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Where do we stand with a 3-D picture of the proton?

  • Alessandro BacchettaEmail author
Review
Part of the following topical collections:
  1. The 3-D Structure of the Nucleon

Abstract.

We are on the way to obtaining multi-dimensional “pictures” of the proton. The field is bursting with activities, both from the theoretical and experimental side. A brief selection of important achievements of the last years and open challenges for the future is presented. They are already well documented in the various reviews of this Topical Issue, but they are gathered here in a more condensed way for convenience, together with some additional remarks. The choice of the items included in this short overview is far from being complete and represents the view of the author.

References

  1. 1.
    X. Ji, J.P. Ma, F. Yuan, Phys. Rev. D 71, 034005 (2005) hep-ph/0404183ADSCrossRefGoogle Scholar
  2. 2.
    J. Collins, Foundations of Perturbative QCD, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (Cambridge University Press, 2011)Google Scholar
  3. 3.
    S. Aybat, T.C. Rogers, Phys. Rev. D 83, 114042 (2011) arXiv:1101.5057 ADSCrossRefGoogle Scholar
  4. 4.
    M.G. Echevarria, A. Idilbi, I. Scimemi, JHEP 07, 002 (2012) arXiv:1111.4996 ADSCrossRefGoogle Scholar
  5. 5.
    M.G. Echevarria, A. Idilbi, I. Scimemi, Phys. Lett. B 726, 795 (2013) arXiv:1211.1947 ADSCrossRefGoogle Scholar
  6. 6.
    T.C. Rogers, Eur. Phys. J. A 52, 153 (2016) arXiv:1509.04766, this Topical IssueCrossRefGoogle Scholar
  7. 7.
    M. Diehl, Eur. Phys. J. A 52, 149 (2016) arXiv:1512.01328, this Topical IssueADSCrossRefGoogle Scholar
  8. 8.
    S.J. Brodsky, D.S. Hwang, I. Schmidt, Phys. Lett. B 530, 99 (2002) hep-ph/0201296ADSCrossRefGoogle Scholar
  9. 9.
    X. Ji, F. Yuan, Phys. Lett. B 543, 66 (2002) hep-ph/0206057ADSCrossRefGoogle Scholar
  10. 10.
    A.V. Belitsky, X. Ji, F. Yuan, Nucl. Phys. B 656, 165 (2003) hep-ph/0208038ADSCrossRefGoogle Scholar
  11. 11.
    J.C. Collins, Phys. Lett. B 536, 43 (2002) hep-ph/0204004ADSCrossRefGoogle Scholar
  12. 12.
    C.J. Bomhof, P.J. Mulders, F. Pijlman, Phys. Lett. B 596, 277 (2004) hep-ph/0406099ADSCrossRefGoogle Scholar
  13. 13.
    A. Bacchetta, C.J. Bomhof, P.J. Mulders, F. Pijlman, Phys. Rev. D 72, 034030 (2005) hep-ph/0505268ADSCrossRefGoogle Scholar
  14. 14.
    J. Collins, J.W. Qiu, Phys. Rev. D 75, 114014 (2007) arXiv:0705.2141 ADSCrossRefGoogle Scholar
  15. 15.
    T.C. Rogers, P.J. Mulders, Phys. Rev. D 81, 094006 (2010) arXiv:1001.2977 ADSCrossRefGoogle Scholar
  16. 16.
    T.C. Rogers, Phys. Rev. D 88, 014002 (2013) arXiv:1304.4251 ADSCrossRefGoogle Scholar
  17. 17.
    J.C. Collins, A. Metz, Phys. Rev. Lett. 93, 252001 (2004) hep-ph/0408249ADSCrossRefGoogle Scholar
  18. 18.
    M.G. Echevarria, A. Idilbi, A. Schäfer, I. Scimemi, Eur. Phys. J. C 73, 2636 (2013) arXiv:1208.1281 ADSCrossRefGoogle Scholar
  19. 19.
    M. Boglione, A. Prokudin, Eur. Phys. J. A 52, 154 (2016) arXiv:1511.06924, this Topical IssueCrossRefGoogle Scholar
  20. 20.
    HERMES Collaboration (A. Airapetian et al.), Phys. Rev. Lett. 94, 012002 (2005) hep-ex/0408013ADSCrossRefGoogle Scholar
  21. 21.
    COMPASS Collaboration (V.Y. Alexakhin et al.), Phys. Rev. Lett. 94, 202002 (2005) hep-ex/0503002CrossRefGoogle Scholar
  22. 22.
    H. Mkrtchyan et al., Phys. Lett. B 665, 20 (2008) arXiv:0709.3020 ADSCrossRefGoogle Scholar
  23. 23.
    CLAS Collaboration (M. Osipenko et al.), Phys. Rev. D 80, 032004 (2009) arXiv:0809.1153 CrossRefGoogle Scholar
  24. 24.
    HERMES Collaboration (A. Airapetian et al.), Phys. Rev. Lett. 103, 152002 (2009) arXiv:0906.3918 ADSCrossRefGoogle Scholar
  25. 25.
    HERMES Collaboration (A. Airapetian et al.), Phys. Lett. B 693, 11 (2010) arXiv:1006.4221 ADSCrossRefGoogle Scholar
  26. 26.
    CLAS Collaboration (H. Avakian et al.), Phys. Rev. Lett. 105, 262002 (2010) arXiv:1003.4549 CrossRefGoogle Scholar
  27. 27.
