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Deep inelastic scattering from polarized spin-1/2 hadrons at low x from string theory

  • Nicolas Kovensky
  • Gustavo Michalski
  • Martin Schvellinger
Open Access
Regular Article - Theoretical Physics
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Abstract

We study polarized deep inelastic scattering of charged leptons from spin-1/2 hadrons at low values of the Bjorken parameter and large ’t Hooft coupling in terms of the gauge/string theory duality. We calculate the structure functions from type IIB superstring theory scattering amplitudes. We discuss the role of the non-Abelian Chern-Simons term and the Pauli term from the five-dimensional SU(4) gauged supergravity. Furthermore, the exponentially small-x regime where Regge physics becomes important is analyzed in detail for the antisymmetric structure functions. In this case the holographic dual picture of the Pomeron exchange is realized by a Reggeized gauge field. We compare our results with experimental data of the proton antisymmetric structure function g1, obtaining a very good level of agreement.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence 

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]
    M. Anselmino, A. Efremov and E. Leader, The Theory and phenomenology of polarized deep inelastic scattering, Phys. Rept. 261 (1995) 1 [Erratum ibid. 281 (1997) 399] [hep-ph/9501369] [INSPIRE].
  2. [2]
    B. Lampe and E. Reya, Spin physics and polarized structure functions, Phys. Rept. 332 (2000) 1 [hep-ph/9810270] [INSPIRE].
  3. [3]
    N. Kovensky, G. Michalski and M. Schvellinger, DIS off glueballs from string theory: the role of the chiral anomaly and the Chern-Simons term, JHEP 04 (2018) 118 [arXiv:1711.06171] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Y. Hatta, T. Ueda and B.-W. Xiao, Polarized DIS in N = 4 SYM: Where is spin at strong coupling?, JHEP 08 (2009) 007 [arXiv:0905.2493] [INSPIRE].
  5. [5]
    J. Polchinski and M.J. Strassler, Deep inelastic scattering and gauge/string duality, JHEP 05 (2003) 012 [hep-th/0209211] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    J.-H. Gao and B.-W. Xiao, Polarized Deep Inelastic and Elastic Scattering From Gauge/String Duality, Phys. Rev. D 80 (2009) 015025 [arXiv:0904.2870] [INSPIRE].
  7. [7]
    J.-H. Gao and B.-W. Xiao, Nonforward Compton scattering in AdS/CFT correspondence, Phys. Rev. D 81 (2010) 035008 [arXiv:0912.4333] [INSPIRE].
  8. [8]
    J.-H. Gao and Z.-G. Mou, Polarized Deep Inelastic Scattering Off the Neutron From Gauge/String Duality, Phys. Rev. D 81 (2010) 096006 [arXiv:1003.3066] [INSPIRE].
  9. [9]
    R.C. Brower, M. Djuric, I. Sarcevic and C.-I. Tan, String-Gauge Dual Description of Deep Inelastic Scattering at Small-x, JHEP 11 (2010) 051 [arXiv:1007.2259] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  10. [10]
    R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    ZEUS and H1 collaborations, F.D. Aaron et al., Combined Measurement and QCD Analysis of the Inclusive e ± p Scattering Cross Sections at HERA, JHEP 01 (2010) 109 [arXiv:0911.0884] [INSPIRE].
  12. [12]
    ZEUS collaboration, J. Breitweg et al., ZEUS results on the measurement and phenomenology of F 2 at low x and low Q 2, Eur. Phys. J. C 7 (1999) 609 [hep-ex/9809005] [INSPIRE].
  13. [13]
    ZEUS collaboration, S. Chekanov et al., Measurement of the neutral current cross-section and F 2 structure function for deep inelastic e + p scattering at HERA, Eur. Phys. J. C 21 (2001) 443 [hep-ex/0105090] [INSPIRE].
  14. [14]
    Spin Muon collaboration, B. Adeva et al., Spin asymmetries A 1 and structure functions g1 of the proton and the deuteron from polarized high-energy muon scattering, Phys. Rev. D 58 (1998) 112001 [INSPIRE].
  15. [15]
    COMPASS collaboration, M.G. Alekseev et al., The Spin-dependent Structure Function of the Proton g 1p and a Test of the Bjorken Sum Rule, Phys. Lett. B 690 (2010) 466 [arXiv:1001.4654] [INSPIRE].
  16. [16]
    COMPASS collaboration, C. Adolph et al., The spin structure function g 1P of the proton and a test of the Bjorken sum rule, Phys. Lett. B 753 (2016) 18 [arXiv:1503.08935] [INSPIRE].
  17. [17]
    European Muon collaboration, J. Ashman et al., A Measurement of the Spin Asymmetry and Determination of the Structure Function g 1 in Deep Inelastic Muon-Proton Scattering, Phys. Lett. B 206 (1988) 364 [INSPIRE].
