ReviewNo Access

Frontiers in lattice nucleon structure

Huey-Wen Lin

Department of Physics and Astronomy, and Computational Mathematics, Science & Engineering, Michigan State University, East Lansing, MI 48824, USA

E-mail Address: hwlin@pa.msu.edu

Search for more papers by this author

https://doi.org/10.1142/S0217751X20300069Cited by:15 (Source: Crossref)

Abstract

In this paper, I review recent progress in lattice-QCD calculations of hadron structure with an emphasis on nucleon structure. A wide range of nucleon observables are being studied in modern lattice calculations, and important progress has been made at physical pion mass, including the spin decomposition of the nucleon and the Bjorken- $x$ dependence of hadron structure. Challenges and perspectives for future lattice hadron-structure calculations will be discussed.

Keywords:

PACS: 12.38.Gc, 14.20.Dh, 13.60.Hb

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. R. Gupta, Y.-C. Jang, B. Yoon, H.-W. Lin, V. Cirigliano and T. Bhattacharya, Phys. Rev. D 98, 034503 (2018), arXiv:1806.09006 [hep-lat]. Web of Science, ADS, Google Scholar
2. H.-W. Lin, J.-W. Chen, X. Ji, L. Jin, R. Li, Y.-S. Liu, Y.-B. Yang, J.-H. Zhang and Y. Zhao, Phys. Rev. Lett. 121, 242003 (2018), arXiv:1807.07431 [hep-lat]. Web of Science, ADS, Google Scholar
3. T. Bhattacharya, V. Cirigliano, S. Cohen, R. Gupta, H.-W. Lin and B. Yoon, Phys. Rev. D 94, 054508 (2016), arXiv:1606.07049 [hep-lat]. Web of Science, ADS, Google Scholar
4. PNDME Collab. (T. Bhattacharya et al.), Phys. Rev. D 92, 094511 (2015), arXiv:1506.06411 [hep-lat]. Google Scholar
5. J. R. Green, J. W. Negele, A. V. Pochinsky, S. N. Syritsyn, M. Engelhardt and S. Krieg, Phys. Rev. D 86, 114509 (2012), arXiv:1206.4527 [hep-lat]. Web of Science, ADS, Google Scholar
6. Y. Aoki, T. Blum, H.-W. Lin, S. Ohta, S. Sasaki, R. Tweedie, J. Zanotti and T. Yamazaki, Phys. Rev. D 82, 014501 (2010), arXiv:1003.3387 [hep-lat]. Web of Science, ADS, Google Scholar
7. A. Abdel-Rehim et al., Phys. Rev. D 92, 114513 (2015) [Erratum: ibid. 93, 039904 (2016)], arXiv:1507.04936 [hep-lat]. Web of Science, ADS, Google Scholar
8. G. S. Bali, S. Collins, B. Glässle, M. Göckeler, J. Najjar, R. H. Rödl, A. Schäfer, R. W. Schiel, W. Söldner and A. Sternbeck, Phys. Rev. D 91, 054501 (2015), arXiv:1412.7336 [hep-lat]. Web of Science, ADS, Google Scholar
9. RBC+UKQCD Collab. (T. Yamazaki et al.), Phys. Rev. Lett. 100, 171602 (2008), arXiv:0801.4016 [hep-lat]. Web of Science, Google Scholar
10. H.-W. Lin, W. Melnitchouk, A. Prokudin, N. Sato and H. Shows, Phys. Rev. Lett. 120, 152502 (2018), arXiv:1710.09858 [hep-ph]. Web of Science, ADS, Google Scholar
11. QCDSF Collab. (M. Gockeler et al.), Phys. Rev. D 71, 114511 (2005), arXiv:hep-ph/0410187. Web of Science, Google Scholar
12. Z. Davoudi and M. J. Savage, Phys. Rev. D 86, 054505 (2012), arXiv:1204.4146 [hep-lat]. Web of Science, ADS, Google Scholar
13. W. Detmold and C. J. D. Lin, Phys. Rev. D 73, 014501 (2006), arXiv:hep-lat/0507007. Web of Science, ADS, Google Scholar
14. K.-F. Liu and S.-J. Dong, Phys. Rev. Lett. 72, 1790 (1994), arXiv:hep-ph/9306299. Web of Science, ADS, Google Scholar
15. K. F. Liu, S. J. Dong, T. Draper, D. Leinweber, J. H. Sloan, W. Wilcox and R. M. Woloshyn, Phys. Rev. D 59, 112001 (1999), arXiv:hep-ph/9806491. Web of Science, ADS, Google Scholar
16. K.-F. Liu, Phys. Rev. D 62, 074501 (2000), arXiv:hep-ph/9910306. Web of Science, ADS, Google Scholar