    COMPASS Collaboration (M. Alekseev et al.), Phys. Lett. B 692, 240 (2010) arXiv:1005.5609 ADSCrossRefGoogle Scholar
  28. 28.
    Jefferson Lab Hall A Collaboration (J. Huang et al.), Phys. Rev. Lett. 108, 052001 (2012) arXiv:1108.0489 CrossRefGoogle Scholar
  29. 29.
    Jefferson Lab Hall A Collaboration (X. Qian et al.), Phys. Rev. Lett. 107, 072003 (2011) arXiv:1106.0363 CrossRefGoogle Scholar
  30. 30.
    HERMES Collaboration (A. Airapetian et al.), Phys. Rev. D 87, 074029 (2013) arXiv:1212.5407 ADSCrossRefGoogle Scholar
  31. 31.
    HERMES Collaboration (A. Airapetian et al.), Phys. Rev. D 87, 012010 (2013) arXiv:1204.4161 ADSCrossRefGoogle Scholar
  32. 32.
    COMPASS Collaboration (C. Adolph et al.), Eur. Phys. J. C 73, 2531 (2013) 75CrossRefGoogle Scholar
  33. 33.
    HERMES Collaboration (A. Airapetian et al.), Phys. Lett. B 728, 183 (2014) arXiv:1310.5070 ADSCrossRefGoogle Scholar
  34. 34.
    A. Accardi, J. Albacete, M. Anselmino, N. Armesto, E. Aschenauer, arXiv:1212.1701 (2012)
  35. 35.
    Jefferson Lab Hall A Collaboration (K. Allada et al.), Phys. Rev. C 89, 042201 (2014) arXiv:1311.1866 ADSCrossRefGoogle Scholar
  36. 36.
    Jefferson Lab Hall A Collaboration (Y. Zhang et al.), Phys. Rev. C 90, 055209 (2014) arXiv:1312.3047 ADSCrossRefGoogle Scholar
  37. 37.
    COMPASS Collaboration (C. Adolph et al.), Nucl. Phys. B 886, 1046 (2014) arXiv:1401.6284 CrossRefGoogle Scholar
  38. 38.
    B. Parsamyan, Int. J. Mod. Phys. Conf. Ser. 40, 1660029 (2016) arXiv:1504.01599 CrossRefGoogle Scholar
  39. 39.
    Belle Collaboration (R. Seidl et al.), Phys. Rev. D 78, 032011 (2008) arXiv:0805.2975 CrossRefGoogle Scholar
  40. 40.
    Belle Collaboration (A. Vossen et al.), Phys. Rev. Lett. 107, 072004 (2011) arXiv:1104.2425 CrossRefGoogle Scholar
  41. 41.
    BaBar Collaboration (J.P. Lees et al.), Phys. Rev. D 90, 052003 (2014) arXiv:1309.5278 ADSCrossRefGoogle Scholar
  42. 42.
    BESIII Collaboration (M. Ablikim et al.), Phys. Rev. Lett. 116, 042001 (2016) arXiv:1507.06824 ADSCrossRefGoogle Scholar
  43. 43.
    J.C. Collins et al., Phys. Rev. D 73, 014021 (2006) hep-ph/0509076ADSCrossRefGoogle Scholar
  44. 44.
    W. Vogelsang, F. Yuan, Phys. Rev. D 72, 054028 (2005) hep-ph/0507266ADSCrossRefGoogle Scholar
  45. 45.
    M. Anselmino et al., Phys. Rev. D 75, 054032 (2007) hep-ph/0701006ADSCrossRefGoogle Scholar
  46. 46.
    M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, S. Melis, Nucl. Phys. Proc. Suppl. 191, 98 (2009) arXiv:0812.4366 ADSCrossRefGoogle Scholar
  47. 47.
    M. Anselmino, M. Boglione, U. D’Alesio, S. Melis, F. Murgia, A. Prokudin, J. Phys. Conf. Ser. 295, 012062 (2011) arXiv:1012.3565 ADSCrossRefGoogle Scholar
  48. 48.
    P. Schweitzer, T. Teckentrup, A. Metz, Phys. Rev. D 81, 094019 (2010) arXiv:1003.2190 ADSCrossRefGoogle Scholar
  49. 49.
    A. Bacchetta, M. Radici, Phys. Rev. Lett. 107, 212001 (2011) arXiv:1107.5755 ADSCrossRefGoogle Scholar
  50. 50.
    A. Signori, A. Bacchetta, M. Radici, G. Schnell, JHEP 11, 194 (2013) arXiv:1309.3507 ADSCrossRefGoogle Scholar
  51. 51.
    M. Anselmino, M. Boglione, J. Gonzalez H., S. Melis, A. Prokudin, JHEP 04, 005 (2014) arXiv:1312.6261 ADSCrossRefGoogle Scholar
  52. 52.
    M. Anselmino, M. Boglione, U. D’Alesio, S. Melis, F. Murgia et al., Phys. Rev. D 87, 094019 (2013) arXiv:1303.3822 ADSCrossRefGoogle Scholar
  53. 53.
    V. Barone, M. Boglione, J. Gonzalez Hernandez, S. Melis, Phys. Rev. D 91, 074019 (2015) arXiv:1502.04214 ADSCrossRefGoogle Scholar
  54. 54.
    J. Collins, T. Rogers, Phys. Rev. D 91, 074020 (2015) arXiv:1412.3820 ADSCrossRefGoogle Scholar
  55. 55.
