Skip to main content
Log in

Overview of Lattice Results for Hadron Structure

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

In recent years, there have been many advances in the hadron structure using lattice QCD. There have also been improvements in hadron charges, form factors and moments, with the continuum-physical limit being taken, removing all lattice artifacts. There was a breakthrough in calculating the Bjorken-x dependence of PDFs in lattice QCD by using large-momentum effective theory and similar frameworks. This breakthrough has led to the emergence and rapid development of direct calculations of Bjorken-x dependent structure. In this talk, I will review recent progress made in lattice QCD and future challenges.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. H.W. Lin, Few Body Syst. 63(4), 65 (2022). https://doi.org/10.1007/s00601-022-01764-y

    Article  ADS  Google Scholar 

  2. H.W. Lin et al., Prog. Part. Nucl. Phys. 100, 107 (2018). https://doi.org/10.1016/j.ppnp.2018.01.007

    Article  ADS  Google Scholar 

  3. M. Constantinou et al., Prog. Part. Nucl. Phys. 121, 103908 (2021). https://doi.org/10.1016/j.ppnp.2021.103908

    Article  Google Scholar 

  4. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, H. Panagopoulos, G. Spanoudes, Phys. Rev. D 101(9), 094513 (2020). https://doi.org/10.1103/PhysRevD.101.094513

    Article  ADS  Google Scholar 

  5. Y.B. Yang, M. Gong, J. Liang, H.W. Lin, K.F. Liu, D. Pefkou, P. Shanahan, Phys. Rev. D 98(7), 074506 (2018). https://doi.org/10.1103/PhysRevD.98.074506

    Article  ADS  Google Scholar 

  6. Y.B. Yang, J. Liang, Y.J. Bi, Y. Chen, T. Draper, K.F. Liu, Z. Liu, Phys. Rev. Lett. 121(21), 212001 (2018). https://doi.org/10.1103/PhysRevLett.121.212001

    Article  ADS  Google Scholar 

  7. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Avilés-Casco, C. Wiese, Phys. Rev. Lett. 119(14), 142002 (2017). https://doi.org/10.1103/PhysRevLett.119.142002

    Article  ADS  Google Scholar 

  8. N. Sato, C. Andres, J.J. Ethier, W. Melnitchouk, Phys. Rev. D 101(7), 074020 (2020). https://doi.org/10.1103/PhysRevD.101.074020

    Article  ADS  Google Scholar 

  9. T.J. Hou et al., Phys. Rev. D 103(1), 014013 (2021). https://doi.org/10.1103/PhysRevD.103.014013

    Article  ADS  Google Scholar 

  10. R.D. Ball et al., Eur. Phys. J. C 77(10), 663 (2017). https://doi.org/10.1140/epjc/s10052-017-5199-5

    Article  ADS  Google Scholar 

  11. S. Dulat, T.J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, C.P. Yuan, Phys. Rev. D 93(3), 033006 (2016). https://doi.org/10.1103/PhysRevD.93.033006

    Article  ADS  Google Scholar 

  12. L.A. Harland-Lang, A.D. Martin, P. Motylinski, R.S. Thorne, Eur. Phys. J. C 75(5), 204 (2015). https://doi.org/10.1140/epjc/s10052-015-3397-6

    Article  ADS  Google Scholar 

  13. S. Alekhin, J. Blümlein, S. Moch, R. Placakyte, Phys. Rev. D 96(1), 014011 (2017). https://doi.org/10.1103/PhysRevD.96.014011

    Article  ADS  Google Scholar 

  14. A. Accardi, L.T. Brady, W. Melnitchouk, J.F. Owens, N. Sato, Phys. Rev. D 93(11), 114017 (2016). https://doi.org/10.1103/PhysRevD.93.114017

