Search
This Journal
This Journal
Anywhere
Quick Search in Journals
Enter words / phrases / DOI / ISBN / keywords / authors / etc
Access type:Only show content I have full access toOnly show Open Access
Advanced Search
0 My Cart
Sign in
Institutional Access

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

ReviewsNo Access

Unraveling high-energy hadron structures with lattice QCD

Yong Zhao

Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

E-mail Address: yzhaoqcd@mit.edu

Search for more papers by this author

https://doi.org/10.1142/S0217751X18300338Cited by:23 (Source: Crossref)

Abstract

Parton distribution functions are key quantities for us to understand the hadronic structures in high-energy scattering, but they are difficult to calculate from lattice QCD. Recent years have seen fast development of the large-momentum effective theory which allows extraction of the x-dependence of parton distribution functions from a quasi-parton distribution function that can be directly calculated on lattice. The extraction is based on a factorization formula for the quasi-parton distribution function that has been derived rigorously in perturbation theory. A systematic procedure that includes renormalization, perturbative matching, and power corrections has been established to calculate parton distribution functions. Latest progress from lattice QCD has shown promising signs that it will become an effective tool for calculating parton physics.

This writing is based on a talk for the T-2 Theory Seminar at Los Alamos National Laboratory on February 1, 2018.

Keywords:

