Hadrons và hạt nhân

Springer Science and Business Media LLC - Tập 55 - Trang 1-27 - 2019
William Detmold1, Robert G. Edwards2, Jozef J. Dudek2,3, Michael Engelhardt4, Huey-Wen Lin5, Stefan Meinel6,7, Kostas Orginos2,3, Phiala Shanahan1
1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, USA
2Thomas Jefferson National Accelerator Facility, Newport News, USA
3Department of Physics, The College of William & Mary, Williamsburg, USA
4Department of Physics, New Mexico State University, Las Cruces, USA
5Department of Physics and Astronomy, Michigan State University, East Lansing, USA
6Department of Physics, University of Arizona, Tucson, USA
7RIKEN/BNL Research Center, Brookhaven National Laboratory, Upton, USA

Tóm tắt

Vào năm 2018, Ủy ban Hành chính của Hợp tác USQCD đã tổ chức một số tiểu ban nhằm nhận diện những cơ hội tương lai và xây dựng các mục tiêu khả thi cho các phép tính lý thuyết lưới trong một số lĩnh vực vật lý. Kết quả của các nghiên cứu này, cùng với sự đóng góp của cộng đồng, được trình bày trong bảy tài liệu trắng. Ở đây, chúng tôi thảo luận về những cơ hội cho các phép tính QCD dạng lưới liên quan đến cấu trúc và phổ của hadron và hạt nhân. Chúng tôi trình bày một tổng quan về các phép tính lưới gần đây của cấu trúc proton và các hadron khác cùng với triển vọng cho các mở rộng trong tương lai. Tiến trình và triển vọng của phổ hadron và nghiên cứu các cộng hưởng trong lĩnh vực quark nhẹ, quark lạ và quark nặng được tóm tắt. Cuối cùng, những tiến bộ gần đây trong nghiên cứu các hạt nhân nhẹ từ lý thuyết QCD lưới được đề cập và phạm vi của các cuộc điều tra trong tương lai đang được dự kiến được phác thảo.

Từ khóa

#QCD #lý thuyết lưới #hadron #hạt nhân #nghiên cứu cộng hưởng #quark nhẹ #quark lạ #quark nặng

Tài liệu tham khảo

USQCD Collaboration (A. Bazavov, F. Karsch, S. Mukherjee, P. Petreczky), https://doi.org/10.1140/epja/i2019-12922-0, http://arXiv:1904.09951 (2019) USQCD Collaboration (R.C. Brower, A. Hasenfratz, E.T. Neil, S. Catterall, G. Fleming, J. Giedt, E. Rinaldi, D. Schaich, E. Weinberg, O. Witzel), https://doi.org/10.1140/epja/i2019-12901-5, http://arXiv:1904.09964 (2019) USQCD Collaboration (V. Cirigliano, Z. Davoudi, T. Bhattacharya, T. Izubuchi, P.E. Shanahan, S. Syritsyn, M.L. Wagman), https://doi.org/10.1140/epja/i2019-12889-8, http://arXiv:1904.09704 (2019) USQCD Collaboration (W. Detmold, R.G. Edwards, J.J. Dudek, M. Engelhardt, H.W. Lin, S. Meinel, K. Orginos, P. Shanahan) this paper, arXiv:1904.09512 (2019) USQCD Collaboration (B. Joó, C. Jung, N.H. Christ, W. Detmold, R. Edwards, M. Savage, P. Shanahan), https://doi.org/10.1140/epja/i2019-12919-7, http://arXiv:1904.09725 (2019) USQCD Collaboration (A.S. Kronfeld, D.G. Richards, W. Detmold, R. Gupta, H.W. Lin, K.F. Liu, A.S. Meyer, R. Sufian, S. Syritsin), https://doi.org/10.1140/epja/i2019-12916-x, http://arXiv:1904.09931 (2019) USQCD Collaboration (C. Lehner), https://doi.org/10.1140/epja/i2019-12891-2, http://arXiv:1904.09479 (2019) Particle Data Group (C. Patrignani et al.), Chin. Phys. C 40, 100001 (2016) T. Bhattacharya, V. Cirigliano, S. Cohen, R. Gupta, H.W. Lin, B. Yoon, Phys. Rev. D 94, 054508 (2016) arXiv:1606.07049 B. Yoon et al., Phys. Rev. D 95, 074508 (2017) arXiv:1611.07452 C.C. Chang et al., Nature 558, 91 (2018) arXiv:1805.12130 R. Gupta, Y.C. Jang, B. Yoon, H.W. Lin, V. Cirigliano, T. Bhattacharya, Phys. Rev. D 98, 034503 (2018) arXiv:1806.09006 R. Gupta, B. Yoon, T. Bhattacharya, V. Cirigliano, Y.C. Jang, H.W. Lin, Phys. Rev. D 98, 091501 (2018) arXiv:1808.07597 P.E. Shanahan, J. Phys. G 43, 124001 (2016) arXiv:1606.08812 S. Capitani, M. Della Morte, D. Djukanovic, G. von Hippel, J. Hua, B. Jäger, B. Knippschild, H.B. Meyer, T.D. Rae, H. Wittig, Phys. Rev. D 92, 054511 (2015) arXiv:1504.04628 N. Hasan, J. Green, S. Meinel, M. Engelhardt, S. Krieg, J. Negele, A. Pochinsky, S. Syritsyn, Phys. Rev. D 97, 034504 (2018) arXiv:1711.11385 C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Aviles-Casco, Phys. Rev. D 96, 034503 (2017) arXiv:1706.00469 PACS Collaboration (K.I. Ishikawa, Y. Kuramashi, S. Sasaki, N. Tsukamoto, A. Ukawa, T. Yamazaki), Phys. Rev. D 98, 074510 (2018) arXiv:1807.03974 W. Detmold, A. Grebe, P. Shanahan, PoS LATTICE2018, 303 (2018) arXiv:1812.00313 C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, A. Vaquero Aviles-Casco, Phys. Rev. D 100, 014509 (2019) arXiv:1812.10311 H.W. Lin et al., Prog. Part. Nucl. Phys. 100, 107 (2018) arXiv:1711.07916 W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 73, 114505 (2006) arXiv:hep-lat/0603026 W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 79, 094505 (2009) arXiv:0904.1586 W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 81, 054502 (2010) arXiv:1001.1131 W. Freeman, A. Alexandru, M. Lujan, F.X. Lee, Phys. Rev. D 90, 054507 (2014) arXiv:1407.2687 M. Lujan, A. Alexandru, W. Freeman, F. Lee, Phys. Rev. D 89, 074506 (2014) arXiv:1402.3025 NPLQCD Collaboration (E. Chang, W. Detmold, K. Orginos, A. Parreno, M.J. Savage, B.C. Tiburzi, S.R. Beane), Phys. Rev. D 92, 114502 (2015) arXiv:1506.05518 M. Lujan, A. Alexandru, W. Freeman, F.X. Lee, Phys. Rev. D 94, 074506 (2016) arXiv:1606.07928 P.E. Shanahan, B.C. Tiburzi, M.L. Wagman, F. Winter, E. Chang, Z. Davoudi, W. Detmold, K. Orginos, M.J. Savage, Phys. Rev. Lett. 119, 062003 (2017) arXiv:1701.03456 B.C. Tiburzi, M.L. Wagman, F. Winter, E. Chang, Z. Davoudi, W. Detmold, K. Orginos, M.J. Savage, P.E. Shanahan, Phys. Rev. D 96, 054505 (2017) arXiv:1702.02929 A. Agadjanov, U.G. Meißner, A. Rusetsky, Phys. Rev. D 95, 031502 (2017) arXiv:1610.05545 