  18. [18]
    European Muon collaboration, J. Ashman et al., An Investigation of the Spin Structure of the Proton in Deep Inelastic Scattering of Polarized Muons on Polarized Protons, Nucl. Phys. B 328 (1989) 1 [INSPIRE].
  19. [19]
    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] [INSPIRE].
  20. [20]
    E143 collaboration, K. Abe et al., Measurements of the proton and deuteron spin structure functions g 1 and g 2, Phys. Rev. D 58 (1998) 112003 [hep-ph/9802357] [INSPIRE].
  21. [21]
    E155 collaboration, P.L. Anthony et al., Measurements of the Q 2 dependence of the proton and neutron spin structure functions g 1p and g 1n, Phys. Lett. B 493 (2000) 19 [hep-ph/0007248] [INSPIRE].
  22. [22]
    CLAS collaboration, Y. Prok et al., Precision measurements of g 1 of the proton and the deuteron with 6 GeV electrons, Phys. Rev. C 90 (2014) 025212 [arXiv:1404.6231] [INSPIRE].
  23. [23]
    COMPASS collaboration, M. Aghasyan et al., Longitudinal double-spin asymmetry A 1P and spin-dependent structure function g 1P of the proton at small values of x and Q 2, Phys. Lett. B 781 (2018) 464 [arXiv:1710.01014] [INSPIRE].
  24. [24]
    E. Koile, S. Macaluso and M. Schvellinger, Deep Inelastic Scattering from Holographic Spin-One Hadrons, JHEP 02 (2012) 103 [arXiv:1112.1459] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    E. Koile, S. Macaluso and M. Schvellinger, Deep inelastic scattering structure functions of holographic spin-1 hadrons with N f ≥ 1, JHEP 01 (2014) 166 [arXiv:1311.2601] [INSPIRE].
  26. [26]
    E. Koile, N. Kovensky and M. Schvellinger, Hadron structure functions at small x from string theory, JHEP 05 (2015) 001 [arXiv:1412.6509] [INSPIRE].
  27. [27]
    E. Koile, N. Kovensky and M. Schvellinger, Deep inelastic scattering cross sections from the gauge/string duality, JHEP 12 (2015) 009 [arXiv:1507.07942] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  28. [28]
    D. Jorrin, N. Kovensky and M. Schvellinger, Towards 1/N corrections to deep inelastic scattering from the gauge/gravity duality, JHEP 04 (2016) 113 [arXiv:1601.01627] [INSPIRE].ADSMathSciNetGoogle Scholar
  29. [29]
    D. Jorrin, M. Schvellinger and N. Kovensky, Deep inelastic scattering off scalar mesons in the 1/N expansion from the D3D7-brane system, JHEP 12 (2016) 003 [arXiv:1609.01202] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    N. Kovensky, G. Michalski and M. Schvellinger, 1/N corrections to F 1 and F 2 structure functions of vector mesons from holography, arXiv:1809.10515 [INSPIRE].
  31. [31]
    R.C. Brower, M.J. Strassler and C.-I. Tan, On The Pomeron at Large ’t Hooft Coupling, JHEP 03 (2009) 092 [arXiv:0710.4378] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    R.C. Brower, M.J. Strassler and C.-I. Tan, On the eikonal approximation in AdS space, JHEP 03 (2009) 050 [arXiv:0707.2408] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    L. Cornalba, M.S. Costa, J. Penedones and R. Schiappa, Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions, Nucl. Phys. B 767 (2007) 327 [hep-th/0611123] [INSPIRE].
  34. [34]
    L. Cornalba, M.S. Costa and J. Penedones, Eikonal approximation in AdS/CFT: Resumming the gravitational loop expansion, JHEP 09 (2007) 037 [arXiv:0707.0120] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    Y. Hatta, E. Iancu and A.H. Mueller, Deep inelastic scattering at strong coupling from gauge/string duality: The Saturation line, JHEP 01 (2008) 026 [arXiv:0710.2148] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    R. Nishio and T. Watari, High-Energy Photon-Hadron Scattering in Holographic QCD, Phys. Rev. D 84 (2011) 075025 [arXiv:1105.2999] [INSPIRE].
  37. [37]
    M.S. Costa and M. Djuric, Deeply Virtual Compton Scattering from Gauge/Gravity Duality, Phys. Rev. D 86 (2012) 016009 [arXiv:1201.1307] [INSPIRE].
  38. [38]
    A. Watanabe and K. Suzuki, Transition from soft- to hard-Pomeron in the structure functions of hadrons at small-x from holography, Phys. Rev. D 86 (2012) 035011 [arXiv:1206.0910] [INSPIRE].