    S.M. Aybat, A. Prokudin, T.C. Rogers, Phys. Rev. Lett. 108, 242003 (2012) arXiv:1112.4423 ADSCrossRefGoogle Scholar
  56. 56.
    M. Anselmino, M. Boglione, S. Melis, Phys. Rev. D 86, 014028 (2012) arXiv:1204.1239 ADSCrossRefGoogle Scholar
  57. 57.
    M.G. Echevarria, A. Idilbi, Z.B. Kang, I. Vitev, Phys. Rev. D 89, 074013 (2014) arXiv:1401.5078 ADSCrossRefGoogle Scholar
  58. 58.
    Z.B. Kang, A. Prokudin, P. Sun, F. Yuan, Phys. Rev. D 93, 014009 (2016) arXiv:1505.05589 ADSCrossRefGoogle Scholar
  59. 59.
    M. Anselmino, M. Boglione, U. D’Alesio, J.O. Gonzalez Hernandez, S. Melis, F. Murgia, A. Prokudin, Phys. Rev. D 92, 114023 (2015) arXiv:1510.05389 ADSCrossRefGoogle Scholar
  60. 60.
    A. Bacchetta, A. Courtoy, M. Radici, Phys. Rev. Lett. 107, 012001 (2011) arXiv:1104.3855 ADSCrossRefGoogle Scholar
  61. 61.
    A. Bacchetta, A. Courtoy, M. Radici, JHEP 03, 119 (2013) arXiv:1212.3568 ADSCrossRefGoogle Scholar
  62. 62.
    M. Radici, A. Courtoy, A. Bacchetta, M. Guagnelli, JHEP 05, 123 (2015) arXiv:1503.03495 ADSCrossRefGoogle Scholar
  63. 63.
    S. Pisano, M. Radici, Eur. Phys. J. A 52, 155 (2016) arXiv:1511.03220, this Topical IssueCrossRefGoogle Scholar
  64. 64.
    J.R. Green, J.W. Negele, A.V. Pochinsky, S.N. Syritsyn, M. Engelhardt, S. Krieg, Phys. Rev. D 86, 114509 (2012) arXiv:1206.4527 ADSCrossRefGoogle Scholar
  65. 65.
    G.S. Bali, S. Collins, B. Glässle, M. Göckeler, J. Najjar, R.H. Rödl, A. Schfäer, R.W. Söchiel, W. Söldner, A. Sternbeck, Phys. Rev. D 91, 054501 (2015) arXiv:1412.7336 ADSCrossRefGoogle Scholar
  66. 66.
    PNDME Collaboration (T. Bhattacharya, V. Cirigliano, S. Cohen, R. Gupta, A. Joseph, H.W. Lin, B. Yoon), Phys. Rev. D 92, 094511 (2015) arXiv:1506.06411 ADSGoogle Scholar
  67. 67.
    A. Abdel-Rehim et al., Phys. Rev. D 92, 114513 (2015) 93ADSCrossRefGoogle Scholar
  68. 68.
    U. D’Alesio, M.G. Echevarria, S. Melis, I. Scimemi, JHEP 11, 098 (2014) arXiv:1407.3311 ADSCrossRefGoogle Scholar
  69. 69.
    M. Burkardt, B. Pasquini, Eur. Phys. J. A 52, 161 (2016) arXiv:1510.02567, this Topical IssueCrossRefGoogle Scholar
  70. 70.
    A. Efremov, P. Schweitzer, JHEP 08, 006 (2003) hep-ph/0212044ADSCrossRefGoogle Scholar
  71. 71.
    M. Burkardt, Phys. Rev. D 69, 057501 (2004) hep-ph/0311013ADSCrossRefGoogle Scholar
  72. 72.
    S. Meissner, A. Metz, K. Goeke, Phys. Rev. D 76, 034002 (2007) hep-ph/0703176ADSCrossRefGoogle Scholar
  73. 73.
    B. Pasquini, S. Cazzaniga, S. Boffi, Phys. Rev. D 78, 034025 (2008) arXiv:0806.2298 ADSCrossRefGoogle Scholar
  74. 74.
    A. Bacchetta, F. Conti, M. Radici, Phys. Rev. D 78, 074010 (2008) arXiv:0807.0323 ADSCrossRefGoogle Scholar
  75. 75.
    C. Bourrely, F. Buccella, J. Soffer, Phys. Rev. D 83, 074008 (2011) arXiv:1008.5322 ADSCrossRefGoogle Scholar
  76. 76.
    H. Avakian, A.V. Efremov, P. Schweitzer, F. Yuan, Phys. Rev. D 81, 074035 (2010) arXiv:1001.5467 ADSCrossRefGoogle Scholar
  77. 77.
    A. Efremov, P. Schweitzer, O. Teryaev, P. Zavada, Phys. Rev. D 83, 054025 (2011) arXiv:1012.5296 ADSCrossRefGoogle Scholar
  78. 78.
    C. Lorcé, B. Pasquini, Phys. Rev. D 84, 034039 (2011) arXiv:1104.5651 ADSCrossRefGoogle Scholar
  79. 79.
    D. Müller, D.S. Hwang, arXiv:1407.1655 (2014)
  80. 80.
    F. Landry, R. Brock, P.M. Nadolsky, C.P. Yuan, Phys. Rev. D 67, 073016 (2003) hep-ph/0212159ADSCrossRefGoogle Scholar
  81. 81.
    A.V. Konychev, P.M. Nadolsky, Phys. Lett. B 633, 710 (2006) hep-ph/0506225ADSCrossRefGoogle Scholar
  82. 82.