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

References

1. R. P. Feynman, Phys. Rev. Lett. 23, 1415 (1969). https://doi.org/10.1103/PhysRevLett.23.1415 Web of Science, ADS, Google Scholar
2. J. C. Collins, D. E. Soper and G. F. Sterman, Adv. Ser. Direct. High Energy Phys. 5, 1 (1989), arXiv:hep-ph/0409313. https://doi.org/10.1142/9789814503266˙0001 Link, ADS, Google Scholar
3. A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt, Eur. Phys. J. C 63, 189 (2009), arXiv:0901.0002 [hep-ph]. https://doi.org/10.1140/epjc/s10052-009-1072-5 Web of Science, ADS, Google Scholar
4. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr and G. Watt, Eur. Phys. J. C 75, 132 (2015), arXiv:1412.7420 [hep-ph]. https://doi.org/10.1140/epjc/s10052-015-3318-8 Web of Science, ADS, Google Scholar
5. NNPDF Collab. (R. D. Ball et al.), J. High Energy Phys. 04, 040 (2015), arXiv:1410.8849 [hep-ph]. https://doi.org/10.1007/JHEP04(2015)040 Google Scholar
6. 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]. https://doi.org/10.1103/PhysRevD.93.033006 Web of Science, ADS, Google Scholar
7. S. Alekhin, J. Blümlein, S. Moch and R. Placakyte, Phys. Rev. D 96, 014011 (2017), arXiv:1701.05838 [hep-ph]. https://doi.org/10.1103/PhysRevD.96.014011 Web of Science, ADS, Google Scholar
8. ATLAS Collab. (G. Aad et al.), Phys. Lett. B 716, 1 (2012), arXiv:1207.7214 [hep-ex]. https://doi.org/10.1016/j.physletb.2012.08.020 Web of Science, ADS, Google Scholar
9. CMS Collab. (S. Chatrchyan et al.), Phys. Lett. B 716, 30 (2012), arXiv:1207.7235 [hep-ex]. https://doi.org/10.1016/j.physletb.2012.08.021 Web of Science, ADS, Google Scholar
10. Particle Data Group (K. A. Olive et al.), Chin. Phys. C 38, 090001 (2014). https://doi.org/10.1088/1674-1137/38/9/090001 Web of Science, Google Scholar
11. G. Martinelli and C. T. Sachrajda, Phys. Lett. B 196, 184 (1987). https://doi.org/10.1016/0370-2693(87)90601-0 Web of Science, ADS, Google Scholar
12. G. Martinelli and C. T. Sachrajda, Phys. Lett. B 217, 319 (1989). https://doi.org/10.1016/0370-2693(89)90874-5 Web of Science, ADS, Google Scholar
13. W. Detmold, W. Melnitchouk and A. W. Thomas, Eur. Phys. J. Direct 3, 13 (2001), arXiv:hep-lat/0108002. https://doi.org/10.1007/s1010501c0013 Google Scholar
14. W. Detmold, W. Melnitchouk and A. W. Thomas, Phys. Rev. D 66, 054501 (2002), arXiv:hep-lat/0206001. https://doi.org/10.1103/PhysRevD.66.054501 Web of Science, ADS, Google Scholar
15. LHPC, TXL Collabs. (D. Dolgov et al.), Phys. Rev. D 66, 034506 (2002), arXiv:hep-lat/0201021. https://doi.org/10.1103/PhysRevD.66.034506 Web of Science, Google Scholar
16. X. Ji, Phys. Rev. Lett. 110, 262002 (2013), arXiv:1305.1539 [hep-ph]. https://doi.org/10.1103/PhysRevLett.110.262002 Web of Science, ADS, Google Scholar
17. X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014), arXiv:1404.6680 [hep-ph]. https://doi.org/10.1007/s11433-014-5492-3 Web of Science, ADS, Google Scholar
18. Y.-B. Yang, R. S. Sufian, A. Alexandru, T. Draper, M. J. Glatzmaier, K.-F. Liu and Y. Zhao, Phys. Rev. Lett. 118, 102001 (2017), arXiv:1609.05937 [hep-ph]. https://doi.org/10.1103/PhysRevLett.118.102001 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]. https://doi.org/10.1103/PhysRevD.91.054510 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]. https://doi.org/10.1103/PhysRevD.92.014502 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]. https://doi.org/10.1016/j.nuclphysb.2016.07.033 Web of Science, ADS, Google Scholar
22. 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]. https://doi.org/10.1103/PhysRevD.96.014513 Web of Science, ADS, Google Scholar
23. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato and F. Steffens, Phys. Rev. Lett. 121, 112001 (2018), arXiv:1803.02685 [hep-lat]. https://doi.org/10.1103/PhysRevLett.121.112001 Web of Science, ADS, Google Scholar
24. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato and F. Steffens, arXiv:1807.00232 [hep-lat]. Google Scholar
25. 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]. https://doi.org/10.1103/PhysRevD.98.054504 Google Scholar
26. 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
27. 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). https://doi.org/10.1103/PhysRevLett.121.242003 Web of Science, ADS, Google Scholar
28. 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
29. J.-W. Chen, L. Jin, H.-W. Lin, Y.-S. Liu, A. Schäfer, Y.-B. Yang, J.-H. Zhang and Y. Zhao, arXiv:1804.01483 [hep-lat]. Google Scholar
30. N. Karthik, T. Izubichi, L. Jin, C. Kallidonis, S. Mukherjee, P. Petreczky, C. Shugert and S. Syritsyn, PoS LATTICE2018, 109 (2018), arXiv:1811.06075 [hep-lat]. Google Scholar
31. C. Shugert, T. Izubichi, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky and S. Syritsyn, Pion quasi-parton distribution function on a fine lattice, in 36th Int. Symp. on Lattice Field Theory (Lattice 2018), East Lansing, MI, US, 22–28 July 2018 (2018), arXiv:1811.06074 [hep-lat]. Google Scholar
32. P. Petreczky, T. Izubuchi, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, C. Shugert and S. Syritsyn, Pion structure from lattice QCD, in 13th Conference on Quark Confinement and the Hadron Spectrum (Confinement XIII), Maynooth, Ireland, 31 July–6 August 2018 (2018), arXiv:1812.04334 [hep-lat]. Google Scholar
33. 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]. https://doi.org/10.1103/PhysRevD.95.094514 Web of Science, ADS, Google Scholar
34. J.-W. Chen, L. Jin, H.-W. Lin, A. Schäfer, P. Sun, Y.-B. Yang, J.-H. Zhang, R. Zhang and Y. Zhao, arXiv:1712.10025 [hep-ph]. Google Scholar
35. Z. Davoudi and M. J. Savage, Phys. Rev. D 86, 054505 (2012), arXiv:1204.4146 [hep-lat]. https://doi.org/10.1103/PhysRevD.86.054505 Web of Science, ADS, Google Scholar
36. W. Detmold and C. J. D. Lin, Phys. Rev. D 73, 014501 (2006), arXiv:hep-lat/0507007. https://doi.org/10.1103/PhysRevD.73.014501 Web of Science, ADS, Google Scholar
37. W. Detmold, I. Kanamori, C. J. D. Lin, S. Mondal and Y. Zhao, Moments of pion distribution amplitude using operator product expansion on the lattice, in 36th Int. Symp. on Lattice Field Theory (Lattice 2018), East Lansing, MI, US, 22–28 July 2018 (2018), arXiv:1810.12194 [hep-lat]. Google Scholar
38. 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]. https://doi.org/10.1103/PhysRevLett.118.242001 Web of Science, ADS, Google Scholar
39. V. Braun and D. Mueller, Eur. Phys. J. C 55, 349 (2008), arXiv:0709.1348 [hep-ph]. https://doi.org/10.1140/epjc/s10052-008-0608-4 Web of Science, ADS, Google Scholar
40. G. S. Bali, V. M. Braun, B. Gläßle, M. Göckeler, M. Gruber, F. Hutzler, P. Korcyl, A. Schäfer, P. Wein and J.-H. Zhang, Phys. Rev. D 98, 094507 (2018), arXiv:1807.06671 [hep-lat]. https://doi.org/10.1103/PhysRevD.98.094507 Web of Science, ADS, Google Scholar
41. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. D 98, 074021 (2018), arXiv:1404.6860 [hep-ph]. https://doi.org/10.1103/PhysRevD.98.074021 Web of Science, ADS, Google Scholar
42. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. Lett. 120, 022003 (2018), arXiv:1709.03018 [hep-ph]. https://doi.org/10.1103/PhysRevLett.120.022003 Web of Science, ADS, Google Scholar
