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Reflections upon the emergence of hadronic mass

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Abstract

With discovery of the Higgs boson, science has located the source for ≲2% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining ≳98%. The instruments at work here must be capable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.

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References

  1. G. Aad et al., Phys. Lett. B 716, 1 (2012)

    Article  ADS  Google Scholar 

  2. S. Chatrchyan et al., Phys. Lett. B 716, 30 (2012)

    Article  ADS  Google Scholar 

  3. F. Englert, Rev. Mod. Phys. 86, 843 (2014)

    Article  ADS  Google Scholar 

  4. P.W. Higgs, Rev. Mod. Phys. 86, 851 (2014)

    Article  ADS  Google Scholar 

  5. M. Limon et al., Wilkinson Microwave Anisotropy Probe (WMAP): Explanatory Supplement (2003) [lambda.gsfc.nasa.gov/data/map/doc/MAP_supplement.pdf]

  6. C. Seife, Science 302, 2038 (2003)

    Article  ADS  Google Scholar 

  7. H.D. Politzer, Proc. Nat. Acad. Sci. 102, 7789 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  8. F. Wilczek, Proc. Nat. Acad. Sci. 102, 8403 (2005)

    Article  ADS  Google Scholar 

  9. D. Gross, Proc. Nat. Acad. Sci. 102, 9099 (2005)

    Article  ADS  Google Scholar 

  10. K.G. Wilson, Phys. Rev. D 10, 2445 (1974)

    Article  ADS  Google Scholar 

  11. J. Carlson, A. Jaffe, A. Wiles, The Millenium Prize Problems (American Mathematical Society, Providence, 2006)

  12. R.E. Taylor, Rev. Mod. Phys. 63, 573 (1991)

    Article  ADS  Google Scholar 

  13. H.W. Kendall, Rev. Mod. Phys. 63, 597 (1991)

    Article  ADS  Google Scholar 

  14. J.I. Friedman, Rev. Mod. Phys. 63, 615 (1991)

    Article  ADS  Google Scholar 

  15. K.D. Lane, Phys. Rev. D 10, 2605 (1974)

    Article  ADS  Google Scholar 

  16. H.D. Politzer, Nucl. Phys. B 117, 397 (1976)

    Article  ADS  Google Scholar 

  17. H. Pagels, Phys. Rev. D 19, 3080 (1979)

    Article  ADS  Google Scholar 

  18. J.M. Cornwall, Phys. Rev. D 26, 1453 (1982)

    Article  ADS  Google Scholar 

  19. K. Higashijima, Phys. Rev. D 29, 1228 (1984)

    Article  ADS  Google Scholar 

  20. H.J. Munczek, A.M. Nemirovsky, Phys. Rev. D 28, 181 (1983)

    Article  ADS  Google Scholar 

  21. P.I. Fomin, V.P. Gusynin, V.A. Miransky, Y.A. Sitenko, Riv. Nuovo Cim. 6N5, 1 (1983)

    Article  Google Scholar 

  22. R.T. Cahill, C.D. Roberts, Phys. Rev. D 32, 2419 (1985)

    Article  ADS  Google Scholar 

  23. A.C. Aguilar, D. Binosi, J. Papavassiliou, Front. Phys. China 11, 111203 (2016)

    ADS  Google Scholar 

  24. Y. Nambu, Phys. Rev. 117, 648 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  25. J. Goldstone, Nuovo Cim. 19, 154 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  26. T. Horn, C.D. Roberts, J. Phys. G 43, 073001 (2016)