A. Agadjanov, U.G. Meißner, A. Rusetsky, Phys. Rev. D 99, 054501 (2019) arXiv:1812.06013 A.J. Chambers et al., PoS LATTICE2015, 125 (2016) arXiv:1511.07090 LHPC Collaboration (M. Engelhardt), Phys. Rev. D 76, 114502 (2007) arXiv:0706.3919 J.C. Collins, D.E. Soper, Nucl. Phys. B 194, 445 (1982) G. Curci, W. Furmanski, R. Petronzio, Nucl. Phys. B 175, 27 (1980) L. Baulieu, E.G. Floratos, C. Kounnas, Nucl. Phys. B 166, 321 (1980) J.C. Collins, D.E. Soper, G.F. Sterman, Adv. Ser. Direct. High Energy Phys. 5, 1 (1989) arXiv:hep-ph/0409313 C. Dawson, G. Martinelli, G.C. Rossi, C.T. Sachrajda, S.R. Sharpe, M. Talevi, M. Testa, Nucl. Phys. B 514, 313 (1998) arXiv:hep-lat/9707009 Z. Davoudi, M.J. Savage, Phys. Rev. D 86, 054505 (2012) arXiv:1204.4146 Z. Davoudi, PoS LATTICE2018, 014 (2018) arXiv:1812.11899 X. Ji, Phys. Rev. Lett. 110, 262002 (2013) arXiv:1305.1539 X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014) arXiv:1404.6680 G. Martinelli, C. Pittori, C.T. Sachrajda, M. Testa, A. Vladikas, Nucl. Phys. B 445, 81 (1995) arXiv:hep-lat/9411010 C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, H. Panagopoulos, F. Steffens, Nucl. Phys. B 923, 394 (2017) arXiv:1706.00265 J.W. Chen, T. Ishikawa, L. Jin, H.W. Lin, Y.B. Yang, J.H. Zhang, Y. Zhao, Phys. Rev. D 97, 014505 (2018) arXiv:1706.01295 J. Green, K. Jansen, F. Steffens, Phys. Rev. Lett. 121, 022004 (2018) arXiv:1707.07152 J.W. Chen, L. Jin, H.W. Lin, Y.S. Liu, Y.B. Yang, J.H. Zhang, Y. Zhao, arXiv:1803.04393 (2018) 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, 242003 (2018) arXiv:1807.07431 B.L. Ioffe, Phys. Lett. B 30, 123 (1969) V. Braun, P. Gornicki, L. Mankiewicz, Phys. Rev. D 51, 6036 (1995) arXiv:hep-ph/9410318 A. Radyushkin, Phys. Lett. B 767, 314 (2017) arXiv:1612.05170 A.V. Radyushkin, Phys. Rev. D 96, 034025 (2017) arXiv:1705.01488 R.A. Briceño, J.V. Guerrero, M.T. Hansen, C.J. Monahan, Phys. Rev. D 98, 014511 (2018) arXiv:1805.01034 K. Orginos, A. Radyushkin, J. Karpie, S. Zafeiropoulos, Phys. Rev. D 96, 094503 (2017) arXiv:1706.05373 J. Karpie, K. Orginos, S. Zafeiropoulos, JHEP 11, 178 (2018) arXiv:1807.10933 NNPDF Collaboration (R.D. Ball et al.), Eur. Phys. J. C 77, 663 (2017) arXiv:1706.00428 A. Accardi, L.T. Brady, W. Melnitchouk, J.F. Owens, N. Sato, Phys. Rev. D 93, 114017 (2016) arXiv:1602.03154 J. Karpie, K. Orginos, A. Rothkopf, S. Zafeiropoulos, JHEP 04, 057 (2019) arXiv:1901.05408 G. Backus, F. Gilbert, Geophys. J. Int. 16, 169 (1968) Y. Burnier, A. Rothkopf, Phys. Rev. Lett. 111, 182003 (2013) arXiv:1307.6106 S. Forte, L. Garrido, J.I. Latorre, A. Piccione, JHEP 05, 062 (2002) arXiv:hep-ph/0204232 Y.Q. Ma, J.W. Qiu, Phys. Rev. D 98, 074021 (2018) arXiv:1404.6860 Y.Q. Ma, J.W. Qiu, Int. J. Mod. Phys. Conf. Ser. 37, 1560041 (2015) arXiv:1412.2688 Y.Q. Ma, J.W. Qiu, Phys. Rev. Lett. 