    Article  ADS  Google Scholar 

  15. H. Abramowicz et al., Eur. Phys. J. C 75(12), 580 (2015). https://doi.org/10.1140/epjc/s10052-015-3710-4

    Article  ADS  Google Scholar 

  16. Z. Fan, H.W. Lin, M. Zeilbeck, Phys. Rev. D 107(3), 034505 (2023). https://doi.org/10.1103/PhysRevD.107.034505

    Article  ADS  Google Scholar 

  17. S. Park, T. Bhattacharya, R. Gupta, H.W. Lin, S. Mondal, B. Yoon, PoS Lattice LATTICE2022, 118 (2023). https://doi.org/10.22323/1.430.0118

    Article  ADS  Google Scholar 

  18. Y. Aoki et al., Eur. Phys. J. C 82(10), 869 (2022). https://doi.org/10.1140/epjc/s10052-022-10536-1

    Article  ADS  Google Scholar 

  19. R. Gupta, S. Park, M. Hoferichter, E. Mereghetti, B. Yoon, T. Bhattacharya, Phys. Rev. Lett. 127(24), 242002 (2021). https://doi.org/10.1103/PhysRevLett.127.242002

    Article  ADS  Google Scholar 

  20. X. Ji, Phys. Rev. Lett. 110, 262002 (2013). https://doi.org/10.1103/PhysRevLett.110.262002

    Article  ADS  Google Scholar 

  21. X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014). https://doi.org/10.1007/s11433-014-5492-3

    Article  ADS  Google Scholar 

  22. X. Ji, J.H. Zhang, Y. Zhao, Nucl. Phys. B 924, 366 (2017). https://doi.org/10.1016/j.nuclphysb.2017.09.001

    Article  ADS  Google Scholar 

  23. H.W. Lin, PoS LATTICE2013, 293 (2014). https://doi.org/10.22323/1.187.0293

    Article  Google Scholar 

  24. H.W. Lin, J.W. Chen, S.D. Cohen, X. Ji, Phys. Rev. D 91, 054510 (2015). https://doi.org/10.1103/PhysRevD.91.054510

    Article  ADS  Google Scholar 

  25. J.W. Chen, S.D. Cohen, X. Ji, H.W. Lin, J.H. Zhang, Nucl. Phys. B 911, 246 (2016). https://doi.org/10.1016/j.nuclphysb.2016.07.033

    Article  ADS  Google Scholar 

  26. H.W. Lin, J.W. Chen, T. Ishikawa, J.H. Zhang, Phys. Rev. D 98(5), 054504 (2018). https://doi.org/10.1103/PhysRevD.98.054504

    Article  ADS  Google Scholar 

  27. C. Alexandrou, K. Cichy, V. Drach, E. Garcia-Ramos, K. Hadjiyiannakou, K. Jansen, F. Steffens, C. Wiese, Phys. Rev. D 92, 014502 (2015). https://doi.org/10.1103/PhysRevD.92.014502

    Article  ADS  Google Scholar 

  28. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, F. Steffens, C. Wiese, Phys. Rev. D 96(1), 014513 (2017). https://doi.org/10.1103/PhysRevD.96.014513

    Article  ADS  Google Scholar 

  29. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, H. Panagopoulos, F. Steffens, Nucl. Phys. B 923, 394 (2017). https://doi.org/10.1016/j.nuclphysb.2017.08.012

    Article  ADS  Google Scholar 

  30. J.W. Chen, T. Ishikawa, L. Jin, H.W. Lin, Y.B. Yang, J.H. Zhang, Y. Zhao, Phys. Rev. D 97(1), 014505 (2018). https://doi.org/10.1103/PhysRevD.97.014505

    Article  ADS  Google Scholar 

  31. J.H. Zhang, X. Ji, A. Schäfer, W. Wang, S. Zhao, Phys. Rev. Lett. 122(14), 142001 (2019). https://doi.org/10.1103/PhysRevLett.122.142001

    Article  ADS  Google Scholar 

  32. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato, F. Steffens, Phys. Rev. Lett. 121(11), 112001 (2018). https://doi.org/10.1103/PhysRevLett.121.112001