    C. Aidala, B. Field, L. Gamberg, T. Rogers, Phys. Rev. D 89, 094002 (2014) arXiv:1401.2654 ADSCrossRefGoogle Scholar
  83. 83.
    STAR Collaboration (B.I. Abelev et al.), Phys. Rev. Lett. 101, 222001 (2008) arXiv:0801.2990 CrossRefGoogle Scholar
  84. 84.
    AnDY Collaboration (L.C. Bland et al.), Phys. Lett. B 750, 660 (2015) arXiv:1304.1454 CrossRefGoogle Scholar
  85. 85.
    STAR Collaboration (L. Adamczyk et al.), Phys. Rev. D 89, 012001 (2014) arXiv:1309.1800 ADSCrossRefGoogle Scholar
  86. 86.
    STAR Collaboration (J.L. Drachenberg) (2014)Google Scholar
  87. 87.
    STAR Collaboration (J.L. Drachenberg), EPJ Web of Conferences 73, 02009 (2014)CrossRefGoogle Scholar
  88. 88.
    E.C. Aschenauer, U. D’Alesio, F. Murgia, Eur. Phys. J. A 52, 156 (2016) arXiv:1512.05379, this Topical IssueCrossRefGoogle Scholar
  89. 89.
    S. Bultmann et al., Phys. Lett. B 632, 167 (2006) nucl-ex/0507030ADSCrossRefGoogle Scholar
  90. 90.
    I.G. Alekseev et al., Phys. Rev. D 79, 094014 (2009)ADSCrossRefGoogle Scholar
  91. 91.
    STAR Collaboration (L. Adamczyk et al.), Phys. Lett. B 719, 62 (2013) arXiv:1206.1928 ADSCrossRefGoogle Scholar
  92. 92.
    X. Ji, J.W. Qiu, W. Vogelsang, F. Yuan, Phys. Rev. D 73, 094017 (2006) hep-ph/0604023ADSCrossRefGoogle Scholar
  93. 93.
    C. Kouvaris, J.W. Qiu, W. Vogelsang, F. Yuan, Phys. Rev. D 74, 114013 (2006) hep-ph/0609238ADSCrossRefGoogle Scholar
  94. 94.
    K. Kanazawa, Y. Koike, Phys. Lett. B 720, 161 (2013) arXiv:1212.3071 ADSCrossRefGoogle Scholar
  95. 95.
    K. Kanazawa, Y. Koike, A. Metz, D. Pitonyak, Phys. Rev. D 89, 111501 (2014) arXiv:1404.1033 ADSCrossRefGoogle Scholar
  96. 96.
    K. Kanazawa, Y. Koike, A. Metz, D. Pitonyak, Phys. Rev. D 91, 014013 (2015) arXiv:1410.3448 ADSCrossRefGoogle Scholar
  97. 97.
    M. Anselmino, M. Boglione, U. D’Alesio, E. Leader, S. Melis, F. Murgia, A. Prokudin, Phys. Rev. D 86, 074032 (2012) arXiv:1207.6529 ADSCrossRefGoogle Scholar
  98. 98.
    M. Anselmino, M. Boglione, U. D’Alesio, S. Melis, F. Murgia, A. Prokudin, Phys. Rev. D 88, 054023 (2013) arXiv:1304.7691 ADSCrossRefGoogle Scholar
  99. 99.
    U. D’Alesio, F. Murgia, C. Pisano, JHEP 09, 119 (2015) arXiv:1506.03078 ADSCrossRefGoogle Scholar
  100. 100.
    S. Wandzura, F. Wilczek, Phys. Lett. B 72, 195 (1977)ADSCrossRefGoogle Scholar
  101. 101.
    L.P. Gamberg, D.S. Hwang, A. Metz, M. Schlegel, Phys. Lett. B 639, 508 (2006) hep-ph/0604022ADSCrossRefGoogle Scholar
  102. 102.
    A. Bacchetta, D. Boer, M. Diehl, P.J. Mulders, JHEP 08, 023 (2008) arXiv:0803.0227 ADSCrossRefGoogle Scholar
  103. 103.
    D. Boer, L. Gamberg, B. Musch, A. Prokudin, JHEP 10, 021 (2011) arXiv:1107.5294 ADSCrossRefGoogle Scholar
  104. 104.
    M.G.A. Buffing, P.J. Mulders, JHEP 07, 065 (2011) arXiv:1105.4804 ADSCrossRefGoogle Scholar
  105. 105.
    M.G.A. Buffing, A. Mukherjee, P.J. Mulders, Phys. Rev. D 86, 074030 (2012) arXiv:1207.3221 ADSCrossRefGoogle Scholar
  106. 106.
    M.G.A. Buffing, A. Mukherjee, P.J. Mulders, Phys. Rev. D 88, 054027 (2013) arXiv:1306.5897 ADSCrossRefGoogle Scholar
  107. 107.
    M.G.A. Buffing, P.J. Mulders, Phys. Rev. Lett. 112, 092002 (2014) arXiv:1309.4681 ADSCrossRefGoogle Scholar
  108. 108.
    D. Boer, M.G.A. Buffing, P.J. Mulders, JHEP 08, 053 (2015) arXiv:1503.03760 ADSCrossRefGoogle Scholar
  109. 109.
    T. Horn, C.D. Roberts, arXiv:1602.04016 (2016)
  110. 110.