17. K.-F. Liu, PoS LATTICE2015, 115 (2016), arXiv:1603.07352 [hep-ph]. Google Scholar
18. X. Ji, Phys. Rev. Lett. 110, 262002 (2013), arXiv:1305.1539 [hep-ph]. Web of Science, ADS, Google Scholar
19. H.-W. Lin, J.-W. Chen, S. D. Cohen and X. Ji, Phys. Rev. D 91, 054510 (2015), arXiv:1402.1462 [hep-ph]. Web of Science, ADS, Google Scholar
20. C. Alexandrou, K. Cichy, V. Drach, E. Garcia-Ramos, K. Hadjiyiannakou, K. Jansen, F. Steffens and C. Wiese, Phys. Rev. D 92, 014502 (2015), arXiv:1504.07455 [hep-lat]. Web of Science, ADS, Google Scholar
21. J.-W. Chen, S. D. Cohen, X. Ji, H.-W. Lin and J.-H. Zhang, Nucl. Phys. B 911, 246 (2016), arXiv:1603.06664 [hep-ph]. Web of Science, ADS, Google Scholar
22. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato and F. Steffens, Phys. Rev. Lett. 121, 112001 (2018), arXiv:1803.02685 [hep-lat]. Web of Science, ADS, Google Scholar
23. J.-W. Chen, L. Jin, H.-W. Lin, Y.-S. Liu, Y.-B. Yang, J.-H. Zhang and Y. Zhao, arXiv:1803.04393 [hep-lat]. Google Scholar
24. H.-W. Lin, Int. J. Mod. Phys. Conf. Ser. 25, 1460039 (2014). Google Scholar
25. H.-W. Lin, PoS LATTICE2013, 293 (2014). Google Scholar
26. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, F. Steffens and C. Wiese, Phys. Rev. D 96, 014513 (2017), arXiv:1610.03689 [hep-lat]. Web of Science, ADS, Google Scholar
27. M. Di Pierro, From Monte Carlo integration to lattice quantum chromodynamics: An Introduction, in GSA Summer School on Physics on the Frontier and in the Future Batavia, Illinois, 31 July–7 August 2000 (2000), arXiv:hep-lat/0009001. Google Scholar
28. G. P. Lepage, Lattice QCD for novices, in Strong Interactions at Low and Intermediate Energies. Proc. 13th Annual Hampton University Graduate Studies, HUGS’98, Newport News, USA, 26 May–12 June 1998 (1998), pp. 49–90, arXiv:hep-lat/0506036. Google Scholar
29. M. Luscher, Advanced lattice QCD, in Probing the Standard Model of Particle Interactions. Proc., Summer School in Theoretical Physics, NATO Advanced Study Institute, 68th session, Les Houches, France, 28 July–5 September 1997 (1998), pp. 229–280, arXiv:hep-lat/9802029. Google Scholar
30. R. Gupta, Introduction to lattice QCD: Course, in Probing the Standard Model of Particle Interactions. Proc., Summer School in Theoretical Physics, NATO Advanced Study Institute, 68th session, Les Houches, France, 28 July–5 September 1997 (1997), pp. 83–219, arXiv:hep-lat/9807028. Google Scholar
31. D. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, 2015). Google Scholar
32. M. Newman and G. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, 1999). Crossref, Google Scholar
33. S. J. Brodsky, A. L. Deshpande, H. Gao, R. D. McKeown, C. A. Meyer, Z.-E. Meziani, R. G. Milner, J. Qiu, D. G. Richards and C. D. Roberts, arXiv:1502.05728 [hep-ph]. Google Scholar
34. E.-C. Aschenauer et al., Eur. Phys. J. A 53, 71 (2017), arXiv:1410.8831 [hep-ph]. Web of Science, ADS, Google Scholar
35. S. Aoki et al., Eur. Phys. J. C 77, 112 (2017), arXiv:1607.00299 [hep-lat]. Web of Science, ADS, Google Scholar
36. H.-W. Lin et al., Prog. Part. Nucl. Phys. 100, 107 (2018), arXiv:1711.07916 [hep-ph]. Web of Science, ADS, Google Scholar
37. Flavour Lattice Averaging Group Collab. (S. Aoki et al.), arXiv:1902.08191 [hep-lat]. Google Scholar
38. M. Golterman, Applications of chiral perturbation theory to lattice QCD, in Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing, 93rd Session, Les Houches, France, 3–28 August 2009 (2009), pp. 423–515, arXiv:0912.4042 [hep-lat]. Google Scholar