    Article  ADS  Google Scholar 

  33. J.W. Chen, L. Jin, H.W. Lin, Y.S. Liu, Y.B. Yang, J.H. Zhang, Y. Zhao (2018)

  34. J.H. Zhang, J.W. Chen, L. Jin, H.W. Lin, A. Schäfer, Y. Zhao, Phys. Rev. D 100(3), 034505 (2019). https://doi.org/10.1103/PhysRevD.100.034505

    Article  ADS  Google Scholar 

  35. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato, F. Steffens, Phys. Rev. D 98(9), 091503 (2018). https://doi.org/10.1103/PhysRevD.98.091503

    Article  ADS  Google Scholar 

  36. H.W. Lin, J.W. Chen, X. Ji, L. Jin, R. Li, Y.S. Liu, Y.B. Yang, J.H. Zhang, Y. Zhao, Phys. Rev. Lett. 121(24), 242003 (2018). https://doi.org/10.1103/PhysRevLett.121.242003

    Article  ADS  Google Scholar 

  37. Z.Y. Fan, Y.B. Yang, A. Anthony, H.W. Lin, K.F. Liu, Phys. Rev. Lett. 121(24), 242001 (2018). https://doi.org/10.1103/PhysRevLett.121.242001

    Article  ADS  Google Scholar 

  38. Y.S. Liu, J.W. Chen, L. Jin, R. Li, H.W. Lin, Y.B. Yang, J.H. Zhang, Y. Zhao (2018)

  39. W. Wang, J.H. Zhang, S. Zhao, R. Zhu, Phys. Rev. D 100(7), 074509 (2019). https://doi.org/10.1103/PhysRevD.100.074509

    Article  ADS  Google Scholar 

  40. H.W. Lin, R. Zhang, Phys. Rev. D 100(7), 074502 (2019). https://doi.org/10.1103/PhysRevD.100.074502

    Article  ADS  Google Scholar 

  41. J.W. Chen, H.W. Lin, J.H. Zhang, Nucl. Phys. B 952, 114940 (2020). https://doi.org/10.1016/j.nuclphysb.2020.114940

    Article  Google Scholar 

  42. H. Liu, Int. J. Mod. Phys. A 35(11n12), 2030006 (2020). https://doi.org/10.1142/S0217751X20300069

    Article  ADS  Google Scholar 

  43. Y. Chai et al., Phys. Rev. D 102(1), 014508 (2020). https://doi.org/10.1103/PhysRevD.102.014508

    Article  ADS  Google Scholar 

  44. S. Bhattacharya, K. Cichy, M. Constantinou, A. Metz, A. Scapellato, F. Steffens, Phys. Rev. D 102(11), 111501 (2020). https://doi.org/10.1103/PhysRevD.102.111501

    Article  ADS  Google Scholar 

  45. H.W. Lin, J.W. Chen, Z. Fan, J.H. Zhang, R. Zhang, Phys. Rev. D 103(1), 014516 (2021). https://doi.org/10.1103/PhysRevD.103.014516

    Article  ADS  Google Scholar 

  46. R. Zhang, H.W. Lin, B. Yoon, Phys. Rev. D 104(9), 094511 (2021). https://doi.org/10.1103/PhysRevD.104.094511

    Article  ADS  Google Scholar 

  47. Z.Y. Li, Y.Q. Ma, J.W. Qiu, Phys. Rev. Lett. 126(7), 072001 (2021). https://doi.org/10.1103/PhysRevLett.126.072001

    Article  ADS  Google Scholar 

  48. Z. Fan, X. Gao, R. Li, H.W. Lin, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, Y.B. Yang, R. Zhang, Phys. Rev. D 102(7), 074504 (2020). https://doi.org/10.1103/PhysRevD.102.074504

    Article  ADS  Google Scholar 

  49. X. Gao, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky, C. Shugert, S. Syritsyn, Y. Zhao, Phys. Rev. D 102(9), 094513 (2020). https://doi.org/10.1103/PhysRevD.102.094513