    H.H. Matevosyan, W. Bentz, I.C. Cloet, A.W. Thomas, Phys. Rev. D 85, 014021 (2012) arXiv:1111.1740 ADSCrossRefGoogle Scholar
  111. 111.
    A. Casey, H.H. Matevosyan, A.W. Thomas, Phys. Rev. D 85, 114049 (2012) arXiv:1202.4036 ADSCrossRefGoogle Scholar
  112. 112.
    D. Boer, S.J. Brodsky, P.J. Mulders, C. Pisano, Phys. Rev. Lett. 106, 132001 (2011) arXiv:1011.4225 ADSCrossRefGoogle Scholar
  113. 113.
    D. Boer, W.J. den Dunnen, C. Pisano, M. Schlegel, W. Vogelsang, Phys. Rev. Lett. 108, 032002 (2012) arXiv:1109.1444 ADSCrossRefGoogle Scholar
  114. 114.
    D. Boer, C. Pisano, Phys. Rev. D 86, 094007 (2012) arXiv:1208.3642 ADSCrossRefGoogle Scholar
  115. 115.
    C. Pisano, D. Boer, S.J. Brodsky, M.G.A. Buffing, P.J. Mulders, JHEP 10, 024 (2013) arXiv:1307.3417 ADSCrossRefGoogle Scholar
  116. 116.
    D. Boer, C. Pisano, Phys. Rev. D 91, 074024 (2015) arXiv:1412.5556 ADSCrossRefGoogle Scholar
  117. 117.
    W.J. den Dunnen, J.P. Lansberg, C. Pisano, M. Schlegel, Phys. Rev. Lett. 112, 212001 (2014) arXiv:1401.7611 ADSCrossRefGoogle Scholar
  118. 118.
    M. Anselmino, U. D’Alesio, S. Melis, Adv. High Energy Phys. 2015, 475040 (2015) arXiv:1504.03791 CrossRefGoogle Scholar
  119. 119.
    C. Marquet, B.W. Xiao, F. Yuan, Phys. Lett. B 682, 207 (2009) arXiv:0906.1454 ADSCrossRefGoogle Scholar
  120. 120.
    F. Dominguez, C. Marquet, B.W. Xiao, F. Yuan, Phys. Rev. D 83, 105005 (2011) arXiv:1101.0715 ADSCrossRefGoogle Scholar
  121. 121.
    R. Angeles-Martinez et al., Acta Phys. Pol. B 46, 2501 (2015) arXiv:1507.05267 ADSCrossRefGoogle Scholar
  122. 122.
    D. Boer, EPJ Web of Conferences 112, 02003 (2016) arXiv:1601.01813 CrossRefGoogle Scholar
  123. 123.
    K. Kumericki, S. Liuti, H. Moutarde, arXiv:1602.02763 (2016)
  124. 124.
    Jefferson Lab Hall A, Hall A DVCS Collaborations (C.M. Camacho et al.), Phys. Rev. Lett. 97, 262002 (2006) nucl-ex/0607029CrossRefGoogle Scholar
  125. 125.
    CLAS Collaboration (F.X. Girod et al.), Phys. Rev. Lett. 100, 162002 (2008) arXiv:0711.4805 CrossRefGoogle Scholar
  126. 126.
    CLAS Collaboration (S. Pisano et al.), Phys. Rev. D 91, 052014 (2015) arXiv:1501.07052 ADSCrossRefGoogle Scholar
  127. 127.
    HERMES Collaboration (A. Airapetian et al.), Phys. Rev. Lett. 87, 182001 (2001) hep-ex/0106068ADSCrossRefGoogle Scholar
  128. 128.
    HERMES Collaboration (A. Airapetian et al.), JHEP 07, 032 (2012) arXiv:1203.6287 Google Scholar
  129. 129.
    HERMES Collaboration (A. Airapetian et al.), JHEP 06, 019 (2010) arXiv:1004.0177 Google Scholar
  130. 130.
    HERMES Collaboration (A. Airapetian et al.), JHEP 06, 066 (2008) arXiv:0802.2499 ADSCrossRefGoogle Scholar
  131. 131.
    HERMES Collaboration (A. Airapetian et al.), Phys. Lett. B 704, 15 (2011) arXiv:1106.2990 ADSCrossRefGoogle Scholar
  132. 132.
    HERMES Collaboration (A. Airapetian et al.), Phys. Rev. D 75, 011103 (2007) hep-ex/0605108ADSCrossRefGoogle Scholar
  133. 133.
    HERMES Collaboration (A. Airapetian et al.), JHEP 11, 083 (2009) arXiv:0909.3587 ADSCrossRefGoogle Scholar
  134. 134.
    HERMES Collaboration (A. Airapetian et al.), Phys. Rev. C 81, 035202 (2010) arXiv:0911.0091 ADSGoogle Scholar
  135. 135.
    ZEUS Collaboration (S. Chekanov et al.), Phys. Lett. B 573, 46 (2003) hep-ex/0305028ADSCrossRefGoogle Scholar
  136. 136.
    H1 Collaboration (A. Aktas et al.), Eur. Phys. J. C 44, 1 (2005) hep-ex/0505061ADSCrossRefGoogle Scholar
  137. 137.
    L. Favart, M. Guidal, T. Horn, P. Kroll, Eur. Phys. J. A 52, 158 (2016) arXiv:1511.04535, this Topical IssueCrossRefGoogle Scholar
  138. 138.