39. A. Savanur and H.-W. Lin, arXiv:1901.00018 [hep-lat]. Google Scholar
40. M. Luscher, Commun. Math. Phys. 104, 177 (1986). Web of Science, ADS, Google Scholar
41. M. Luscher, Commun. Math. Phys. 105, 153 (1986). Web of Science, ADS, Google Scholar
42. G. P. Lepage, The Analysis of Algorithms for Lattice Field Theory, Boulder (ASI, 1989), pp. 97–120. Google Scholar
43. H.-W. Lin, S. D. Cohen, R. G. Edwards, K. Orginos and D. G. Richards, PoS LATTICE2008, 140 (2008), arXiv:0810.5141 [hep-lat]. Google Scholar
44. H.-W. Lin, S. D. Cohen, R. G. Edwards and D. G. Richards, Phys. Rev. D 78, 114508 (2008), arXiv:0803.3020 [hep-lat]. Web of Science, ADS, Google Scholar
45. H.-W. Lin, S. D. Cohen, R. G. Edwards, K. Orginos and D. G. Richards, arXiv:1005.0799 [hep-lat]. Google Scholar
46. T. Bhattacharya, S. D. Cohen, R. Gupta, A. Joseph, H.-W. Lin and B. Yoon, Phys. Rev. D 89, 094502 (2014), arXiv:1306.5435 [hep-lat]. Web of Science, ADS, Google Scholar
47. G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa and A. Vladikas, Nucl. Phys. B 445, 81 (1995), arXiv:hep-lat/9411010. Web of Science, ADS, Google Scholar
48. M. Gockeler, R. Horsley, E.-M. Ilgenfritz, H. Perlt, P. E. L. Rakow, G. Schierholz and A. Schiller, Phys. Rev. D 54, 5705 (1996), arXiv:hep-lat/9602029. Web of Science, ADS, Google Scholar
49. V. Bernard, N. Kaiser, J. Kambor and U. G. Meissner, Nucl. Phys. B 388, 315 (1992). Web of Science, ADS, Google Scholar
50. V. Bernard, N. Kaiser and U.-G. Meissner, Int. J. Mod. Phys. E 4, 193 (1995), arXiv:hep-ph/9501384. Link, ADS, Google Scholar
51. V. Bernard and U.-G. Meissner, Annu. Rev. Nucl. Part. Sci. 57, 33 (2007), arXiv:hep-ph/0611231. Web of Science, ADS, Google Scholar
52. V. Bernard and U.-G. Meissner, Phys. Lett. B 639, 278 (2006), arXiv:hep-lat/0605010. Web of Science, ADS, Google Scholar
53. A. A. Khan et al., Phys. Rev. D 74, 094508 (2006), arXiv:hep-lat/0603028. Web of Science, ADS, Google Scholar
54. G. Colangelo, A. Fuhrer and S. Lanz, Phys. Rev. D 82, 034506 (2010), arXiv:1005.1485 [hep-lat]. Web of Science, ADS, Google Scholar
55. J. de Vries, R. G. E. Timmermans, E. Mereghetti and U. van Kolck, Phys. Lett. B 695, 268 (2011), arXiv:1006.2304 [hep-ph]. Web of Science, ADS, Google Scholar
56. S. Aoki et al., Eur. Phys. J. C 74, 2890 (2014), arXiv:1310.8555 [hep-lat]. Web of Science, ADS, Google Scholar
57. G. Colangelo et al., Eur. Phys. J. C 71, 1695 (2011), arXiv:1011.4408 [hep-lat]. Web of Science, ADS, Google Scholar
58. H.-W. Lin, T. Blum, S. Ohta, S. Sasaki and T. Yamazaki, Phys. Rev. D 78, 014505 (2008), arXiv:0802.0863 [hep-lat]. Web of Science, ADS, Google Scholar
59. A. Metz, Phys. Lett. B 549, 139 (2002), arXiv:hep-ph/0209054. Web of Science, ADS, Google Scholar
60. M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin and C. Turk, Phys. Rev. D 75, 054032 (2007), arXiv:hep-ph/0701006. Web of Science, ADS, Google Scholar
61. M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin and S. Melis, Nucl. Phys. B (Proc. Suppl.) 191, 98 (2009), arXiv:0812.4366 [hep-ph]. ADS, Google Scholar
62. M. Anselmino, M. Boglione, U. D’Alesio, S. Melis, F. Murgia and A. Prokudin, Phys. Rev. D 87, 094019 (2013), arXiv:1303.3822 [hep-ph]. Web of Science, ADS, Google Scholar
63. Z.-B. Kang, A. Prokudin, P. Sun and F. Yuan, Phys. Rev. D 91, 071501 (2015), arXiv:1410.4877 [hep-ph]. Web of Science, ADS, Google Scholar