    Article  ADS  Google Scholar 

  27. M. Tanabashi et al., Phys. Rev. D 98, 030001 (2018)

    Article  ADS  Google Scholar 

  28. C.M.G. Lattes, H. Muirhead, G.P.S. Occhialini, C.F. Powell, Nature 159, 694 (1947)

    Article  ADS  Google Scholar 

  29. G.D. Rochester, C.C. Butler, Nature 160, 855 (1947)

    Article  ADS  Google Scholar 

  30. W.J. Marciano, H. Pagels, Phys. Rep 36, 137 (1978)

    Article  ADS  Google Scholar 

  31. J. Bjorken, E.A. Paschos, Phys. Rev. 185, 1975 (1969)

    Article  ADS  Google Scholar 

  32. C.D. Roberts, Few Body Syst. 58, 5 (2017)

    Article  ADS  Google Scholar 

  33. M.S. Bhagwat, M.A. Pichowsky, C.D. Roberts, P.C. Tandy, Phys. Rev. C 68, 015203 (2003)

    Article  ADS  Google Scholar 

  34. P.O. Bowman et al., Phys. Rev. D 71, 054507 (2005)

    Article  ADS  Google Scholar 

  35. M.S. Bhagwat, P.C. Tandy, AIP Conf. Proc. 842, 225 (2006)

    Article  ADS  Google Scholar 

  36. P. Maris, C.D. Roberts, P.C. Tandy, Phys. Lett. B 420, 267 (1998)

    Article  ADS  Google Scholar 

  37. S.-X. Qin, C.D. Roberts, S.M. Schmidt, Phys. Lett. B 733, 202 (2014)

    Article  ADS  Google Scholar 

  38. D. Binosi, L. Chang, S.-X. Qin, J. Papavassiliou, C.D. Roberts, Phys. Rev. D 93, 096010 (2016)

    Article  ADS  Google Scholar 

  39. A. Bender, C.D. Roberts, L. von Smekal, Phys. Lett. B 380, 7 (1996)

    Article  ADS  Google Scholar 

  40. P. Maris, C.D. Roberts, Phys. Rev. C 56, 3369 (1997)

    Article  ADS  Google Scholar 

  41. G. Eichmann, R. Alkofer, A. Krassnigg, D. Nicmorus, Phys. Rev. Lett. 104, 201601 (2010)

    Article  ADS  Google Scholar 

  42. V. Gribov, Eur. Phys. J. C 10, 71 (1999), [239 (1998)]

    Article  ADS  MathSciNet  Google Scholar 

  43. Y.L. Dokshitzer, Perturbative QCD theory (includes our knowledge of α(s)) - hep-ph/9812252, in Proceedings, 29th International Conference, ICHEP’98, Vancouver, Canada, July 23–29, 1998 (High Energ. Phys., Vancouver, 1998), Vol. 1, 2, pp. 305–324.

  44. G. Grunberg, Phys. Rev. D 29, 2315 (1984)

    Article  ADS  Google Scholar 

  45. M. Gell-Mann, F.E. Low, Phys. Rev. 95, 1300 (1954)

    Article  ADS  MathSciNet  Google Scholar 

  46. J.M. Cornwall, J. Papavassiliou, Phys. Rev. D 40, 3474 (1989)

    Article  ADS  Google Scholar 

  47. A. Pilaftsis, Nucl. Phys. B 487, 467 (1997)

    Article  ADS  Google Scholar 

  48. D. Binosi, J. Papavassiliou, Phys. Rep 479, 1 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  49. L.F. Abbott, Nucl. Phys. B 185, 189 (1981)