120, 022003 (2018) arXiv:1709.03018 R.S. Sufian, J. Karpie, C. Egerer, K. Orginos, J.W. Qiu, D.G. Richards, Phys. Rev. D 99, 074507 (2019) arXiv:1901.03921 K.F. Liu, S.J. Dong, Phys. Rev. Lett. 72, 1790 (1994) arXiv:hep-ph/9306299 U. Aglietti, M. Ciuchini, G. Corbo, E. Franco, G. Martinelli, L. Silvestrini, Phys. Lett. B 432, 411 (1998) arXiv:hep-ph/9804416 W. Detmold, C.J.D. Lin, Phys. Rev. D 73, 014501 (2006) arXiv:hep-lat/0507007 K.F. Liu, PoS LATTICE2015, 115 (2016) arXiv:1603.07352 J. Liang, K.F. Liu, Y.B. Yang, EPJ Web of Conferences 175, 14014 (2018) arXiv:1710.11145 W. Detmold, I. Kanamori, C.J.D. Lin, S. Mondal, Y. Zhao, PoS LATTICE2018, 106 (2018) arXiv:1810.12194 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, 242001 (2017) arXiv:1703.01153 X.d. Ji, C.w. Jung, Phys. Rev. Lett. 86, 208 (2001) arXiv:hep-lat/0101014 A.V. Radyushkin, Phys. Rev. D 56, 5524 (1997) arXiv:hep-ph/9704207 M. Diehl, Phys. Rep. 388, 41 (2003) arXiv:hep-ph/0307382 A.V. Belitsky, A.V. Radyushkin, Phys. Rep. 418, 1 (2005) arXiv:hep-ph/0504030 M. Burkardt, Phys. Rev. D 62, 071503 (2000) Phys. Rev. D 66 LHPC, SESAM Collaborations (P. Hagler, J.W. Negele, D.B. Renner, W. Schroers, T. Lippert, K. Schilling), Phys. Rev. D 68, 034505 (2003) arXiv:hep-lat/0304018 LHPC Collaboration (P. Hagler et al.), Phys. Rev. D 77, 094502 (2008) arXiv:0705.4295 P. Hagler, B.U. Musch, J.W. Negele, A. Schafer, EPL 88, 61001 (2009) arXiv:0908.1283 X.D. Ji, Phys. Rev. Lett. 78, 610 (1997) arXiv:hep-ph/9603249 R.L. Jaffe, A. Manohar, Nucl. Phys. B 337, 509 (1990) Y.B. Yang, R.S. Sufian, A. Alexandru, T. Draper, M.J. Glatzmaier, K.F. Liu, Y. Zhao, Phys. Rev. Lett. 118, 102001 (2017) arXiv:1609.05937 C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Aviles-Casco, C. Wiese, Phys. Rev. Lett. 119, 142002 (2017) arXiv:1706.02973 M.V. Polyakov, P. Schweitzer, Int. J. Mod. Phys. A 33, 1830025 (2018) arXiv:1805.06596 S.N. Syritsyn, J.R. Green, J.W. Negele, A.V. Pochinsky, M. Engelhardt, P. Hagler, B. Musch, W. Schroers, PoS LATTICE2011, 178 (2011) arXiv:1111.0718 G.S. Bali et al., PoS Lattice2013, 291 (2014) arXiv:1312.0828 LHPC Collaboration (J.D. Bratt et al.), Phys. Rev. D 82, 094502 (2010) arXiv:1001.3620 A. Sternbeck et al., PoS LATTICE2011, 177 (2011) arXiv:1203.6579 QCDSF-UKQCD Collaboration (D. Brommel et al.), PoS LATTICE2007, 158 (2007) arXiv:0710.1534 QCDSF Collaboration (M. Gockeler, R. Horsley, D. Pleiter, P.E.L. Rakow, A. Schafer, G. Schierholz, W. Schroers), Phys. Rev. Lett. 92, 042002 (2004) arXiv:hep-ph/0304249 C. Alexandrou, J. Carbonell, M. Constantinou, P.A. Harraud, P. Guichon, K. Jansen, C. Kallidonis, T. Korzec, M. Papinutto, Phys. Rev. D 83, 114513 (2011) arXiv:1104.1600 M. Deka et al., Phys. Rev. D 91, 014505 (2015) arXiv:1312.4816 