    Article  ADS  Google Scholar 

  50. H.W. Lin, J.W. Chen, R. Zhang (2020)

  51. K. Zhang, Y.Y. Li, Y.K. Huo, A. Schäfer, P. Sun, Y.B. Yang, Phys. Rev. D 104(7), 074501 (2021). https://doi.org/10.1103/PhysRevD.104.074501

    Article  ADS  Google Scholar 

  52. C. Alexandrou, K. Cichy, M. Constantinou, J.R. Green, K. Hadjiyiannakou, K. Jansen, F. Manigrasso, A. Scapellato, F. Steffens, Phys. Rev. D 103, 094512 (2021). https://doi.org/10.1103/PhysRevD.103.094512

    Article  ADS  Google Scholar 

  53. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, A. Scapellato, F. Steffens, Phys. Rev. Lett. 125(26), 262001 (2020). https://doi.org/10.1103/PhysRevLett.125.262001

    Article  ADS  Google Scholar 

  54. H.W. Lin, Phys. Rev. Lett. 127(18), 182001 (2021). https://doi.org/10.1103/PhysRevLett.127.182001

    Article  ADS  Google Scholar 

  55. X. Gao, K. Lee, S. Mukherjee, C. Shugert, Y. Zhao, Phys. Rev. D 103(9), 094504 (2021). https://doi.org/10.1103/PhysRevD.103.094504

    Article  ADS  Google Scholar 

  56. M. Constantinou et al., Prog. Part. Nucl. Phys. 121, 103908 (2021). https://doi.org/10.1016/j.ppnp.2021.103908

    Article  Google Scholar 

  57. H.W. Lin, Phys. Lett. B 824, 136821 (2022). https://doi.org/10.1016/j.physletb.2021.136821

    Article  Google Scholar 

  58. S. Bhattacharya, K. Cichy, M. Constantinou, J. Dodson, X. Gao, A. Metz, S. Mukherjee, A. Scapellato, F. Steffens, Y. Zhao, Phys. Rev. D 106(11), 114512 (2022). https://doi.org/10.1103/PhysRevD.106.114512

    Article  ADS  Google Scholar 

  59. U. Aglietti, M. Ciuchini, G. Corbo, E. Franco, G. Martinelli, L. Silvestrini, Phys. Lett. B 441, 371 (1998). https://doi.org/10.1016/S0370-2693(98)01138-1

    Article  ADS  Google Scholar 

  60. G. Martinelli, Nucl. Phys. B, Proc. Suppl. 73, 58 (1999). https://doi.org/10.1016/S0920-5632(99)85007-5

    Article  ADS  Google Scholar 

  61. C. Dawson, G. Martinelli, G.C. Rossi, C.T. Sachrajda, S.R. Sharpe, M. Talevi, M. Testa, Nucl. Phys. B 514, 313 (1998). https://doi.org/10.1016/S0550-3213(97)00756-6

    Article  ADS  Google Scholar 

  62. S. Capitani, M. Gockeler, R. Horsley, H. Oelrich, D. Petters, P.E.L. Rakow, G. Schierholz, Nucl. Phys. B, Proc. Suppl. 73, 288 (1999). https://doi.org/10.1016/S0920-5632(99)85050-6

    Article  ADS  Google Scholar 

  63. S. Capitani, M. Gockeler, R. Horsley, D. Petters, D. Pleiter, P.E.L. Rakow, G. Schierholz, Nucl. Phys. B, Proc. Suppl. 79, 173 (1999). https://doi.org/10.1016/S0920-5632(99)00666-0

