler, Spin densities in the transverse plane and generalized transversity distributions, Eur. Phys. J. C 44 (2005) 87 [hep-ph/0504175] [SPIRES].ADSCrossRefGoogle Scholar
  35. [35]
    M. Burkardt, Chromodynamic lensing and transverse single spin asymmetries, Nucl. Phys. A 735 (2004) 185 [hep-ph/0302144] [SPIRES].ADSGoogle Scholar
  36. [36]
    M. Burkardt and D.S. Hwang, Sivers asymmetry and generalized parton distributions in impact parameter space, Phys. Rev. D 69 (2004) 074032 [hep-ph/0309072] [SPIRES].ADSGoogle Scholar
  37. [37]
    S. Meissner, A. Metz and K. Goeke, Relations between generalized and transverse momentum dependent parton distributions, Phys. Rev. D 76 (2007) 034002 [hep-ph/0703176] [SPIRES].ADSGoogle Scholar
  38. [38]
    J. Ossmann, M.V. Polyakov, P. Schweitzer, D. Urbano and K. Goeke, The generalized parton distribution function (E(u) + E(d))(x, ξ, t) of the nucleon in the chiral quark soliton model, Phys. Rev. D 71 (2005) 034011 [hep-ph/0411172] [SPIRES].ADSGoogle Scholar
  39. [39]
    M.V. Polyakov and C. Weiss, Skewed and double distributions in pion and nucleon, Phys. Rev. D 60 (1999) 114017 [hep-ph/9902451] [SPIRES].ADSGoogle Scholar
  40. [40]
    M. Penttinen, M.V. Polyakov and K. Goeke, Helicity skewed quark distributions of the nucleon and chiral symmetry, Phys. Rev. D 62 (2000) 014024 [hep-ph/9909489] [SPIRES].ADSGoogle Scholar
  41. [41]
    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] [SPIRES].ADSCrossRefGoogle Scholar
  42. [42]
    M. Wakamatsu, Chiral-odd GPDs, transversity decomposition of angular momentum and tensor charges of the nucleon, Phys. Rev. D 79 (2009) 014033 [arXiv:0811.4196] [SPIRES].ADSGoogle Scholar
  43. [43]
    M. Wakamatsu and Y. Nakakoji, Generalized form factors, generalized parton distributions and the spin contents of the nucleon, Phys. Rev. D 74 (2006) 054006 [hep-ph/0605279] [SPIRES].ADSGoogle Scholar
  44. [44]
    M. Wakamatsu and H. Tsujimoto, The generalized parton distribution functions and the nucleon spin sum rules in the chiral quark soliton model, Phys. Rev. D 71 (2005) 074001 [hep-ph/0502030] [SPIRES].ADSGoogle Scholar
  45. [45]
    A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [SPIRES].ADSCrossRefGoogle Scholar
  46. [46]
    E. Leader, A.V. Sidorov and D.B. Stamenov, Impact of CLAS and COMPASS data on polarized parton densities and higher twist, Phys. Rev. D 75 (2007) 074027 [hep-ph/0612360] [SPIRES].ADSGoogle Scholar
  47. [47]
    B. Pasquini and P. Schweitzer, Naive time-reversal odd phenomena in semi-inclusive deep-inelastic scattering from light-cone constituent quark models, 1103.5977 [SPIRES].
  48. [48]
    M. Anselmino et al., Transversity and Collins functions from SIDIS and e + e data, Phys. Rev. D 75 (2007) 054032 [hep-ph/0701006] [SPIRES].ADSGoogle Scholar
  49. [49]
    M. Anselmino et al., Update on transversity and Collins functions from SIDIS and e + e data, Nucl. Phys. Proc. Suppl. 191 (2009) 98 [arXiv:0812.4366] [SPIRES].ADSCrossRefGoogle Scholar
  50. [50]
    J. Soffer, Positivity constraints for spin dependent parton distributions, Phys. Rev. Lett. 74 (1995) 1292 [hep-ph/9409254] [SPIRES].ADSCrossRefGoogle Scholar
  51. [51]
    S. Boffi, A.V. Efremov, B. Pasquini and P. Schweitzer, Azimuthal spin asymmetries in light-cone constituent quark models, Phys. Rev. D 79 (2009) 094012 [arXiv:0903.1271] [SPIRES].ADSGoogle Scholar
  52. [52]
    HERMES collaboration, M. Diefenthaler, Transversity measurements at HERMES, AIP Conf. Proc. 792 (2005) 933 [hep-ex/0507013] [SPIRES].ADSCrossRefGoogle Scholar
  53. [53]
    COMPASS collaboration, M. Alekseev et al., Collins and Sivers asymmetries for pions and kaons in muon-deuteron DIS, Phys. Lett. B 673 (2009) 127 [arXiv:0802.2160] [SPIRES].ADSGoogle Scholar
  54. [54]
    A.V. Efremov, K. Goeke and P. Schweitzer, Collins effect in semi-inclusive deeply inelastic scattering and in e + e annihilation, Phys. Rev. D 73 (2006) 094025 [hep-ph/0603054] [SPIRES].ADSGoogle Scholar
  55. [55]
    W. Vogelsang and F. Yuan, Single-transverse spin asymmetries: from DIS to hadronic collisions, Phys. Rev. D 72 (2005) 054028 [hep-ph/0507266] [SPIRES].ADSGoogle Scholar
  56. [56]
    D. Boer, Sudakov suppression in azimuthal spin asymmetries, Nucl. Phys. B 603 (2001) 195 [hep-ph/0102071] [SPIRES].ADSCrossRefGoogle Scholar
  57. [57]
    Belle collaboration, K. Abe et al., Measurement of azimuthal asymmetries in inclusive production of hadron pairs in e + e annihilation at Belle, Phys. Rev. Lett. 96 (2006) 232002 [hep-ex/0507063] [SPIRES].ADSCrossRefGoogle Scholar