    M. Guidal, M.V. Polyakov, A.V. Radyushkin, M. Vanderhaeghen, Phys. Rev. D 72, 054013 (2005) hep-ph/0410251ADSCrossRefGoogle Scholar
  139. 139.
    S.V. Goloskokov, P. Kroll, Eur. Phys. J. C 53, 367 (2008) arXiv:0708.3569 ADSCrossRefGoogle Scholar
  140. 140.
    G.R. Goldstein, J.O.G. Hernandez, S. Liuti, Phys. Rev. D 91, 114013 (2015) arXiv:1311.0483 ADSCrossRefGoogle Scholar
  141. 141.
    M. Diehl, P. Kroll, Eur. Phys. J. C 73, 2397 (2013) arXiv:1302.4604 ADSCrossRefGoogle Scholar
  142. 142.
    K. Kumerički, D. Müller, M. Murray, Phys. Part. Nucl. 45, 723 (2014) arXiv:1301.1230 CrossRefGoogle Scholar
  143. 143.
    K. Kumerički, D. Müller, arXiv:1512.09014 (2015)
  144. 144.
    M. Guidal, H. Moutarde, M. Vanderhaeghen, Rep. Prog. Phys. 76, 066202 (2013) arXiv:1303.6600 ADSCrossRefGoogle Scholar
  145. 145.
    M. Guidal, Phys. Lett. B 693, 17 (2010) arXiv:1005.4922 ADSCrossRefGoogle Scholar
  146. 146.
    H. Moutarde, Phys. Rev. D 79, 094021 (2009) arXiv:0904.1648 ADSCrossRefGoogle Scholar
  147. 147.
    M. Boër, M. Guidal, J. Phys. G 42, 034023 (2015) arXiv:1412.4651 ADSCrossRefGoogle Scholar
  148. 148.
    K. Kumerički, D. Mueller, Int. J. Mod. Phys. Conf. Ser. 37, 1560042 (2015)CrossRefGoogle Scholar
  149. 149.
    S.V. Goloskokov, P. Kroll, Eur. Phys. J. C 50, 829 (2007) hep-ph/0611290ADSCrossRefGoogle Scholar
  150. 150.
    M. Diehl, W. Kugler, Eur. Phys. J. C 52, 933 (2007) arXiv:0708.1121 ADSCrossRefGoogle Scholar
  151. 151.
    M. Meskauskas, D. Müller, Eur. Phys. J. C 74, 2719 (2014) arXiv:1112.2597 ADSCrossRefGoogle Scholar
  152. 152.
    S.V. Goloskokov, P. Kroll, Eur. Phys. J. C 65, 137 (2010) arXiv:0906.0460 ADSCrossRefGoogle Scholar
  153. 153.
    S.V. Goloskokov, P. Kroll, Eur. Phys. J. A 47, 112 (2011) arXiv:1106.4897 ADSCrossRefGoogle Scholar
  154. 154.
    A.D. Martin, M.G. Ryskin, T. Teubner, Phys. Rev. D 62, 014022 (2000) hep-ph/9912551ADSCrossRefGoogle Scholar
  155. 155.
    G.R. Goldstein, J.O. Hernandez, S. Liuti, Phys. Rev. D 84, 034007 (2011) arXiv:1012.3776 ADSCrossRefGoogle Scholar
  156. 156.
    A.V. Radyushkin, Phys. Rev. D 59, 014030 (1999) hep-ph/9805342ADSCrossRefGoogle Scholar
  157. 157.
    D. Müller, D. Robaschik, B. Geyer, F.M. Dittes, J. Hořejši, Fortsch. Phys. 42, 101 (1994) hep-ph/9812448ADSCrossRefGoogle Scholar
  158. 158.
    V. Guzey, M.V. Polyakov, Eur. Phys. J. C 46, 151 (2006) hep-ph/0507183ADSCrossRefGoogle Scholar
  159. 159.
    V. Guzey, T. Teckentrup, Phys. Rev. D 74, 054027 (2006) hep-ph/0607099ADSCrossRefGoogle Scholar
  160. 160.
    V. Guzey, T. Teckentrup, Phys. Rev. D 79, 017501 (2009) arXiv:0810.3899 ADSCrossRefGoogle Scholar
  161. 161.
    M.V. Polyakov, M. Vanderhaeghen, arXiv:0803.1271 (2008)
  162. 162.
    K. Kumerički, D. Mueller, Nucl. Phys. B 841, 1 (2010) arXiv:0904.0458 ADSCrossRefGoogle Scholar
  163. 163.
    K. Kumericki, T. Lautenschlager, D. Mueller, K. Passek-Kumericki, A. Schaefer, M. Meskauskas, arXiv:1105.0899 (2011)
  164. 164.
    X. Ji, Phys. Rev. Lett. 91, 062001 (2003) hep-ph/0304037ADSCrossRefGoogle Scholar
  165. 165.
    A.V. Belitsky, X. Ji, F. Yuan, Phys. Rev. D 69, 074014 (2004) hep-ph/0307383ADSCrossRefGoogle Scholar
  166. 166.
    C. Lorcé, B. Pasquini, Phys. Rev. D 84, 014015 (2011) arXiv:1106.0139 ADSCrossRefGoogle Scholar
  167. 167.
    S. Meissner, A. Metz, M. Schlegel, JHEP 08, 056 (2009) arXiv:0906.5323 ADSCrossRefGoogle Scholar
  168. 168.
    S. Meissner, A. Metz, M. Schlegel, K. Goeke, JHEP 08, 038 (2008) arXiv:0805.3165 ADSCrossRefGoogle Scholar
  169. 169.