64. Z.-B. Kang, A. Prokudin, P. Sun and F. Yuan, Phys. Rev. D 93, 014009 (2016), arXiv:1505.05589 [hep-ph]. Web of Science, ADS, Google Scholar
65. J. C. Collins, D. E. Soper and G. F. Sterman, Nucl. Phys. B 250, 199 (1985). Web of Science, ADS, Google Scholar
66. A. Bacchetta, A. Courtoy and M. Radici, J. High Energy Phys. 03, 119 (2013), arXiv:1212.3568 [hep-ph]. Web of Science, ADS, Google Scholar
67. A. Bacchetta, A. Courtoy and M. Radici, Phys. Rev. Lett. 107, 012001 (2011), arXiv:1104.3855 [hep-ph]. Web of Science, ADS, Google Scholar
68. HERMES Collab. (A. Airapetian et al.), Phys. Lett. B 693, 11 (2010), arXiv:1006.4221 [hep-ex]. Web of Science, ADS, Google Scholar
69. COMPASS Collab. (M. Alekseev et al.), Phys. Lett. B 673, 127 (2009), arXiv:0802.2160 [hep-ex]. Web of Science, ADS, Google Scholar
70. COMPASS Collab. (C. Adolph et al.), Phys. Lett. B 744, 250 (2015), arXiv:1408.4405 [hep-ex]. Web of Science, Google Scholar
71. T. Bhattacharya, V. Cirigliano, S. D. Cohen, A. Filipuzzi, M. Gonzalez-Alonso, M. L. Graesser, R. Gupta and H.-W. Lin, Phys. Rev. D 85, 054512 (2012), arXiv:1110.6448 [hep-ph]. Web of Science, ADS, Google Scholar
72. Nab Collab. (D. Pocanic et al.), Nucl. Instrum. Methods A 611, 211 (2009), arXiv:0810.0251 [nucl-ex]. Web of Science, Google Scholar
73. V. Cirigliano, M. Gonzalez-Alonso and M. L. Graesser, J. High Energy Phys. 02, 046 (2013), arXiv:1210.4553 [hep-ph]. Web of Science, ADS, Google Scholar
74. M. Gonzalez-Alonso, O. Naviliat-Cuncic and N. Severijns, Prog. Part. Nucl. Phys. 104, 165 (2019), arXiv:1803.08732 [hep-ph]. Web of Science, ADS, Google Scholar
75. ATLAS Collab. (M. Aaboud et al.), Eur. Phys. J. C 78, 401 (2018), arXiv:1706.04786 [hep-ex]. Web of Science, ADS, Google Scholar
76. S. Alioli, W. Dekens, M. Girard and E. Mereghetti, J. High Energy Phys. 08, 205 (2018), arXiv:1804.07407 [hep-ph]. Web of Science, ADS, Google Scholar
77. CMS Collab. (A. M. Sirunyan et al.), J. High Energy Phys. 06, 128 (2018), arXiv:1803.11133 [hep-ex]. Google Scholar
78. CMS Collab. (A. M. Sirunyan et al.), J. High Energy Phys. 06, 120 (2018), arXiv:1803.06292 [hep-ex]. Google Scholar
79. Particle Data Group (M. Tanabashi et al.), Phys. Rev. D 98, 030001 (2018). Web of Science, Google Scholar
80. MILC Collab. (A. Bazavov et al.), Phys. Rev. D 87, 054505 (2013), arXiv:1212.4768 [hep-lat]. Google Scholar
81. A. Bazavov et al., Phys. Rev. D 98, 074512 (2018), arXiv:1712.09262 [hep-lat]. Web of Science, ADS, Google Scholar
82. V. Bernard, L. Elouadrhiri and U.-G. Meissner, J. Phys. G 28, R1 (2002), arXiv:hep-ph/0107088. Web of Science, ADS, Google Scholar
83. MiniBooNE Collab. (A. A. Aguilar-Arevalo et al.), Phys. Rev. D 81, 092005 (2010), arXiv:1002.2680 [hep-ex]. Web of Science, Google Scholar
84. A. S. Meyer, M. Betancourt, R. Gran and R. J. Hill, Phys. Rev. D 93, 113015 (2016), arXiv:1603.03048 [hep-ph]. Web of Science, ADS, Google Scholar
85. J. Morfín, Past and future of $ν / \bar{ν}$ deuterium/hydrogen experiments, talk at INT Seattle, June, 2018. Google Scholar
86. R. J. Hill, P. Kammel, W. J. Marciano and A. Sirlin, Rep. Prog. Phys. 81, 096301 (2018), arXiv:1708.08462 [hep-ph]. Web of Science, Google Scholar
87. S. Capitani, M. Della Morte, D. Djukanovic, G. M. von Hippel, J. Hua, B. Jäger, P. M. Junnarkar, H. B. Meyer, T. D. Rae and H. Wittig, Int. J. Mod. Phys. A 34, 1950009 (2019), arXiv:1705.06186 [hep-lat]. Link, Web of Science, ADS, Google Scholar
88. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou and A. Vaquero Aviles-Casco, Phys. Rev. D 96, 054507 (2017), arXiv:1705.03399 [hep-lat]. Web of Science, ADS, Google Scholar
89. G. S. Bali, S. Collins, M. Gruber, A. Schäfer, P. Wein and T. Wurm, Phys. Lett. B 789, 666 (2019), arXiv:1810.05569 [hep-lat]. Web of Science, ADS, Google Scholar
90. N. Hasan, J. Green, S. Meinel, M. Engelhardt, S. Krieg, J. Negele, A. Pochinsky and S. Syritsyn, Phys. Rev. D 97, 034504 (2018), arXiv:1711.11385 [hep-lat]. Web of Science, ADS, Google Scholar
91. E. Shintani, K.-I. Ishikawa, Y. Kuramashi, S. Sasaki and T. Yamazaki, Phys. Rev. D 99, 014510 (2019), arXiv:1811.07292 [hep-lat]. Web of Science, ADS, Google Scholar
92. R. Gupta, Y.-C. Jang, H.-W. Lin, B. Yoon and T. Bhattacharya, Phys. Rev. D 96, 114503 (2017), arXiv:1705.06834 [hep-lat]. Web of Science, ADS, Google Scholar
93. A. Bodek, S. Avvakumov, R. Bradford and H. S. Budd, Eur. Phys. J. C 53, 349 (2008), arXiv:0708.1946 [hep-ex]. Web of Science, ADS, Google Scholar
94. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou and A. Vaquero Avilés-Casco, Phys. Rev. D 100, 014509 (2019), arXiv:1812.10311 [hep-lat]. Web of Science, ADS, Google Scholar
95. J. R. Green, J. W. Negele, A. V. Pochinsky, S. N. Syritsyn, M. Engelhardt and S. Krieg, Phys. Rev. D 90, 074507 (2014), arXiv:1404.4029 [hep-lat]. Web of Science, ADS, Google Scholar
96. PNDME Collab. (Y.-C. Jang, T. Bhattacharya, R. Gupta, H.-W. Lin and B. Yoon), PoS LATTICE2018, 123 (2018), arXiv:1901.00060 [hep-lat]. Google Scholar
97. A. L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers and Y. Xu, arXiv:1211.2818 [hep-ph]. Google Scholar
98. R. J. Hill and M. P. Solon, Phys. Rev. D 91, 043505 (2015), arXiv:1409.8290 [hep-ph]. Web of Science, ADS, Google Scholar
99. H.-W. Lin, R. Gupta, B. Yoon, Y.-C. Jang and T. Bhattacharya, Phys. Rev. D 98, 094512 (2018), arXiv:1806.10604 [hep-lat]. Web of Science, ADS, Google Scholar
100. S. Collins, G. Bali and A. Schäfer, PoS LATTICE2007, 141 (2007), arXiv:0709.3217 [hep-lat]. Google Scholar
101. G. S. Bali, S. Collins and A. Schäfer, Comput. Phys. Commun. 181, 1570 (2010), arXiv:0910.3970 [hep-lat]. Web of Science, ADS, Google Scholar
102. C. Thron, S. J. Dong, K. F. Liu and H. P. Ying, Phys. Rev. D 57, 1642 (1998), arXiv:hep-lat/9707001. Web of Science, ADS, Google Scholar
103. UKQCD Collab. (C. Michael, M. S. Foster and C. McNeile), Nucl. Phys. B (Proc. Suppl.) 83, 185 (2000), arXiv:hep-lat/9909036. Google Scholar
104. T. Blum, T. Izubuchi and E. Shintani, Phys. Rev. D 88, 094503 (2013), arXiv:1208.4349 [hep-lat]. Web of Science, ADS, Google Scholar
105. T. Bhattacharya, V. Cirigliano, R. Gupta, H.-W. Lin and B. Yoon, Phys. Rev. Lett. 115, 212002 (2015), arXiv:1506.04196 [hep-lat]. Web of Science, ADS, Google Scholar
106. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Avilés-Casco and C. Wiese, Phys. Rev. Lett. 119, 142002 (2017), arXiv:1706.02973 [hep-lat]. Web of Science, ADS, Google Scholar
107. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou and A. V. Avilés-Casco, EPJ Web Conf. 175, 06003 (2018), arXiv:1807.11203 [hep-lat]. Google Scholar
108. COMPASS Collab. (C. Adolph et al.), Phys. Lett. B 753, 18 (2016), arXiv:1503.08935 [hep-ex]. Web of Science, Google Scholar