  58. [58]
    K. Goeke, P.V. Pobylitsa, M.V. Polyakov, P. Schweitzer and D. Urbano, Quark distribution functions in the chiral quark-soliton model: cancellation of quantum anomalies, Acta Phys. Polon. B 32 (2001) 1201 [hep-ph/0001272] [SPIRES].ADSGoogle Scholar
  59. [59]
    P. Schweitzer et al., Transversity distributions in the nucleon in the large-N c limit, Phys. Rev. D 64 (2001) 034013 [hep-ph/0101300] [SPIRES].ADSGoogle Scholar
  60. [60]
    M. Diehl, Generalized parton distributions with helicity flip, Eur. Phys. J. C 19 (2001) 485 [hep-ph/0101335] [SPIRES].ADSCrossRefGoogle Scholar
  61. [61]
    C.F. Perdrisat, V. Punjabi and M. Vanderhaeghen, Nucleon electromagnetic form factors, Prog. Part. Nucl. Phys. 59 (2007) 694 [hep-ph/0612014] [SPIRES].ADSCrossRefGoogle Scholar
  62. [62]
    B. Pasquini and S. Boffi, Electroweak structure of the nucleon, meson cloud and light-cone wavefunctions, Phys. Rev. D 76 (2007) 074011 [arXiv:0707.2897] [SPIRES].ADSGoogle Scholar
  63. [63]
    B. Pasquini and S. Boffi, Nucleon spin densities in a light-front constituent quark model, Phys. Lett. B 653 (2007) 23 [arXiv:0705.4345] [SPIRES].ADSGoogle Scholar
  64. [64]
    B. Pasquini, M. Pincetti and S. Boffi, Drell-Yan processes, transversity and light-cone wavefunctions, Phys. Rev. D 76 (2007) 034020 [hep-ph/0612094] [SPIRES].ADSGoogle Scholar
  65. [65]
    HERMES collaboration, A. Airapetian et al., Precise determination of the spin structure function g(1) of the proton, deuteron and neutron, Phys. Rev. D 75 (2007) 012007 [hep-ex/0609039] [SPIRES].ADSGoogle Scholar
  66. [66]
    Particle Data Group collaboration, Review of particle physics, J. Phys. G 37 (2010) 075021 [SPIRES].ADSGoogle Scholar
  67. [67]
    D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Extraction of spin-dependent parton densities and their uncertainties, Phys. Rev. D 80 (2009) 034030 [arXiv:0904.3821] [SPIRES].ADSGoogle Scholar
  68. [68]
    Z. Dziembowski, Relativistic model of nucleon and pion structure: static properties and electromagnetic soft form-factors, Phys. Rev. D 37 (1988) 778 [SPIRES].ADSGoogle Scholar
  69. [69]
    P.L. Chung and F. Coester, Relativistic constituent quark model of nucleon form-factors, Phys. Rev. D 44 (1991) 229 [SPIRES].ADSGoogle Scholar
  70. [70]
    F. Cardarelli, E. Pace, G. Salme and S. Simula, Nucleon and pion electromagnetic form-factors in a light front constituent quark model, Phys. Lett. B 357 (1995) 267 [nucl-th/9507037] [SPIRES].ADSGoogle Scholar
  71. [71]
    B.-Q. Ma, D. Qing and I. Schmidt, Electromagnetic form factors of nucleons in a light-cone diquark model, Phys. Rev. C 65 (2002) 035205 [hep-ph/0202015] [SPIRES].ADSGoogle Scholar
  72. [72]
    T. Ledwig, A. Silva and H.-C. Kim, Tensor charges and form factors of SU(3) baryons in the self-consistent SU(3) chiral quark-soliton model, Phys. Rev. D 82 (2010) 034022 [arXiv:1004.3612] [SPIRES].ADSGoogle Scholar
  73. [73]
    B. Pasquini and F. Yuan, Sivers and Boer-Mulders functions in light-cone quark models, Phys. Rev. D 81 (2010) 114013 [arXiv:1001.5398] [SPIRES].ADSGoogle Scholar
  74. [74]
    QCDSF collaboration, M. Gockeler et al., Transverse spin structure of the nucleon from lattice QCD simulations, Phys. Rev. Lett. 98 (2007) 222001 [hep-lat/0612032] [SPIRES].ADSCrossRefGoogle Scholar
  75. [75]
    T. Ledwig, A. Silva and H.-C. Kim, Anomalous tensor magnetic moments and form factors of the proton in the self-consistent chiral quark-soliton model, Phys. Rev. D 82 (2010) 054014 [arXiv:1007.1355] [SPIRES].ADSGoogle Scholar
  76. [76]
    F. Schlumpf, Relativistic constituent quark model for baryons, hep-ph/9211255 [SPIRES].
  77. [77]
    D. Diakonov, V. Petrov, P. Pobylitsa, M.V. Polyakov and C. Weiss, Nucleon parton distributions at low normalization point in the large-N c limit, Nucl. Phys. B 480 (1996) 341 [hep-ph/9606314] [SPIRES].ADSCrossRefGoogle Scholar
  78. [78]
    D. Diakonov et al., Unpolarized and polarized quark distributions in the large-N c limit, Phys. Rev. D 56 (1997) 4069 [hep-ph/9703420] [SPIRES].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Institut für KernphysikJohannes Gutenberg-UniversitätMainzGermany
  2. 2.Dipartimento di Fisica Nucleare e TeoricaUniversità degli Studi di PaviaPaviaItaly
  3. 3.INFN — Sezione di PaviaPaviaItaly

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