    C. Lorcé, B. Pasquini, JHEP 09, 138 (2013) arXiv:1307.4497 ADSCrossRefGoogle Scholar
  170. 170.
    Y. Hatta, B.W. Xiao, F. Yuan, arXiv:1601.01585 (2016)
  171. 171.
    M.G. Echevarria, A. Idilbi, K. Kanazawa, C. Lorcé, A. Metz, B. Pasquini, M. Schlegel, arXiv:1602.06953 (2016)
  172. 172.
    J.R. Gaunt, W.J. Stirling, JHEP 03, 005 (2010) arXiv:0910.4347 ADSCrossRefGoogle Scholar
  173. 173.
    G. Calucci, D. Treleani, Phys. Rev. D 83, 016012 (2011) arXiv:1009.5881 ADSCrossRefGoogle Scholar
  174. 174.
    M. Diehl, D. Ostermeier, A. Schafer, JHEP 03, 089 (2012) arXiv:1111.0910 ADSCrossRefGoogle Scholar
  175. 175.
    M. Strikman, W. Vogelsang, Phys. Rev. D 83, 034029 (2011) arXiv:1009.6123 ADSCrossRefGoogle Scholar
  176. 176.
    M. Rinaldi, S. Scopetta, V. Vento, Phys. Rev. D 87, 114021 (2013) arXiv:1302.6462 ADSCrossRefGoogle Scholar
  177. 177.
    K.F. Liu, C. Lorcé, Eur. Phys. J. A 52, 160 (2016) arXiv:1508.00911, this Topical IssueCrossRefGoogle Scholar
  178. 178.
    X.D. Ji, Phys. Rev. Lett. 78, 610 (1997) hep-ph/9603249ADSCrossRefGoogle Scholar
  179. 179.
    R.L. Jaffe, A. Manohar, Nucl. Phys. B 337, 509 (1990)ADSCrossRefGoogle Scholar
  180. 180.
    D. de Florian, R. Sassot, M. Stratmann, W. Vogelsang, Phys. Rev. Lett. 113, 012001 (2014) arXiv:1404.4293 ADSCrossRefGoogle Scholar
  181. 181.
    NNPDF Collaboration (E.R. Nocera, R.D. Ball, S. Forte, G. Ridolfi, J. Rojo), Nucl. Phys. B 887, 276 (2014) arXiv:1406.5539 ADSCrossRefGoogle Scholar
  182. 182.
    E. Leader, arXiv:1211.3957 (2012)
  183. 183.
    Y. Hatta, K. Tanaka, S. Yoshida, JHEP 02, 003 (2013) arXiv:1211.2918 ADSCrossRefGoogle Scholar
  184. 184.
    A. Harindranath, R. Kundu, A. Mukherjee, Phys. Lett. B 728, 63 (2014) arXiv:1308.1519 ADSCrossRefGoogle Scholar
  185. 185.
    E. Leader, C. Lorcé, Phys. Rep. 541, 163 (2014) arXiv:1309.4235 ADSMathSciNetCrossRefGoogle Scholar
  186. 186.
    C. Lorcé, B. Pasquini, X. Xiong, F. Yuan, Phys. Rev. D 85, 114006 (2012) arXiv:1111.4827 ADSCrossRefGoogle Scholar
  187. 187.
    Y. Hatta, arXiv:1111.3547 (2011)
  188. 188.
    X. Ji, X. Xiong, F. Yuan, Phys. Rev. Lett. 109, 152005 (2012) arXiv:1202.2843 ADSCrossRefGoogle Scholar
  189. 189.
    M. Burkardt, Phys. Rev. D 88, 014014 (2013) arXiv:1205.2916 ADSCrossRefGoogle Scholar
  190. 190.
    M. Penttinen, M.V. Polyakov, A.G. Shuvaev, M. Strikman, Phys. Lett. B 491, 96 (2000) hep-ph/0006321ADSCrossRefGoogle Scholar
  191. 191.
    D.V. Kiptily, M.V. Polyakov, Eur. Phys. J. C 37, 105 (2004) hep-ph/0212372ADSCrossRefGoogle Scholar
  192. 192.
    P. Hagler, A. Mukherjee, A. Schafer, Phys. Lett. B 582, 55 (2004) hep-ph/0310136ADSCrossRefGoogle Scholar
  193. 193.
    Y. Hatta, S. Yoshida, JHEP 10, 080 (2012) arXiv:1207.5332 ADSCrossRefGoogle Scholar
  194. 194.
    C. Lorcé, JHEP 08, 045 (2015) arXiv:1502.06656 ADSCrossRefGoogle Scholar
  195. 195.
    A. Courtoy, G.R. Goldstein, J.O.G. Hernandez, S. Liuti, A. Rajan, Phys. Lett. B 731, 141 (2014) arXiv:1310.5157 ADSCrossRefGoogle Scholar
  196. 196.
    A. Rajan, A. Courtoy, M. Engelhardt, S. Liuti, arXiv:1601.06117 (2016)
  197. 197.
    T. Liu, B.Q. Ma, Phys. Lett. B 741, 256 (2015) arXiv:1501.00062 CrossRefGoogle Scholar
  198. 198.
    X. Ji, A. Schäfer, F. Yuan, J.H. Zhang, Y. Zhao, Phys. Rev. D 93, 054013 (2016) arXiv:1511.08817 ADSCrossRefGoogle Scholar
  199. 199.