    Article  ADS  Google Scholar 

  50. J.C. Taylor, Nucl. Phys. B 33, 436 (1971)

    Article  ADS  Google Scholar 

  51. A.A. Slavnov, Theor. Math. Phys. 10, 99 (1972)

    Article  Google Scholar 

  52. Z.-F. Cui et al., Chin. Phys. C 44, 083102 (2020)

    Article  ADS  Google Scholar 

  53. J. Rodríguez-Quintero, D. Binosi, C. Mezrag, J. Papavassiliou, C.D. Roberts, Few Body Syst. 59, 121 (2018)

    Article  ADS  Google Scholar 

  54. A. Deur, V. Burkert, J.-P. Chen, W. Korsch, Phys. Lett. B 650, 244 (2007)

    Article  ADS  Google Scholar 

  55. A. Deur, V. Burkert, J.-P. Chen, W. Korsch, Phys. Lett. B 665, 349 (2008)

    Article  ADS  Google Scholar 

  56. A. Deur, S.J. Brodsky, G.F. de Teramond, Prog. Part. Nucl. Phys. 90, 1 (2016)

    Article  ADS  Google Scholar 

  57. D. Binosi, C. Mezrag, J. Papavassiliou, C.D. Roberts, J. Rodríguez-Quintero, Phys. Rev. D 96, 054026 (2017)

    Article  ADS  Google Scholar 

  58. C. Becchi, A. Rouet, R. Stora, Ann. Phys. 98, 287 (1976)

    Article  ADS  Google Scholar 

  59. I.V. Tyutin, Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism (1975), arXiv:0812.0580 [hep-th]

  60. M. Ding et al., Chin. Phys. (Lett.) 44, 031002 (2020)

    ADS  Google Scholar 

  61. M. Ding et al., Phys. Rev. D 101, 054014 (2020)

    Article  ADS  Google Scholar 

  62. Y.L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)

    ADS  Google Scholar 

  63. V.N. Gribov, L.N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)

    Google Scholar 

  64. L.N. Lipatov, Sov. J. Nucl. Phys. 20, 94 (1975)

    Google Scholar 

  65. G. Altarelli, G. Parisi, Nucl. Phys. B 126, 298 (1977)

    Article  ADS  Google Scholar 

  66. H.L.L. Roberts, C.D. Roberts, A. Bashir, L.X. Gutiérrez-Guerrero, P.C. Tandy, Phys. Rev. C 82, 065202 (2010)

    Article  ADS  Google Scholar 

  67. H.L.L. Roberts, A. Bashir, L.X. Gutiérrez-Guerrero, C.D. Roberts, D.J. Wilson, Phys. Rev. C 83, 065206 (2011)

    Article  ADS  Google Scholar 

  68. C. Chen et al., Phys. Rev. C 87, 045207 (2013)

    Article  ADS  Google Scholar 

  69. Y. Lu et al., Phys. Rev. C 96, 015208 (2017)

    Article  ADS  Google Scholar 

  70. K. Raya, M.A. Bedolla, J.J. Cobos-Martínez, A. Bashir, Few Body Syst. 59, 133 (2018)

    Article  ADS  Google Scholar 

  71. P.-L. Yin et al., Phys. Rev. D 100, 034008 (2019)

    Article  ADS  Google Scholar 

  72. G.S. Bali, H. Neff, T. Duessel, T. Lippert, K. Schilling, Phys. Rev. D 71, 114513 (2005)

    Article  ADS  Google Scholar 

  73. Z. Prkacin et al., PoS LAT2005, 308 (2006)

    Google Scholar 

  74. L. Chang, I.C. Cloët, B. El-Bennich, T. Klähn, C.D. Roberts, Chin. Phys. C 33, 1189 (2009)

    Article  ADS  Google Scholar 

  75. J. Glimm, A. Jaffee, Quantum Physics. A Functional Point of View (Springer-Verlag, New York, 1981)

  76. M. Stingl, Phys. Rev. D 34, 3863 (1986), [Erratum: Phys. Rev. D 36, 651 (1987)]

    Article  ADS  Google Scholar 

  77. C.D. Roberts, A.G. Williams, G. Krein, Int. J. Mod. Phys. A 7, 5607 (1992)

    Article  ADS  Google Scholar 

  78. C.J. Burden, C.D. Roberts, A.G. Williams, Phys. Lett. B 285, 347 (1992)

    Article  ADS  Google Scholar 

  79. F.T. Hawes, C.D. Roberts, A.G. Williams, Phys. Rev. D 49, 4683 (1994)

    Article  ADS  Google Scholar 

  80. P. Maris, Phys. Rev. D 50, 4189 (1994)

    Article  ADS  Google Scholar 

  81. C.D. Roberts, A.G. Williams, Prog. Part. Nucl. Phys. 33, 477 (1994)

    Article  ADS  Google Scholar 

  82. M. Bhagwat, M. Pichowsky, P.C. Tandy, Phys. Rev. D 67, 054019 (2003)

    Article  ADS  Google Scholar 

  83. C.D. Roberts, Prog. Part. Nucl. Phys. 61, 50 (2008)

    Article  ADS  Google Scholar 

  84. A. Bashir, A. Raya, S. Sánchez-Madrigal, C.D. Roberts, Few Body Syst. 46, 229 (2009)

    Article  ADS  Google Scholar 

  85. S. Strauss, C.S. Fischer, C. Kellermann, Phys. Rev. Lett. 109, 252001 (2012)

    Article  ADS  Google Scholar 

  86. A. Bashir, A. Raya, J. Rodríguez-Quintero, Phys. Rev. D 88, 054003 (2013)

    Article  ADS  Google Scholar 

  87. S.-X. Qin, D.H. Rischke, Phys. Rev. D 88, 056007 (2013)

    Article  ADS  Google Scholar 

  88. P. Lowdon, J. Math. Phys. 57, 102302 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  89. W. Lucha and F.F. Schöberl, Phys. Rev. D 93, 056006 (2016)