C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, H. Panagopoulos, C. Wiese, Phys. Rev. D 96, 054503 (2017) arXiv:1611.06901 D. Boer, arXiv:1108.1713 (2011) COMPASS Collaboration (M. Alekseev et al.), Phys. Lett. B 673, 127 (2009) arXiv:0802.2160 COMPASS Collaboration (C. Adolph et al.), Phys. Lett. B 736, 124 (2014) arXiv:1401.7873 HERMES Collaboration (A. Airapetian et al.), Phys. Rev. Lett. 103, 152002 (2009) arXiv:0906.3918 HERMES Collaboration (A. Airapetian et al.), Phys. Lett. B 728, 183 (2014) arXiv:1310.5070 Jefferson Lab Hall A Collaboration (X. Qian et al.), Phys. Rev. Lett. 107, 072003 (2011) arXiv:1106.0363 CLAS Collaboration (H. Avakian et al.), Phys. Rev. Lett. 105, 262002 (2010) arXiv:1003.4549 COMPASS Collaboration (F. Gautheron), CERN experimental proposal, CERN-SPSC-2010-014. SPSC-P-340 (2010) C. Brown, FERMILAB proposal, FERMILAB-PROPOSAL-1039 (2014) PHENIX Collaboration (A. Adare et al.), Phys. Rev. D 90, 012006 (2014) arXiv:1312.1995 STAR Collaboration (L. Adamczyk et al.), Phys. Rev. D 86, 051101 (2012) arXiv:1205.6826 M.G. Echevarria, A. Idilbi, Z.B. Kang, I. Vitev, Int. J. Mod. Phys. Conf. Ser. 37, 1560025 (2015) arXiv:1411.3682 A. Accardi et al., Eur. Phys. J. A 52, 268 (2016) arXiv:1212.1701 B.U. Musch, P. Hagler, M. Engelhardt, J.W. Negele, A. Schafer, Phys. Rev. D 85, 094510 (2012) arXiv:1111.4249 M. Engelhardt, P. Hägler, B. Musch, J. Negele, A. Schäfer, Phys. Rev. D 93, 054501 (2016) arXiv:1506.07826 B.U. Musch, P. Hagler, J.W. Negele, A. Schafer, Phys. Rev. D 83, 094507 (2011) arXiv:1011.1213 B. Yoon, M. Engelhardt, R. Gupta, T. Bhattacharya, J.R. Green, B.U. Musch, J.W. Negele, A.V. Pochinsky, A. Schäfer, S.N. Syritsyn, Phys. Rev. D 96, 094508 (2017) arXiv:1706.03406 M. Engelhardt, Phys. Rev. D 95, 094505 (2017) arXiv:1701.01536 M. Constantinou, H. Panagopoulos, Phys. Rev. D 96, 054506 (2017) arXiv:1705.11193 M. Engelhardt, B. Musch, T. Bhattacharya, R. Gupta, P. Hägler, S. Krieg, J. Negele, A. Pochinsky, S. Syritsyn, B. Yoon, PoS LATTICE2015, 117 (2016) A. Stathopoulos, J. Laeuchli, K. Orginos, arXiv:1302.4018 (2013) S. Meissner, A. Metz, M. Schlegel, JHEP 08, 056 (2009) arXiv:0906.5323 PHENIX Collaboration (A. Adare et al.), Phys. Rev. D 90, 012007 (2014) arXiv:1402.6296 STAR Collaboration (P. Djawotho), Nuovo Cimento C 036, 35 (2013) arXiv:1303.0543 N. Kalantarians, J. Phys. Conf. Ser. 543, 012008 (2014) A. Aprahamian, Reaching for the horizon: The 2015 long range plan for nuclear science (2015) https://science.osti.gov/-/media/np/nsac/pdf/2015LRP/2015_LRPNS_091815.pdf J. Maxwell, arXiv:1803.11206 (2018) CLAS Collaboration (M. Hattawy et al.), Phys. Rev. Lett. 119, 202004 (2017) arXiv:1707.03361 GlueX Collaboration (S. Dobbs), PoS Hadron2017, 047 (2018) arXiv:1712.07214 A.J. Baltz, Phys. Rep. 458, 1 (2008) arXiv:0706.3356 