43. A. V. Radyushkin, Phys. Rev. D 96, 034025 (2017), arXiv:1705.01488 [hep-ph]. https://doi.org/10.1103/PhysRevD.96.034025 Web of Science, ADS, Google Scholar
44. K. Orginos, A. Radyushkin, J. Karpie and S. Zafeiropoulos, Phys. Rev. D 96, 094503 (2017), arXiv:1706.05373 [hep-ph]. https://doi.org/10.1103/PhysRevD.96.094503 Web of Science, ADS, Google Scholar
45. A. V. Radyushkin, Phys. Lett. B 781, 433 (2018), arXiv:1710.08813 [hep-ph]. https://doi.org/10.1016/j.physletb.2018.04.023 Web of Science, ADS, Google Scholar
46. J. Karpie, K. Orginos and S. Zafeiropoulos, J. High Energy Phys. 11, 178 (2018), arXiv:1807.10933 [hep-lat]. https://doi.org/10.1007/JHEP11(2018)178 Web of Science, ADS, Google Scholar
47. X. Ji, J.-H. Zhang and Y. Zhao, Nucl. Phys. B 924, 366 (2017), arXiv:1706.07416 [hep-ph]. https://doi.org/10.1016/j.nuclphysb.2017.09.001 Web of Science, ADS, Google Scholar
48. T. Izubuchi, X. Ji, L. Jin, I. W. Stewart and Y. Zhao, Phys. Rev. D 98, 056004 (2018), arXiv:1801.03917 [hep-ph]. https://doi.org/10.1103/PhysRevD.98.056004 Web of Science, ADS, Google Scholar
49. K.-F. Liu and S.-J. Dong, Phys. Rev. Lett. 72, 1790 (1994), arXiv:hep-ph/9306299. https://doi.org/10.1103/PhysRevLett.72.1790 Web of Science, ADS, Google Scholar
50. 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. https://doi.org/10.1103/PhysRevD.59.112001 Web of Science, ADS, Google Scholar
51. K.-F. Liu, Phys. Rev. D 62, 074501 (2000), arXiv:hep-ph/9910306. https://doi.org/10.1103/PhysRevD.62.074501 Web of Science, ADS, Google Scholar
52. K.-F. Liu, PoS LATTICE2015, 115 (2016), arXiv:1603.07352 [hep-ph]. https://doi.org/10.22323/1.251.0115 Google Scholar
53. J. Liang, K.-F. Liu and Y.-B. Yang, EPJ Web Conf. 175, 14014 (2018), arXiv:1710.11145 [hep-lat]. https://doi.org/10.1051/epjconf/201817514014 Google Scholar
54. C. Monahan, PoS LATTICE2018, 018 (2018), arXiv:1811.00678 [hep-lat]. Google Scholar
55. K. Cichy and M. Constantinou, arXiv:1811.07248 [hep-lat]. Google Scholar
56. S. Weinberg, Phys. Rev. 150, 1313 (1966). https://doi.org/10.1103/PhysRev.150.1313 Web of Science, ADS, Google Scholar
57. X. Ji, Y. Xu and Y. Zhao, J. High Energy Phys. 08, 082 (2012), arXiv:1205.0156 [hep-ph]. https://doi.org/10.1007/JHEP08(2012)082 Web of Science, ADS, Google Scholar
58. X. Ji, J.-H. Zhang and Y. Zhao, Phys. Rev. Lett. 111, 112002 (2013), arXiv:1304.6708 [hep-ph]. https://doi.org/10.1103/PhysRevLett.111.112002 Web of Science, ADS, Google Scholar
59. Y. Hatta, X. Ji and Y. Zhao, Phys. Rev. D 89, 085030 (2014), arXiv:1310.4263 [hep-ph]. https://doi.org/10.1103/PhysRevD.89.085030 Web of Science, ADS, Google Scholar
60. X. Ji, J.-H. Zhang and Y. Zhao, Phys. Lett. B 743, 180 (2015), arXiv:1409.6329 [hep-ph]. https://doi.org/10.1016/j.physletb.2015.02.054 Web of Science, ADS, Google Scholar
61. R. L. Jaffe and A. Manohar, Nucl. Phys. B 337, 509 (1990). https://doi.org/10.1016/0550-3213(90)90506-9 Web of Science, ADS, Google Scholar
62. X. Xiong, X. Ji, J.-H. Zhang and Y. Zhao, Phys. Rev. D 90, 014051 (2014), arXiv:1310.7471 [hep-ph]. https://doi.org/10.1103/PhysRevD.90.014051 Web of Science, ADS, Google Scholar
63. S. Capitani, Phys. Rep. 382, 113 (2003), arXiv:hep-lat/0211036. https://doi.org/10.1016/S0370-1573(03)00211-4 Web of Science, ADS, Google Scholar
64. T. Ishikawa, Y.-Q. Ma, J.-W. Qiu and S. Yoshida, arXiv:1609.02018 [hep-lat]. Google Scholar
65. X. Xiong, T. Luu and U.-G. Meißner, arXiv:1705.00246 [hep-ph]. Google Scholar
66. M. Constantinou and H. Panagopoulos, Phys. Rev. D 96, 054506 (2017), arXiv:1705.11193 [hep-lat]. https://doi.org/10.1103/PhysRevD.96.054506 Web of Science, ADS, Google Scholar