109. NNPDF Collab. (E. R. Nocera, R. D. Ball, S. Forte, G. Ridolfi and J. Rojo), Nucl. Phys. B 887, 276 (2014), arXiv:1406.5539 [hep-ph]. Web of Science, ADS, Google Scholar
110. D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Phys. Rev. Lett. 101, 072001 (2008), arXiv:0804.0422 [hep-ph]. Web of Science, ADS, Google Scholar
111. D. de Florian, R. Sassot, M. Stratmann and W. Vogelsang, Phys. Rev. D 80, 034030 (2009), arXiv:0904.3821 [hep-ph]. Web of Science, ADS, Google Scholar
112. Jefferson Lab Angular Momentum Collab. (N. Sato, W. Melnitchouk, S. E. Kuhn, J. J. Ethier and A. Accardi), Phys. Rev. D 93, 074005 (2016), arXiv:1601.07782 [hep-ph]. Web of Science, Google Scholar
113. J. J. Ethier, N. Sato and W. Melnitchouk, Phys. Rev. Lett. 119, 132001 (2017), arXiv:1705.05889 [hep-ph]. Web of Science, ADS, Google Scholar
114. J. Engel, M. J. Ramsey-Musolf and U. van Kolck, Prog. Part. Nucl. Phys. 71, 21 (2013), arXiv:1303.2371 [nucl-th]. Web of Science, ADS, Google Scholar
115. M. Pospelov and A. Ritz, Ann. Phys. 318, 119 (2005), arXiv:hep-ph/0504231. Web of Science, ADS, Google Scholar
116. J. R. Ellis and R. A. Flores, Phys. Lett. B 377, 83 (1996), arXiv:hep-ph/9602211. Web of Science, ADS, Google Scholar
117. T. Bhattacharya, V. Cirigliano and R. Gupta, PoS LATTICE2012, 179 (2012), arXiv:1212.4918 [hep-lat]. Google Scholar
118. R. Gupta, B. Yoon, T. Bhattacharya, V. Cirigliano, Y.-C. Jang and H.-W. Lin, Phys. Rev. D 98, 091501 (2018), arXiv:1808.07597 [hep-lat]. Web of Science, ADS, Google Scholar
119. C. A. Baker et al., Phys. Rev. Lett. 97, 131801 (2006), arXiv:hep-ex/0602020. Web of Science, ADS, Google Scholar
120. N. Arkani-Hamed and S. Dimopoulos, J. High Energy Phys. 06, 073 (2005), arXiv:hep-th/0405159. Web of Science, ADS, Google Scholar
121. G. F. Giudice and A. Romanino, Nucl. Phys. B 699, 65 (2004) [Erratum: ibid. 706, 487 (2005)], arXiv:hep-ph/0406088. Web of Science, ADS, Google Scholar
122. N. Arkani-Hamed, S. Dimopoulos, G. F. Giudice and A. Romanino, Nucl. Phys. B 709, 3 (2005), arXiv:hep-ph/0409232. Web of Science, ADS, Google Scholar
123. G. F. Giudice and A. Romanino, Phys. Lett. B 634, 307 (2006), arXiv:hep-ph/0510197. Web of Science, ADS, Google Scholar
124. ACME Collab. (V. Andreev et al.), Nature 562, 355 (2018). Web of Science, ADS, Google Scholar
125. ACME Collab. (J. Baron et al.), Science 343, 269 (2014), arXiv:1310.7534 [physics.atom-ph]. Web of Science, Google Scholar
126. CMS Collab. (A. M. Sirunyan et al.), J. High Energy Phys. 05, 025 (2018), arXiv:1802.02110 [hep-ex]. Google Scholar
127. X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014), arXiv:1404.6680 [hep-ph]. Web of Science, ADS, Google Scholar
128. B. L. Ioffe, Phys. Lett. B 30, 123 (1969). Web of Science, ADS, Google Scholar
129. V. Braun, P. Gornicki and L. Mankiewicz, Phys. Rev. D 51, 6036 (1995), arXiv:hep-ph/9410318. Web of Science, ADS, Google Scholar
130. A. Radyushkin, Phys. Lett. B 767, 314 (2017), arXiv:1612.05170 [hep-ph]. Web of Science, ADS, Google Scholar
131. A. V. Radyushkin, Phys. Rev. D 96, 034025 (2017), arXiv:1705.01488 [hep-ph]. Web of Science, ADS, Google Scholar
132. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. D 98, 074021 (2018), arXiv:1404.6860 [hep-ph]. Web of Science, ADS, Google Scholar
133. Y.-Q. Ma and J.-W. Qiu, Int. J. Mod. Phys. Conf. Ser. 37, 1560041 (2015), arXiv:1412.2688 [hep-ph]. Google Scholar
134. U. Aglietti, M. Ciuchini, G. Corbo, E. Franco, G. Martinelli and L. Silvestrini, Phys. Lett. B 432, 411 (1998), arXiv:hep-ph/9804416. Web of Science, ADS, Google Scholar