    Article  ADS  Google Scholar 

  90. D. Binosi, C.D. Roberts, J. Rodríguez-Quintero, Phys. Rev. D 95, 114009 (2017)

    Article  ADS  Google Scholar 

  91. D. Binosi and R.-A. Tripolt, Phys. Lett. B 801, 135171 (2020)

    Article  Google Scholar 

  92. V.N. Gribov, L.N. Lipatov, Phys. Lett. B 37, 78 (1971)

    Article  ADS  Google Scholar 

  93. Y. Nambu, AIP Conf. Proc. 1388, 86 (2011)

    Article  ADS  Google Scholar 

  94. S.J. Brodsky, R. Shrock, Proc. Nat. Acad. Sci. 108, 45 (2011)

    Article  ADS  Google Scholar 

  95. S.J. Brodsky, C.D. Roberts, R. Shrock, P.C. Tandy, Phys. Rev. C 82, 022201(R) (2010)

    Article  ADS  Google Scholar 

  96. L. Chang, C.D. Roberts, P.C. Tandy, Phys. Rev. C 85, 012201(R) (2012)

    Article  ADS  Google Scholar 

  97. S.J. Brodsky, C.D. Roberts, R. Shrock, P.C. Tandy, Phys. Rev. C 85, 065202 (2012)

    Article  ADS  Google Scholar 

  98. C.D. Roberts, J. Phys. Conf. Ser. 706, 022003 (2016)

    Article  Google Scholar 

  99. M. Gell-Mann, R.J. Oakes, B. Renner, Phys. Rev. 175, 2195 (1968)

    Article  ADS  Google Scholar 

  100. A. Bender, D. Blaschke, Y. Kalinovsky, C.D. Roberts, Phys. Rev. Lett. 77, 3724 (1996)

    Article  ADS  Google Scholar 

  101. V.V. Flambaum et al., Few Body Syst. 38, 31 (2006)

    Article  ADS  Google Scholar 

  102. S. Okubo, Prog. Theor. Phys. 27, 949 (1962)

    Article  ADS  Google Scholar 

  103. M. Gell-Mann, Phys. Rev. 125, 1067 (1962), See also “The Eightfold Way: A Theoryof Strong Interaction Symmetry,” DOE Technical Report TID-12608 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  104. S.-X. Qin, C.D. Roberts, S.M. Schmidt, Phys. Rev. D 97, 114017 (2018)