67. T. Ishikawa, EPJ Web Conf. 175, 06028 (2018), arXiv:1802.02333 [hep-lat]. https://doi.org/10.1051/epjconf/201817506028 Google Scholar
68. X. Ji and J.-H. Zhang, Phys. Rev. D 92, 034006 (2015), arXiv:1505.07699 [hep-ph]. https://doi.org/10.1103/PhysRevD.92.034006 Web of Science, ADS, Google Scholar
69. N. S. Craigie and H. Dorn, Nucl. Phys. B 185, 204 (1981). https://doi.org/10.1016/0550-3213(81)90372-2 Web of Science, ADS, Google Scholar
70. H. Dorn, Fortschr. Phys. 34, 11 (1986). https://doi.org/10.1002/prop.19860340104 Web of Science, Google Scholar
71. V. S. Dotsenko and S. N. Vergeles, Nucl. Phys. B 169, 527 (1980). https://doi.org/10.1016/0550-3213(80)90103-0 Web of Science, ADS, Google Scholar
72. B. U. Musch, P. Hagler, J. W. Negele and A. Schäfer, Phys. Rev. D 83, 094507 (2011), arXiv:1011.1213 [hep-lat]. https://doi.org/10.1103/PhysRevD.83.094507 Web of Science, ADS, Google Scholar
73. J.-W. Chen, X. Ji and J.-H. Zhang, Nucl. Phys. B 915, 1 (2017), arXiv:1609.08102 [hep-ph]. https://doi.org/10.1016/j.nuclphysb.2016.12.004 Web of Science, ADS, Google Scholar
74. X. Ji, J.-H. Zhang and Y. Zhao, Phys. Rev. Lett. 120, 112001 (2018), arXiv:1706.08962 [hep-ph]. https://doi.org/10.1103/PhysRevLett.120.112001 Web of Science, ADS, Google Scholar
75. J. Green, K. Jansen and F. Steffens, Phys. Rev. Lett. 121, 022004 (2018), arXiv:1707.07152 [hep-lat]. https://doi.org/10.1103/PhysRevLett.121.022004 Web of Science, ADS, Google Scholar
76. T. Ishikawa, Y.-Q. Ma, J.-W. Qiu and S. Yoshida, Phys. Rev. D 96, 094019 (2017), arXiv:1707.03107 [hep-ph]. https://doi.org/10.1103/PhysRevD.96.094019 Web of Science, ADS, Google Scholar
77. J.-H. Zhang, X. Ji, A. Schäfer, W. Wang and S. Zhao, arXiv:1808.10824 [hep-ph]. Google Scholar
78. Z.-Y. Li, Y.-Q. Ma and J.-W. Qiu, arXiv:1809.01836 [hep-ph]. Google Scholar
79. O. Nachtmann, Nucl. Phys. B 63, 237 (1973). https://doi.org/10.1016/0550-3213(73)90144-2 Web of Science, ADS, Google Scholar
80. H. Georgi and H. D. Politzer, Phys. Rev. D 14, 1829 (1976). https://doi.org/10.1103/PhysRevD.14.1829 Web of Science, ADS, Google Scholar
81. V. M. Braun, A. Vladimirov and J.-H. Zhang, arXiv:1810.00048 [hep-ph]. Google Scholar
82. G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa and A. Vladikas, Nucl. Phys. B 445, 81 (1995), arXiv:hep-lat/9411010. https://doi.org/10.1016/0550-3213(95)00126-D Web of Science, ADS, Google Scholar
83. I. W. Stewart and Y. Zhao, Phys. Rev. D 97, 054512 (2018), arXiv:1709.04933 [hep-ph]. https://doi.org/10.1103/PhysRevD.97.054512 Web of Science, ADS, Google Scholar
84. J.-W. Chen, T. Ishikawa, L. Jin, H.-W. Lin, Y.-B. Yang, J.-H. Zhang and Y. Zhao, arXiv:1710.01089 [hep-lat]. Google Scholar
85. Y.-S. Liu, J.-W. Chen, L. Jin, H.-W. Lin, Y.-B. Yang, J.-H. Zhang and Y. Zhao, arXiv:1807.06566 [hep-lat]. Google Scholar
86. G. Spanoudes and H. Panagopoulos, Phys. Rev. D 98, 014509 (2018), arXiv:1805.01164 [hep-lat]. https://doi.org/10.1103/PhysRevD.98.014509 Web of Science, ADS, Google Scholar
87. 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]. https://doi.org/10.1016/j.nuclphysb.2017.08.012 Web of Science, ADS, Google Scholar
88. 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]. https://doi.org/10.1103/PhysRevD.97.014505 Web of Science, ADS, Google Scholar
89. C. Monahan and K. Orginos, J. High Energy Phys. 03, 116 (2017), arXiv:1612.01584 [hep-lat]. https://doi.org/10.1007/JHEP03(2017)116 Web of Science, ADS, Google Scholar