W. Detmold, P.E. Shanahan, Phys. Rev. D 94, 014507 (2016) Phys. Rev. D 95 W. Detmold, D. Pefkou, P.E. Shanahan, Phys. Rev. D 95, 114515 (2017) arXiv:1703.08220 F. Winter, W. Detmold, A.S. Gambhir, K. Orginos, M.J. Savage, P.E. Shanahan, M.L. Wagman, Phys. Rev. D 96, 094512 (2017) arXiv:1709.00395 H.B. Meyer, J.W. Negele, Phys. Rev. D 77, 037501 (2008) arXiv:0707.3225 QCDSF, UKQCD Collaborations (R. Horsley, R. Millo, Y. Nakamura, H. Perlt, D. Pleiter, P.E.L. Rakow, G. Schierholz, A. Schiller, F. Winter, J.M. Zanotti), Phys. Lett. B 714, 312 (2012) arXiv:1205.6410 C. Alexandrou, V. Drach, K. Hadjiyiannakou, K. Jansen, B. Kostrzewa, C. Wiese, PoS LATTICE2013, 289 (2014) arXiv:1311.3174 D. de Florian, R. Sassot, M. Stratmann, W. Vogelsang, Phys. Rev. Lett. 113, 012001 (2014) arXiv:1404.4293 M.J. Glatzmaier, K.F. Liu, Y.B. Yang, Phys. Rev. D 95, 074513 (2017) arXiv:1403.7211 Y.B. Yang, M. Gong, J. Liang, H.W. Lin, K.F. Liu, D. Pefkou, P. Shanahan, Phys. Rev. D 98, 074506 (2018) arXiv:1805.00531 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, 033006 (2016) arXiv:1506.07443 P.E. Shanahan, W. Detmold, Phys. Rev. Lett. 122, 072003 (2019) arXiv:1810.07589 P.E. Shanahan, W. Detmold, Phys. Rev. D 99, 014511 (2019) arXiv:1810.04626 V.D. Burkert, L. Elouadrhiri, F.X. Girod, Nature 557, 396 (2018) E. Chudakov, D. Higinbotham, C. Hyde, S. Furletov, Yu. Furletova, D. Nguyen, M. Stratmann, M. Strikman, C. Weiss, R. Yoshida, PoS DIS2016, 143 (2016) arXiv:1608.08686 H.W. Lin, J.W. Chen, S.D. Cohen, X. Ji, Phys. Rev. D 91, 054510 (2015) arXiv:1402.1462 C. Alexandrou, K. Cichy, V. Drach, E. Garcia-Ramos, K. Hadjiyiannakou, K. Jansen, F. Steffens, C. Wiese, Phys. Rev. D 92, 014502 (2015) arXiv:1504.07455 C.A. Meyer, E.S. Swanson, Prog. Part. Nucl. Phys. 82, 21 (2015) arXiv:1502.07276 R.F. Lebed, R.E. Mitchell, E.S. Swanson, Prog. Part. Nucl. Phys. 93, 143 (2017) arXiv:1610.04528 F.K. Guo, C. Hanhart, U.G. Meißner, Q. Wang, Q. Zhao, B.S. Zou, Rev. Mod. Phys. 90, 015004 (2018) arXiv:1705.00141 A. Duncan, E. Eichten, H. Thacker, Phys. Rev. Lett. 76, 3894 (1996) arXiv:hep-lat/9602005 T. Blum, T. Doi, M. Hayakawa, T. Izubuchi, N. Yamada, Phys. Rev. D 76, 114508 (2007) arXiv:0708.0484 S. Borsanyi et al., Science 347, 1452 (2015) arXiv:1406.4088 R. Horsley et al., J. Phys. G 43, 10LT02 (2016) arXiv:1508.06401 T. Blum, R. Zhou, T. Doi, M. Hayakawa, T. Izubuchi, S. Uno, N. Yamada, Phys. Rev. D 82, 094508 (2010) arXiv:1006.1311 S. Aoki et al., Phys. Rev. D 86, 034507 (2012) arXiv:1205.2961 RM123 Collaboration (G.M. de Divitiis, R. Frezzotti, V. Lubicz, G. Martinelli, R. Petronzio, G.C. Rossi, F. Sanfilippo, S. Simula, N. Tantalo), Phys. Rev. D 87, 114505 (2013) arXiv:1303.4896 J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards, C.E. Thomas, Phys. Rev. D 82, 034508 (2010) arXiv:1004.4930 