  39. [39]
    M.S. Costa, M. Djurić and N. Evans, Vector meson production at low x from gauge/gravity duality, JHEP 09 (2013) 084 [arXiv:1307.0009] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    R. Nally, T.G. Raben and C.-I. Tan, Inclusive Production Through AdS/CFT, JHEP 11 (2017) 075 [arXiv:1702.05502] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    C.A. Ballon Bayona, H. Boschi-Filho and N.R.F. Braga, Deep inelastic scattering from gauge string duality in the soft wall model, JHEP 03 (2008) 064 [arXiv:0711.0221] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  42. [42]
    C.A. Ballon Bayona, H. Boschi-Filho and N.R.F. Braga, Deep inelastic scattering from gauge string duality in D3-D7 brane model, JHEP 09 (2008) 114 [arXiv:0807.1917] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    C.A. Ballon Bayona, H. Boschi-Filho and N.R.F. Braga, Deep Inelastic Scattering in Holographic AdS/QCD Models, Nucl. Phys. Proc. Suppl. 199 (2010) 97 [arXiv:0910.1309] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  44. [44]
    C.A. Ballon Bayona, H. Boschi-Filho, N.R.F. Braga and M.A.C. Torres, Deep inelastic scattering for vector mesons in holographic D4-D8 model, JHEP 10 (2010) 055 [arXiv:1007.2448] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  45. [45]
    C.A.B. Bayona, H. Boschi-Filho, N.R.F. Braga, M. Ihl and M.A.C. Torres, Generalized baryon form factors and proton structure functions in the Sakai-Sugimoto model, Nucl. Phys. B 866 (2013) 124 [arXiv:1112.1439] [INSPIRE].
  46. [46]
    A. Ballon-Bayona, R. Carcassés Quevedo and M.S. Costa, Unity of Pomerons from gauge/string duality, JHEP 08 (2017) 085 [arXiv:1704.08280] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The Mass Spectrum of Chiral N = 2 D = 10 Supergravity on S5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
  48. [48]
    M. Günaydin, L.J. Romans and N.P. Warner, Gauged N = 8 Supergravity in Five-Dimensions, Phys. Lett. B 154 (1985) 268 [INSPIRE].
  49. [49]
    M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged N = 8 D = 5 Supergravity, Nucl. Phys. B 259 (1985) 460 [INSPIRE].
  50. [50]
    M. Günaydin, L.J. Romans and N.P. Warner, Compact and Noncompact Gauged Supergravity Theories in Five-Dimensions, Nucl. Phys. B 272 (1986) 598 [INSPIRE].
  51. [51]
    D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFTd/AdSd+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
  52. [52]
    H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
  53. [53]
    K. Becker, M. Becker, I.V. Melnikov, D. Robbins and A.B. Royston, Some tree-level string amplitudes in the NSR formalism, JHEP 12 (2015) 010 [arXiv:1507.02172] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  54. [54]
    J.H. Schwarz, Superstring Theory, Phys. Rept. 89 (1982) 223 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    M.R. Garousi and R.C. Myers, Superstring scattering from D-branes, Nucl. Phys. B 475 (1996) 193 [hep-th/9603194] [INSPIRE].
  56. [56]
    C. Best et al., Pion and rho structure functions from lattice QCD, Phys. Rev. D 56 (1997) 2743 [hep-lat/9703014] [INSPIRE].
  57. [57]
    A. Baguet, O. Hohm and H. Samtleben, Consistent Type IIB Reductions to Maximal 5D Supergravity, Phys. Rev. D 92 (2015) 065004 [arXiv:1506.01385] [INSPIRE].
  58. [58]
    J. Erlich, E. Katz, D.T. Son and M.A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602 [hep-ph/0501128] [INSPIRE].
  59. [59]
    L. Da Rold and A. Pomarol, Chiral symmetry breaking from five dimensional spaces, Nucl. Phys. B 721 (2005) 79 [hep-ph/0501218] [INSPIRE].
  60. [60]
    T. Hambye, B. Hassanain, J. March-Russell and M. Schvellinger, On the Delta I = 1/2 rule in holographic QCD, Phys. Rev. D 74 (2006) 026003 [hep-ph/0512089] [INSPIRE].
  61. [61]
    T. Hambye, B. Hassanain, J. March-Russell and M. Schvellinger, Four-point functions and Kaon decays in a minimal AdS/QCD model, Phys. Rev. D 76 (2007) 125017 [hep-ph/0612010] [INSPIRE].
  62. [62]
    A.V. Manohar, An Introduction to spin dependent deep inelastic scattering, in Lake Louise Winter Institute: Symmetry and Spin in the Standard Model, Lake Louise, Alberta, Canada, February 23-29, 1992, pp. 1-46 (1992) [hep-ph/9204208] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Nicolas Kovensky
    • 1
    • 2
  • Gustavo Michalski
    • 1
    • 2
  • Martin Schvellinger
    • 1
    • 2
  1. 1.Instituto de Física La Plata-UNLP-CONICETLa PlataArgentina
  2. 2.Departamento de Física, Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataArgentina

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