90. C. Monahan, Phys. Rev. D 97, 054507 (2018), arXiv:1710.04607 [hep-lat]. https://doi.org/10.1103/PhysRevD.97.054507 Web of Science, ADS, Google Scholar
91. HPQCD, UKQCD Collabs. (E. Follana, Q. Mason, C. Davies, K. Hornbostel, G. P. Lepage, J. Shigemitsu, H. Trottier and K. Wong), Phys. Rev. D 75, 054502 (2007), arXiv:hep-lat/0610092. https://doi.org/10.1103/PhysRevD.75.054502 Google Scholar
92. MILC Collab. (A. Bazavov et al.), Phys. Rev. D 87, 054505 (2013), arXiv:1212.4768 [hep-lat]. https://doi.org/10.1103/PhysRevD.87.054505 Google Scholar
93. G. S. Bali, B. Lang, B. U. Musch and A. Schäfer, Phys. Rev. D 93, 094515 (2016), arXiv:1602.05525 [hep-lat]. https://doi.org/10.1103/PhysRevD.93.094515 Web of Science, ADS, Google Scholar
94. 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]. https://doi.org/10.1103/PhysRevD.89.094502 Web of Science, ADS, Google Scholar
95. 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]. https://doi.org/10.1016/j.nuclphysb.2014.08.008 Web of Science, ADS, Google Scholar
96. J. J. Ethier, N. Sato and W. Melnitchouk, Phys. Rev. Lett. 119, 132001 (2017), arXiv:1705.05889 [hep-ph]. https://doi.org/10.1103/PhysRevLett.119.132001 Web of Science, ADS, Google Scholar
97. H.-W. Lin, W. Melnitchouk, A. Prokudin, N. Sato and H. Shows, Phys. Rev. Lett. 120, 152502 (2018), arXiv:1710.09858 [hep-ph]. https://doi.org/10.1103/PhysRevLett.120.152502 Web of Science, ADS, Google Scholar
98. R. A. Briceño, J. V. Guerrero, M. T. Hansen and C. J. Monahan, Phys. Rev. D 98, 014511 (2018), arXiv:1805.01034 [hep-lat]. https://doi.org/10.1103/PhysRevD.98.014511 Web of Science, ADS, Google Scholar
99. Z.-Y. Fan, Y.-B. Yang, A. Anthony, H.-W. Lin and K.-F. Liu, arXiv:1808.02077 [hep-lat]. Google Scholar
100. W. Wang, S. Zhao and R. Zhu, Eur. Phys. J. C 78, 147 (2018), arXiv:1708.02458 [hep-ph]. https://doi.org/10.1140/epjc/s10052-018-5617-3 Web of Science, ADS, Google Scholar
101. W. Wang and S. Zhao, J. High Energy Phys. 05, 142 (2018), arXiv:1712.09247 [hep-ph]. https://doi.org/10.1007/JHEP05(2018)142 Web of Science, ADS, Google Scholar
102. W. Wang, J. Xu, J.-H. Zhang and S. Zhao, in preparation. Google Scholar
103. X. Ji, A. Schäfer, X. Xiong and J.-H. Zhang, Phys. Rev. D 92, 014039 (2015), arXiv:1506.00248 [hep-ph]. https://doi.org/10.1103/PhysRevD.92.014039 Web of Science, ADS, Google Scholar
104. X. Xiong and J.-H. Zhang, Phys. Rev. D 92, 054037 (2015), arXiv:1509.08016 [hep-ph]. https://doi.org/10.1103/PhysRevD.92.054037 Web of Science, ADS, Google Scholar
105. Y.-S. Liu, W. Wang, J. Xu, Q.-A. Zhang, J.-H. Zhang, S. Zhao and Y. Zhao, in preparation. Google Scholar
106. Y.-S. Liu, W. Wang, J. Xu, Q.-A. Zhang, S. Zhao and Y. Zhao, arXiv:1810.10879 [hep-ph]. Google Scholar
107. J. Collins, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 32, 1 (2011). Google Scholar
108. X. Ji, P. Sun, X. Xiong and F. Yuan, Phys. Rev. D 91, 074009 (2015), arXiv:1405.7640 [hep-ph]. https://doi.org/10.1103/PhysRevD.91.074009 Web of Science, ADS, Google Scholar
109. X. Ji, L.-C. Jin, F. Yuan, J.-H. Zhang and Y. Zhao, arXiv:1801.05930 [hep-ph]. Google Scholar
110. M. A. Ebert, I. W. Stewart and Y. Zhao, in preparation. Google Scholar
111. M. A. Ebert, I. W. Stewart and Y. Zhao, arXiv:1811.00026 [hep-ph]. Google Scholar
112. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016), arXiv:1212.1701 [nucl-ex]. https://doi.org/10.1140/epja/i2016-16268-9 Web of Science, ADS, Google Scholar

Journal cover image

Vol. 33, No. 36

Metrics

Downloaded 31 times

History

Received 7 December 2018

Accepted 18 December 2018

Published: 11 January 2019

Keywords