    Article  ADS  Google Scholar 

  64. X.D. Ji, C.W. Jung, Phys. Rev. Lett. 86, 208 (2001). https://doi.org/10.1103/PhysRevLett.86.208

    Article  ADS  Google Scholar 

  65. W. Detmold, C.J.D. Lin, Phys. Rev. D 73, 014501 (2006). https://doi.org/10.1103/PhysRevD.73.014501

    Article  ADS  Google Scholar 

  66. V. Braun, D. Müller, Eur. Phys. J. C 55, 349 (2008). https://doi.org/10.1140/epjc/s10052-008-0608-4

    Article  ADS  Google Scholar 

  67. A.J. Chambers, R. Horsley, Y. Nakamura, H. Perlt, P.E.L. Rakow, G. Schierholz, A. Schiller, K. Somfleth, R.D. Young, J.M. Zanotti, Phys. Rev. Lett. 118(24), 242001 (2017). https://doi.org/10.1103/PhysRevLett.118.242001

    Article  ADS  Google Scholar 

  68. W. Detmold, I. Kanamori, C.J.D. Lin, S. Mondal, Y. Zhao, PoS Lattice LATTICE2018, 106 (2018). https://doi.org/10.22323/1.334.0106

    Article  ADS  Google Scholar 

  69. A. Hannaford-Gunn, R. Horsley, Y. Nakamura, H. Perlt, P.E.L. Rakow, G. Schierholz, K. Somfleth, H. Stüben, R.D. Young, J.M. Zanotti, PoS Lattice LATTICE2019, 278 (2020). https://doi.org/10.22323/1.363.0278

    Article  Google Scholar 

  70. R. Horsley, Y. Nakamura, H. Perlt, P.E.L. Rakow, G. Schierholz, K. Somfleth, R.D. Young, J.M. Zanotti, PoS Lattice LATTICE2019, 137 (2020). https://doi.org/10.22323/1.363.0137

    Article  Google Scholar 

  71. W. Detmold, A.V. Grebe, I. Kanamori, C.J.D. Lin, R.J. Perry, Y. Zhao, Phys. Rev. D 104(7), 074511 (2021). https://doi.org/10.1103/PhysRevD.104.074511

    Article  ADS  Google Scholar 

  72. K.F. Liu, S.J. Dong, Phys. Rev. Lett. 72, 1790 (1994). https://doi.org/10.1103/PhysRevLett.72.1790

    Article  ADS  Google Scholar 

  73. K.F. Liu, S.J. Dong, T. Draper, D. Leinweber, J.H. Sloan, W. Wilcox, R.M. Woloshyn, Phys. Rev. D 59, 112001 (1999). https://doi.org/10.1103/PhysRevD.59.112001

    Article  ADS  Google Scholar 

  74. K.F. Liu, Phys. Rev. D 62, 074501 (2000). https://doi.org/10.1103/PhysRevD.62.074501

    Article  ADS  Google Scholar 

  75. K.F. Liu, PoS Lattice LATTICE2015, 115 (2016). https://doi.org/10.22323/1.251.0115

    Article  Google Scholar 

  76. K.F. Liu, Phys. Rev. D 96(3), 033001 (2017). https://doi.org/10.1103/PhysRevD.96.033001

    Article  ADS  MathSciNet  Google Scholar 

  77. K.F. Liu, Phys. Rev. D 102(7), 074502 (2020). https://doi.org/10.1103/PhysRevD.102.074502

    Article  ADS  MathSciNet  Google Scholar 

  78. Y.Q. Ma, J.W. Qiu, Phys. Rev. Lett. 120(2), 022003 (2018). https://doi.org/10.1103/PhysRevLett.120.022003

    Article  ADS  Google Scholar 

  79. G.S. Bali et al., Eur. Phys. J. C 78(3), 217 (2018). https://doi.org/10.1140/epjc/s10052-018-5700-9

    Article  ADS  Google Scholar 

  80. G.S. Bali, V.M. Braun, B. Gläßle, M. Göckeler, M. Gruber, F. Hutzler, P. Korcyl, A. Schäfer, P. Wein, J.H. Zhang, Phys. Rev. D 98(9), 094507 (2018). https://doi.org/10.1103/PhysRevD.98.094507