    Article  ADS  Google Scholar 

  105. S.-X. Qin, C.D. Roberts, S.M. Schmidt, Few Body Syst. 60, 26 (2019)

    Article  ADS  Google Scholar 

  106. L. Chang et al., Phys. Rev. Lett. 110, 132001 (2013)

    Article  ADS  Google Scholar 

  107. J. Segovia et al., Phys. Lett. B 731, 13 (2014)

    Article  ADS  Google Scholar 

  108. G.P. Lepage, S.J. Brodsky, Phys. Lett. B 87, 359 (1979)

    Article  ADS  Google Scholar 

  109. A.V. Efremov, A.V. Radyushkin, Phys. Lett. B 94, 245 (1980)

    Article  ADS  Google Scholar 

  110. G.P. Lepage, S.J. Brodsky, Phys. Rev. D 22, 2157 (1980)

    Article  ADS  Google Scholar 

  111. S.J. Brodsky, G.F. de Teramond, Phys. Rev. Lett. 96, 201601 (2006)

    Article  ADS  Google Scholar 

  112. C. Shi et al., Phys. Rev. D 92, 014035 (2015)

    Article  ADS  Google Scholar 

  113. C. Chen, L. Chang, C.D. Roberts, S. Wan, H.-S. Zong, Phys. Rev. D 93, 074021 (2016)

    Article  ADS  Google Scholar 

  114. F. Gao, L. Chang, Y.-X. Liu, C.D. Roberts, P.C. Tandy, Phys. Rev. D 96, 034024 (2017)

    Article  ADS  Google Scholar 

  115. Z.F. Ezawa, Nuovo Cim. A 23, 271 (1974)

    Article  ADS  Google Scholar 

  116. G.R. Farrar, D.R. Jackson, Phys. Rev. Lett. 35, 1416 (1975)

    Article  ADS  Google Scholar 

  117. E.L. Berger, S.J. Brodsky, Phys. Rev. Lett. 42, 940 (1979)

    Article  ADS  Google Scholar 

  118. L. Chang, K. Raya, X. Wang, (arXiv:2001.07352 [hep-ph])

  119. J. Badier et al., Phys. Lett. B 93, 354 (1980)

    Article  ADS  Google Scholar 

  120. J. Badier et al., Z. Phys. C 18, 281 (1983)

    Article  ADS  Google Scholar 

  121. B. Betev et al., Z. Phys. C 28, 15 (1985)

    Article  ADS  Google Scholar 

  122. S. Falciano et al., Z. Phys. C 31, 513 (1986)

    Article  ADS  Google Scholar 

  123. M. Guanziroli et al., Z. Phys. C 37, 545 (1988)

    Article  ADS  Google Scholar 

  124. J.S. Conway et al., Phys. Rev. D 39, 92 (1989)

    Article  ADS  Google Scholar 

  125. J. Heinrich et al., Phys. Rev. D 44, 1909 (1991)

    Article  ADS  Google Scholar 

  126. R.J. Holt, C.D. Roberts, Rev. Mod. Phys. 82, 2991 (2010)

    Article  ADS  Google Scholar 

  127. M.B. Hecht, C.D. Roberts, S.M. Schmidt, Phys. Rev. C 63, 025213 (2001)

    Article  ADS  Google Scholar 

  128. K. Wijesooriya, P.E. Reimer, R.J. Holt, Phys. Rev. C 72, 065203 (2005)

    Article  ADS  Google Scholar 

  129. M. Aicher, A. Schäfer, W. Vogelsang, Phys. Rev. Lett. 105, 252003 (2010)

    Article  ADS  Google Scholar 

  130. R.S. Sufian et al., Phys. Rev. D 99, 074507 (2019)

    Article  ADS  Google Scholar 

  131. P.C. Barry, N. Sato, W. Melnitchouk, C.-R. Ji, Phys. Rev. Lett. 121, 152001 (2018)

    Article  ADS  Google Scholar 

  132. D. Westmark, J.F. Owens, Phys. Rev. D 95, 056024 (2017)

    Article  ADS  Google Scholar 

  133. D. Adikaram et al., Measurement of Tagged Deep Inelastic Scattering (TDIS), approved Jefferson Lab experiment E12-15-006 (2015)

  134. D. Adikaram et al., Measurement of Kaon Structure Function through Tagged Deep Inelastic Scattering (TDIS), approved Jefferson Lab experiment C12-15-006A (2015)

  135. J.R. McKenney, N. Sato, W. Melnitchouk, C.-R. Ji, Phys. Rev. D 93, 054011 (2016)

    Article  ADS  Google Scholar 

  136. V.A. Petrov, R.A. Ryutin, A.E. Sobol, M.J. Murray, Eur. Phys. J. C 72, 1886 (2012)

    Article  ADS  Google Scholar 

  137. J.-C. Peng, J.-W. Qiu, The Universe 4, 34 (2016)

    Google Scholar 

  138. J.-C. Peng, W.-C. Chang, S. Platchkov, T. Sawada, Valence Quark and Gluon Distributions of Kaon from J/Psi Production, arXiv:1711.00839 [hep-ph] (2017)

  139. T. Horn, AIP Conf. Proc. 1970, 030003 (2018)

    Article  Google Scholar 

  140. O. Denisov et al., in arXiv:1808.00848 [hep-ex] Letter of Intent (Draft 2.0): A New QCD Facility at the M2 Beam Line of the CERN SPS (2019)