135. J. Liang, K.-F. Liu and Y.-B. Yang, EPJ Web Conf. 175, 14014 (2018), arXiv:1710.11145 [hep-lat]. Google Scholar
136. W. Detmold, I. Kanamori, C. J. D. Lin, S. Mondal and Y. Zhao, PoS LATTICE2018, 106 (2018), arXiv:1810.12194 [hep-lat]. Google Scholar
137. A. J. Chambers, R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, A. Schiller, K. Somfleth, R. D. Young and J. M. Zanotti, Phys. Rev. Lett. 118, 242001 (2017), arXiv:1703.01153 [hep-lat]. Web of Science, ADS, Google Scholar
138. X. Xiong, X. Ji, J.-H. Zhang and Y. Zhao, Phys. Rev. D 90, 014051 (2014), arXiv:1310.7471 [hep-ph]. Web of Science, ADS, Google Scholar
139. K. Orginos, A. Radyushkin, J. Karpie and S. Zafeiropoulos, Phys. Rev. D 96, 094503 (2017), arXiv:1706.05373 [hep-ph]. Web of Science, ADS, Google Scholar
140. C. Monahan and K. Orginos, J. High Energy Phys. 03, 116 (2017), arXiv:1612.01584 [hep-lat]. Web of Science, ADS, Google Scholar
141. J.-W. Chen, T. Ishikawa, L. Jin, H.-W. Lin, Y.-B. Yang, J.-H. Zhang and Y. Zhao, Phys. Rev. D 97, 014505 (2018), arXiv:1706.01295 [hep-lat]. Web of Science, ADS, Google Scholar
142. J. Green, K. Jansen and F. Steffens, Phys. Rev. Lett. 121, 022004 (2018), arXiv:1707.07152 [hep-lat]. Web of Science, ADS, Google Scholar
143. LP3 Collab. (H.-W. Lin, J.-W. Chen, T. Ishikawa and J.-H. Zhang), Phys. Rev. D 98, 054504 (2018), arXiv:1708.05301 [hep-lat]. Google Scholar
144. Y.-S. Liu, J.-W. Chen, L. Jin, R. Li, H.-W. Lin, Y.-B. Yang, J.-H. Zhang and Y. Zhao, arXiv:1810.05043 [hep-lat]. Google Scholar
145. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato and F. Steffens, Phys. Rev. D 98, 091503 (2018), arXiv:1807.00232 [hep-lat]. Web of Science, ADS, Google Scholar
146. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, A. Scapellato and F. Steffens, Phys. Rev. D 99, 114504 (2019), arXiv:1902.00587 [hep-lat]. Web of Science, ADS, Google Scholar
147. T. Izubuchi, X. Ji, L. Jin, I. W. Stewart and Y. Zhao, Phys. Rev. D 98, 056004 (2018), arXiv:1801.03917 [hep-ph]. Web of Science, ADS, Google Scholar
148. W. Wang, S. Zhao and R. Zhu, Eur. Phys. J. C 78, 147 (2018), arXiv:1708.02458 [hep-ph]. Web of Science, ADS, Google Scholar
149. W. Wang and S. Zhao, J. High Energy Phys. 05, 142 (2018), arXiv:1712.09247 [hep-ph]. Web of Science, ADS, Google Scholar
150. X. Ji, J.-H. Zhang and Y. Zhao, Phys. Rev. Lett. 120, 112001 (2018), arXiv:1706.08962 [hep-ph]. Web of Science, ADS, Google Scholar
151. T. Ishikawa, Y.-Q. Ma, J.-W. Qiu and S. Yoshida, Phys. Rev. D 96, 094019 (2017), arXiv:1707.03107 [hep-ph]. Web of Science, ADS, Google Scholar
152. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, H. Panagopoulos and F. Steffens, Nucl. Phys. B 923, 394 (2017), arXiv:1706.00265 [hep-lat]. Web of Science, ADS, Google Scholar
153. M. Constantinou and H. Panagopoulos, Phys. Rev. D 96, 054506 (2017), arXiv:1705.11193 [hep-lat]. Web of Science, ADS, Google Scholar
154. X. Xiong, T. Luu and U.-G. Meißner, arXiv:1705.00246 [hep-ph]. Google Scholar
155. J.-W. Chen, X. Ji and J.-H. Zhang, Nucl. Phys. B 915, 1 (2017), arXiv:1609.08102 [hep-ph]. Web of Science, ADS, Google Scholar
156. T. Ishikawa, Y.-Q. Ma, J.-W. Qiu and S. Yoshida, arXiv:1609.02018 [hep-lat]. Google Scholar
157. HPQCD and UKQCD Collabs. (E. Follana et al.), Phys. Rev. D 75, 054502 (2007), arXiv:hep-lat/0610092. Google Scholar