    Article  ADS  MathSciNet  Google Scholar 

  81. B. Joó, J. Karpie, K. Orginos, A.V. Radyushkin, D.G. Richards, S. Zafeiropoulos, Phys. Rev. Lett. 125(23), 232003 (2020). https://doi.org/10.1103/PhysRevLett.125.232003

    Article  ADS  Google Scholar 

  82. R.S. Sufian, J. Karpie, C. Egerer, K. Orginos, J.W. Qiu, D.G. Richards, Phys. Rev. D 99(7), 074507 (2019). https://doi.org/10.1103/PhysRevD.99.074507

    Article  ADS  Google Scholar 

  83. R.S. Sufian, C. Egerer, J. Karpie, R.G. Edwards, B. Joó, Y.Q. Ma, K. Orginos, J.W. Qiu, D.G. Richards, Phys. Rev. D 102(5), 054508 (2020). https://doi.org/10.1103/PhysRevD.102.054508

    Article  ADS  Google Scholar 

  84. A.V. Radyushkin, Phys. Rev. D 96(3), 034025 (2017). https://doi.org/10.1103/PhysRevD.96.034025

    Article  ADS  MathSciNet  Google Scholar 

  85. I. Balitsky, W. Morris, A. Radyushkin, Phys. Lett. B 808, 135621 (2020). https://doi.org/10.1016/j.physletb.2020.135621

    Article  MathSciNet  Google Scholar 

  86. K. Orginos, A. Radyushkin, J. Karpie, S. Zafeiropoulos, Phys. Rev. D 96(9), 094503 (2017). https://doi.org/10.1103/PhysRevD.96.094503

    Article  ADS  MathSciNet  Google Scholar 

  87. J. Karpie, K. Orginos, A. Radyushkin, S. Zafeiropoulos, EPJ Web Conf. 175, 06032 (2018). https://doi.org/10.1051/epjconf/201817506032

    Article  Google Scholar 

  88. J. Karpie, K. Orginos, S. Zafeiropoulos, JHEP 11, 178 (2018). https://doi.org/10.1007/JHEP11(2018)178

    Article  ADS  Google Scholar 

  89. J. Karpie, K. Orginos, A. Rothkopf, S. Zafeiropoulos, JHEP 04, 057 (2019). https://doi.org/10.1007/JHEP04(2019)057

    Article  ADS  Google Scholar 

  90. B. Joó, J. Karpie, K. Orginos, A. Radyushkin, D. Richards, S. Zafeiropoulos, JHEP 12, 081 (2019). https://doi.org/10.1007/JHEP12(2019)081

    Article  ADS  Google Scholar 

  91. B. Joó, J. Karpie, K. Orginos, A.V. Radyushkin, D.G. Richards, R.S. Sufian, S. Zafeiropoulos, Phys. Rev. D 100(11), 114512 (2019). https://doi.org/10.1103/PhysRevD.100.114512

    Article  ADS  Google Scholar 

  92. A. Radyushkin, Phys. Rev. D 98(1), 014019 (2018). https://doi.org/10.1103/PhysRevD.98.014019

    Article  ADS  MathSciNet  Google Scholar 

  93. J.H. Zhang, J.W. Chen, C. Monahan, Phys. Rev. D 97(7), 074508 (2018). https://doi.org/10.1103/PhysRevD.97.074508

    Article  ADS  MathSciNet  Google Scholar 

  94. T. Izubuchi, X. Ji, L. Jin, I.W. Stewart, Y. Zhao, Phys. Rev. D 98(5), 056004 (2018). https://doi.org/10.1103/PhysRevD.98.056004

    Article  ADS  MathSciNet  Google Scholar 

  95. M. Bhat, K. Cichy, M. Constantinou, A. Scapellato, Phys. Rev. D 103(3), 034510 (2021). https://doi.org/10.1103/PhysRevD.103.034510