  141. A.C. Aguilar et al., Eur. Phys. J. A 55, 190 (2019)

    Article  ADS  Google Scholar 

  142. X. Cao et al., Nucl. Tech. 43, 020001 (2020)

    Google Scholar 

  143. W. Broniowski, E. Ruiz Arriola, K. Golec-Biernat, Phys. Rev. D 77, 034023 (2008)

    Article  ADS  Google Scholar 

  144. G.F. de Teramond et al., Phys. Rev. Lett. 120, 182001 (2018)

    Article  ADS  Google Scholar 

  145. J. Lan, C. Mondal, S. Jia, X. Zhao, J.P. Vary, Phys. Rev. D 101, 034024 (2020)

    Article  ADS  Google Scholar 

  146. K.-F. Liu, S.-J. Dong, Phys. Rev. Lett. 72, 1790 (1994)

    Article  ADS  Google Scholar 

  147. X. Ji, Phys. Rev. Lett. 110, 262002 (2013)

    Article  ADS  Google Scholar 

  148. A.V. Radyushkin, Phys. Lett. B 767, 314 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  149. A.V. Radyushkin, Phys. Rev. D 96, 034025 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  150. A.J. Chambers et al., Phys. Rev. Lett. 118, 242001 (2017)

    Article  ADS  Google Scholar 

  151. S.-S. Xu, L. Chang, C.D. Roberts, H.-S. Zong, Phys. Rev. D 97, 094014 (2018)

    Article  ADS  Google Scholar 

  152. J.-H. Zhang et al., Phys. Rev. D 100, 034505 (2019)

    Article  ADS  Google Scholar 

  153. M. Oehm et al., Phys. Rev. D 99, 014508 (2019)

    Article  ADS  Google Scholar 

  154. N. Karthik et al., PoS LATTICE2018, 109 (2018)

    Google Scholar 

  155. R.A. Montgomery et al., AIP Conf. Proc. 1819, 030004 (2017)

    Article  Google Scholar 

  156. ZEUS, S. Chekanov et al., Nucl. Phys. B 637, 3 (2002)

    Article  ADS  Google Scholar 

  157. H1, F. Aaron et al., Eur. Phys. J. C 68, 381 (2010)

    Article  ADS  Google Scholar 

  158. M. Glück, E. Reya, I. Schienbein, Eur. Phys. J. C 10, 313 (1999)

    Article  ADS  Google Scholar 

  159. P.J. Sutton, A.D. Martin, R.G. Roberts, W.J. Stirling, Phys. Rev. D 45, 2349 (1992)

    Article  ADS  Google Scholar 

  160. J.T. Londergan, G.Q. Liu, E.N. Rodionov, A.W. Thomas, Phys. Lett. B 361, 110 (1995)

    Article  ADS  Google Scholar 

  161. L.D. Landau, I. Pomeranchuk, Dokl. Akad. Nauk Ser. Fiz. 92, 535 (1953)

    Google Scholar 

  162. A.B. Migdal, Phys. Rev. 103, 1811 (1956)

    Article  ADS  Google Scholar 

  163. S. Catani, Z. Phys. C 75, 665 (1997)

    Article  Google Scholar 

  164. S.M. Kim, Mod. Phys. Lett. A 16, 467 (2001)

    Article  ADS  Google Scholar 

  165. C. Pascaud, (arXiv:1111.3262 [hep-ph]), Generalisation of DGLAP equations to massive partons

  166. J.-H. Zhang, J.-W. Chen, X. Ji, L. Jin, H.-W. Lin, Phys. Rev. D 95, 094514 (2017)

    Article  ADS  Google Scholar 

  167. L. Chang, C.D. Roberts, Phys. Rev. Lett. 103, 081601 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  168. D. Binosi, L. Chang, J. Papavassiliou, C.D. Roberts, Phys. Lett. B 742, 183 (2015)

    Article  ADS  Google Scholar 

  169. H. Yukawa, Proc. Phys. Math. Soc. Jap. 17, 48 (1935)

    Google Scholar 

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Authors and Affiliations

  1. School of Physics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China

    Craig D. Roberts

  2. Institute for Nonperturbative Physics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China

    Craig D. Roberts

  3. RWTH Aachen University, III. Physikalisches Institut B, Aachen, 52074, Germany

    Sebastian M. Schmidt

  4. Helmholtz-Zentrum Dresden-Rossendorf, Dresden, 01314, Germany

    Sebastian M. Schmidt

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Roberts, C.D., Schmidt, S.M. Reflections upon the emergence of hadronic mass. Eur. Phys. J. Spec. Top. 229, 3319–3340 (2020). https://doi.org/10.1140/epjst/e2020-000064-6

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