158. G. S. Bali, B. Lang, B. U. Musch and A. Schäfer, Phys. Rev. D 93, 094515 (2016), arXiv:1602.05525 [hep-lat]. Web of Science, ADS, Google Scholar
159. Y.-S. Liu et al., arXiv:1807.06566 [hep-lat]. Google Scholar
160. S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump and C. P. Yuan, Phys. Rev. D 93, 033006 (2016), arXiv:1506.07443 [hep-ph]. Web of Science, ADS, Google Scholar
161. T. Ishikawa, L. Jin, H.-W. Lin, A. Schäfer, Y.-B. Yang, J.-H. Zhang and Y. Zhao, Sci. China Phys. Mech. Astron. 62, 991021 (2019), arXiv:1711.07858 [hep-ph]. Web of Science, ADS, Google Scholar
162. J. Karpie, K. Orginos, A. Rothkopf and S. Zafeiropoulos, J. High Energy Phys. 04, 057 (2019), arXiv:1901.05408 [hep-lat]. Web of Science, ADS, Google Scholar
163. NNPDF Collab. (R. D. Ball et al.), Eur. Phys. J. C 77, 663 (2017), arXiv:1706.00428 [hep-ph]. Web of Science, Google Scholar
164. A. Accardi, L. T. Brady, W. Melnitchouk, J. F. Owens and N. Sato, Phys. Rev. D 93, 114017 (2016), arXiv:1602.03154 [hep-ph]. Web of Science, ADS, Google Scholar
165. QCDSF and UKQCD Collabs. (R. Horsley et al.), Phys. Lett. B 714, 312 (2012), arXiv:1205.6410 [hep-lat]. Web of Science, ADS, Google Scholar
166. M. Deka et al., Phys. Rev. D 91, 014505 (2015), arXiv:1312.4816 [hep-lat]. Web of Science, ADS, Google Scholar
167. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, H. Panagopoulos and C. Wiese, Phys. Rev. D 96, 054503 (2017), arXiv:1611.06901 [hep-lat]. Web of Science, ADS, Google Scholar
168. Y.-B. Yang, M. Gong, J. Liang, H.-W. Lin, K.-F. Liu, D. Pefkou and P. Shanahan, Phys. Rev. D 98, 074506 (2018), arXiv:1805.00531 [hep-lat]. Web of Science, ADS, Google Scholar
169. Z.-Y. Fan, Y.-B. Yang, A. Anthony, H.-W. Lin and K.-F. Liu, Phys. Rev. Lett. 121, 242001 (2018), arXiv:1808.02077 [hep-lat]. Web of Science, ADS, Google Scholar
170. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. Lett. 120, 022003 (2018), arXiv:1709.03018 [hep-ph]. Web of Science, ADS, Google Scholar
171. Y.-B. Yang, M. Glatzmaier, K.-F. Liu and Y. Zhao, arXiv:1612.02855 [nucl-th]. Google Scholar
172. J. Butterworth et al., J. Phys. G 43, 023001 (2016), arXiv:1510.03865 [hep-ph]. Web of Science, Google Scholar
173. I. Balitsky, W. Morris and A. Radyushkin, arXiv:1910.13963 [hep-ph]. Google Scholar
174. W. Wang, J.-H. Zhang, S. Zhao and R. Zhu, Phys. Rev. D 100, 074509 (2019), arXiv:1904.00978 [hep-ph]. Web of Science, ADS, Google Scholar
175. J.-H. Zhang, X. Ji, A. Schäfer, W. Wang and S. Zhao, Phys. Rev. Lett. 122, 142001 (2019), arXiv:1808.10824 [hep-ph]. Web of Science, ADS, Google Scholar
176. J.-H. Zhang, J.-W. Chen, X. Ji, L. Jin and H.-W. Lin, Phys. Rev. D 95, 094514 (2017), arXiv:1702.00008 [hep-lat]. Web of Science, ADS, Google Scholar
177. LP3 Collab. (J.-H. Zhang et al.), Nucl. Phys. B 939, 429 (2019), arXiv:1712.10025 [hep-ph]. Web of Science, Google Scholar
178. J.-H. Zhang, J.-W. Chen, L. Jin, H.-W. Lin, A. Schäfer and Y. Zhao, Phys. Rev. D 100, 034505 (2019), arXiv:1804.01483 [hep-lat]. Web of Science, ADS, Google Scholar
179. J.-W. Chen, H.-W. Lin and J.-H. Zhang, arXiv:1904.12376 [hep-lat]. Google Scholar
180. H.-W. Lin and R. Zhang, Phys. Rev. D 100, 074502 (2019). Web of Science, ADS, Google Scholar
181. R. Zhang, Z. Fan, R. Li, H.-W. Lin and B. Yoon, arXiv:1909.10990 [hep-lat]. Google Scholar
182. SciDAC, LHPC and UKQCD Collabs. (R. G. Edwards and B. Joo), Nucl. Phys. B (Proc. Suppl.) 140, 832 (2005), arXiv:hep-lat/0409003. Google Scholar