    Article  ADS  Google Scholar 

  96. Z. Fan, R. Zhang, H.W. Lin, Int. J. Mod. Phys. A 36(13), 2150080 (2021). https://doi.org/10.1142/S0217751X21500809

    Article  ADS  Google Scholar 

  97. R.S. Sufian, T. Liu, A. Paul, Phys. Rev. D 103(3), 036007 (2021). https://doi.org/10.1103/PhysRevD.103.036007

    Article  ADS  Google Scholar 

  98. N. Karthik, Phys. Rev. D 103(7), 074512 (2021). https://doi.org/10.1103/PhysRevD.103.074512

    Article  ADS  MathSciNet  Google Scholar 

  99. T. Khan et al., Phys. Rev. D 104(9), 094516 (2021). https://doi.org/10.1103/PhysRevD.104.094516

    Article  ADS  Google Scholar 

  100. Z. Fan, H.W. Lin, Phys. Lett. B 823, 136778 (2021). https://doi.org/10.1016/j.physletb.2021.136778

    Article  Google Scholar 

  101. C. Egerer et al., Phys. Rev. D 106(9), 094511 (2022). https://doi.org/10.1103/PhysRevD.106.094511

    Article  ADS  Google Scholar 

  102. A. Salas-Chavira, Z. Fan, H.W. Lin, Phys. Rev. D 106(9), 094510 (2022). https://doi.org/10.1103/PhysRevD.106.094510

    Article  ADS  Google Scholar 

  103. Z. Fan, W. Good, H.W. Lin (2022)

  104. J. Karpie, K. Orginos, A. Radyushkin, S. Zafeiropoulos, JHEP 11, 024 (2021). https://doi.org/10.1007/JHEP11(2021)024

    Article  ADS  Google Scholar 

  105. R. Zhang, C. Honkala, H.W. Lin, J.W. Chen, Phys. Rev. D 102(9), 094519 (2020). https://doi.org/10.1103/PhysRevD.102.094519

    Article  ADS  Google Scholar 

  106. X. Gao, A.D. Hanlon, N. Karthik, S. Mukherjee, P. Petreczky, P. Scior, S. Shi, S. Syritsyn, Y. Zhao, K. Zhou, Phys. Rev. D 106(11), 114510 (2022). https://doi.org/10.1103/PhysRevD.106.114510

    Article  ADS  Google Scholar 

  107. X. Xiong, X. Ji, J.H. Zhang, Y. Zhao, Phys. Rev. D 90(1), 014051 (2014). https://doi.org/10.1103/PhysRevD.90.014051

    Article  ADS  Google Scholar 

  108. Y.Q. Ma, J.W. Qiu, Phys. Rev. D 98(7), 074021 (2018). https://doi.org/10.1103/PhysRevD.98.074021

    Article  ADS  MathSciNet  Google Scholar 

  109. X. Ji, Y.S. Liu, Y. Liu, J.H. Zhang, Y. Zhao, Rev. Mod. Phys. 93(3), 035005 (2021). https://doi.org/10.1103/RevModPhys.93.035005

    Article  ADS  Google Scholar 

  110. X. Gao, A.D. Hanlon, S. Mukherjee, P. Petreczky, P. Scior, S. Syritsyn, Y. Zhao, Phys. Rev. Lett. 128(14), 142003 (2022). https://doi.org/10.1103/PhysRevLett.128.142003

    Article  ADS  Google Scholar 

  111. L.B. Chen, W. Wang, R. Zhu, Phys. Rev. Lett. 126(7), 072002 (2021). https://doi.org/10.1103/PhysRevLett.126.072002

    Article  ADS  Google Scholar 

  112. M. Constantinou, et al., (2022)

  113. S. Chatrchyan et al., Science 338, 1569 (2012). https://doi.org/10.1126/science.1230816

    Article  ADS  Google Scholar 

  114. R. Kogler et al., Rev. Mod. Phys. 91(4), 045003 (2019). https://doi.org/10.1103/RevModPhys.91.045003

    Article  ADS  Google Scholar 

  115. J. Mammei, S. Riordan, K. Kumar, J. Wexler, K. Paschke, G. Cates, M. Dalton, X. Zheng, P. Souder, R. Holmes, et al

  116. E. Moffat, W. Melnitchouk, T.C. Rogers, N. Sato, Phys. Rev. D 104(1), 016015 (2021). https://doi.org/10.1103/PhysRevD.104.016015