    S. Ahmad, H. Honkanen, S. Liuti, S.K. Taneja, Phys. Rev. D 75, 094003 (2007) hep-ph/0611046ADSCrossRefGoogle Scholar
  200. 200.
    S. Goloskokov, P. Kroll, Eur. Phys. J. C 59, 809 (2009) arXiv:0809.4126 ADSCrossRefGoogle Scholar
  201. 201.
    M. Deka et al., Phys. Rev. D 91, 014505 (2015) arXiv:1312.4816 ADSCrossRefGoogle Scholar
  202. 202.
    V. Cirigliano, S. Gardner, B. Holstein, Prog. Part. Nucl. Phys. 71, 93 (2013) arXiv:1303.6953 ADSCrossRefGoogle Scholar
  203. 203.
    T. Bhattacharya, V. Cirigliano, R. Gupta, H.W. Lin, B. Yoon, Phys. Rev. Lett. 115, 212002 (2015) arXiv:1506.04196 ADSCrossRefGoogle Scholar
  204. 204.
    A. Courtoy, S. Baeßler, M. González-Alonso, S. Liuti, Phys. Rev. Lett. 115, 162001 (2015) arXiv:1503.06814 ADSCrossRefGoogle Scholar
  205. 205.
    P. Schweitzer, Phys. Rev. D 67, 114010 (2003) hep-ph/0303011ADSCrossRefGoogle Scholar
  206. 206.
    Y. Ohnishi, M. Wakamatsu, Phys. Rev. D 69, 114002 (2004) hep-ph/0312044ADSCrossRefGoogle Scholar
  207. 207.
    C. Cebulla, J. Ossmann, P. Schweitzer, D. Urbano, Acta Phys. Polon. B 39, 609 (2008) arXiv:0710.3103 ADSGoogle Scholar
  208. 208.
    A. Mukherjee, Phys. Lett. B 687, 180 (2010) arXiv:0912.1446 ADSCrossRefGoogle Scholar
  209. 209.
    C. Lorcé, B. Pasquini, P. Schweitzer, JHEP 01, 103 (2015) arXiv:1411.2550 ADSCrossRefGoogle Scholar
  210. 210.
    A.V. Efremov, K. Goeke, P. Schweitzer, Phys. Rev. D 67, 114014 (2003) hep-ph/0208124ADSCrossRefGoogle Scholar
  211. 211.
    A. Bacchetta, M. Radici, Phys. Rev. D 69, 074026 (2004) hep-ph/0311173ADSCrossRefGoogle Scholar
  212. 212.
    W. Mao, Z. Lu, Eur. Phys. J. C 73, 2557 (2013) arXiv:1306.1004 ADSCrossRefGoogle Scholar
  213. 213.
    A. Courtoy, arXiv:1405.7659 (2014)
  214. 214.
    CLAS Collaboration (W. Gohn et al.), Phys. Rev. D 89, 072011 (2014) arXiv:1402.4097 ADSCrossRefGoogle Scholar
  215. 215.
    P. Jimenez-Delgado, A. Accardi, W. Melnitchouk, Phys. Rev. D 89, 034025 (2014) arXiv:1310.3734 ADSCrossRefGoogle Scholar
  216. 216.
    S. Taheri Monfared, Z. Haddadi, A.N. Khorramian, Phys. Rev. D 89, 074052 (2014) 89ADSCrossRefGoogle Scholar
  217. 217.
    B.U. Musch, P. Hagler, J.W. Negele, A. Schafer, Phys. Rev. D 83, 094507 (2011) arXiv:1011.1213 ADSCrossRefGoogle Scholar
  218. 218.
    P. Hagler, B.U. Musch, J.W. Negele, A. Schafer, Europhys. Lett. 88, 61001 (2009) arXiv:0908.1283 ADSCrossRefGoogle Scholar
  219. 219.
    B.U. Musch, P. Hagler, M. Engelhardt, J.W. Negele, A. Schafer, Phys. Rev. D 85, 094510 (2012) arXiv:1111.4249 ADSCrossRefGoogle Scholar
  220. 220.
    M. Engelhardt, P. Hägler, B. Musch, J. Negele, A. Schäfer, Phys. Rev. D 93, 054501 (2016) arXiv:1506.07826 ADSCrossRefGoogle Scholar
  221. 221.
    X. Ji, Phys. Rev. Lett. 110, 262002 (2013) arXiv:1305.1539 ADSCrossRefGoogle Scholar
  222. 222.
    X. Xiong, X. Ji, J.H. Zhang, Y. Zhao, Phys. Rev. D 90, 014051 (2014) arXiv:1310.7471 ADSCrossRefGoogle Scholar
  223. 223.
    X. Ji, P. Sun, X. Xiong, F. Yuan, Phys. Rev. D 91, 074009 (2015) arXiv:1405.7640 ADSCrossRefGoogle Scholar
  224. 224.
    X. Ji, J.H. Zhang, Phys. Rev. D 92, 034006 (2015) arXiv:1505.07699 ADSCrossRefGoogle Scholar
  225. 225.
    X. Ji, A. Schäfer, X. Xiong, J.H. Zhang, Phys. Rev. D 92, 014039 (2015) arXiv:1506.00248 ADSCrossRefGoogle Scholar
  226. 226.
    J.W. Chen, S.D. Cohen, X. Ji, H.W. Lin, J.H. Zhang, arXiv:1603.06664 (2016)

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversità degli Studi di Pavia, and INFN, Sez. di PaviaPaviaItaly

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