    Article  ADS  Google Scholar 

  117. T.J. Hou, H.W. Lin, M. Yan, C.P. Yuan (2022)

  118. X. Ji, Y. Liu, A. Schäfer, W. Wang, Y.B. Yang, J.H. Zhang, Y. Zhao, Nucl. Phys. B 964, 115311 (2021). https://doi.org/10.1016/j.nuclphysb.2021.115311

    Article  Google Scholar 

  119. D. Stump, J. Pumplin, R. Brock, D. Casey, J. Huston, J. Kalk, H.L. Lai, W.K. Tung, Phys. Rev. D 65, 014012 (2001). https://doi.org/10.1103/PhysRevD.65.014012

    Article  ADS  Google Scholar 

  120. M. Aaboud et al., Eur. Phys. J. C 77(6), 367 (2017). https://doi.org/10.1140/epjc/s10052-017-4911-9

    Article  ADS  Google Scholar 

  121. J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P.M. Nadolsky, W.K. Tung, JHEP 07, 012 (2002). https://doi.org/10.1088/1126-6708/2002/07/012

    Article  ADS  Google Scholar 

  122. X.D. Ji, Phys. Rev. Lett. 78, 610 (1997). https://doi.org/10.1103/PhysRevLett.78.610

    Article  ADS  Google Scholar 

  123. G. Wang, J. Liang, T. Draper, K.F. Liu, Y.B. Yang, Phys. Rev. D 104, 074502 (2021). https://doi.org/10.1103/PhysRevD.104.074502

    Article  ADS  Google Scholar 

  124. X. Gao, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, Y. Zhao, Phys. Rev. D 104(11), 114515 (2021). https://doi.org/10.1103/PhysRevD.104.114515

    Article  ADS  Google Scholar 

  125. G.M. Huber et al., Phys. Rev. C 78, 045203 (2008). https://doi.org/10.1103/PhysRevC.78.045203

    Article  ADS  Google Scholar 

  126. H.P. Blok et al., Phys. Rev. C 78, 045202 (2008). https://doi.org/10.1103/PhysRevC.78.045202

    Article  ADS  Google Scholar 

  127. T. Horn et al., Phys. Rev. C 78, 058201 (2008). https://doi.org/10.1103/PhysRevC.78.058201

    Article  ADS  Google Scholar 

  128. T. Horn et al., Phys. Rev. Lett. 97, 192001 (2006). https://doi.org/10.1103/PhysRevLett.97.192001

    Article  ADS  Google Scholar 

  129. J. Volmer et al., Phys. Rev. Lett. 86, 1713 (2001). https://doi.org/10.1103/PhysRevLett.86.1713

    Article  ADS  Google Scholar 

  130. S.R. Amendolia et al., Nucl. Phys. B 277, 168 (1986). https://doi.org/10.1016/0550-3213(86)90437-2

    Article  ADS  Google Scholar 

  131. M. Burkardt, Int. J. Mod. Phys. A 18, 173 (2003). https://doi.org/10.1142/S0217751X03012370

    Article  ADS  Google Scholar 

  132. M. Diehl, Phys. Rept. 388, 41 (2003). https://doi.org/10.1016/j.physrep.2003.08.002

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work of HL is partly supported by the NSF under grant PHY 2209424 & 1653405 and the Research Corpora on for Science Advancement through the Cottrell Scholar Award.

Author information

Authors and Affiliations

Authors

Contributions

H. L. wrote the main manuscript text, added all figures.

Corresponding author

Correspondence to Huey-Wen Lin.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, HW. Overview of Lattice Results for Hadron Structure. Few-Body Syst 64, 58 (2023). https://doi.org/10.1007/s00601-023-01842-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-023-01842-9

Navigation