Hadron Spectrum Collaboration (J.J. Dudek, R.G. Edwards, P. Guo, C.E. Thomas), Phys. Rev. D 88, 094505 (2013) arXiv:1309.2608 Hadron Spectrum Collaboration (L. Liu, G. Moir, M. Peardon, S.M. Ryan, C.E. Thomas, P. Vilaseca, J.J. Dudek, R.G. Edwards, B. Joo, D.G. Richards), JHEP 07, 126 (2012) arXiv:1204.5425 J.J. Dudek, R.G. Edwards, Phys. Rev. D 85, 054016 (2012) arXiv:1201.2349 J.J. Dudek, Phys. Rev. D 84, 074023 (2011) arXiv:1106.5515 M. Luscher, Commun. Math. Phys. 105, 153 (1986) M. Lüscher, Nucl. Phys. B 354, 531 (1991) K. Rummukainen, S.A. Gottlieb, Nucl. Phys. B 450, 397 (1995) arXiv:hep-lat/9503028 X. Feng, X. Li, C. Liu, Phys. Rev. D 70, 014505 (2004) arXiv:hep-lat/0404001 S. He, X. Feng, C. Liu, JHEP 07, 011 (2005) arXiv:hep-lat/0504019 P.F. Bedaque, Phys. Lett. B 593, 82 (2004) arXiv:nucl-th/0402051 C. Liu, X. Feng, S. He, Int. J. Mod. Phys. A 21, 847 (2006) arXiv:hep-lat/0508022 C.h. Kim, C.T. Sachrajda, S.R. Sharpe, Nucl. Phys. B 727, 218 (2005) arXiv:hep-lat/0507006 N.H. Christ, C. Kim, T. Yamazaki, Phys. Rev. D 72, 114506 (2005) arXiv:hep-lat/0507009 M. Lage, U.G. Meissner, A. Rusetsky, Phys. Lett. B 681, 439 (2009) arXiv:0905.0069 V. Bernard, M. Lage, U.G. Meissner, A. Rusetsky, JHEP 01, 019 (2011) arXiv:1010.6018 Z. Fu, Phys. Rev. D 85, 014506 (2012) arXiv:1110.0319 M. Gockeler, R. Horsley, M. Lage, U.G. Meissner, P.E.L. Rakow, A. Rusetsky, G. Schierholz, J.M. Zanotti, Phys. Rev. D 86, 094513 (2012) arXiv:1206.4141 L. Leskovec, S. Prelovsek, Phys. Rev. D 85, 114507 (2012) arXiv:1202.2145 R.A. Briceno, Z. Davoudi, Phys. Rev. D 88, 094507 (2013) arXiv:1204.1110 M.T. Hansen, S.R. Sharpe, Phys. Rev. D 86, 016007 (2012) arXiv:1204.0826 P. Guo, J. Dudek, R. Edwards, A.P. Szczepaniak, Phys. Rev. D 88, 014501 (2013) arXiv:1211.0929 N. Li, C. Liu, Phys. Rev. D 87, 014502 (2013) arXiv:1209.2201 R.A. Briceño, Z. Davoudi, T.C. Luu, M.J. Savage, Phys. Rev. D 89, 074509 (2014) arXiv:1311.7686 R.A. Briceño, Phys. Rev. D 89, 074507 (2014) arXiv:1401.3312 CP-PACS Collaboration (S. Aoki et al.), Phys. Rev. D 76, 094506 (2007) arXiv:0708.3705 X. Feng, K. Jansen, D.B. Renner, Phys. Rev. D 83, 094505 (2011) arXiv:1011.5288 C.B. Lang, D. Mohler, S. Prelovsek, M. Vidmar, Phys. Rev. D 84, 054503 (2011) Phys. Rev. D 89 CS Collaboration (S. Aoki et al.), Phys. Rev. D 84, 094505 (2011) arXiv:1106.5365 Hadron Spectrum Collaboration (J.J. Dudek, R.G. Edwards, C.E. Thomas), Phys. Rev. D 87, 034505 (2013) Phys. Rev. D 90 C. Pelissier, A. Alexandru, Phys. Rev. D 87, 014503 (2013) arXiv:1211.0092 D.J. Wilson, R.A. Briceño, J.J. Dudek, R.G. Edwards, C.E. Thomas, Phys. Rev. D 92, 094502 (2015) arXiv:1507.02599 RQCD Collaboration (G.S. Bali, S. Collins, A. Cox, G. Donald, M. Göckeler, C.B. Lang, A. Schäfer), Phys. Rev. D 93, 054509 (2016) arXiv:1512.08678 J. Bulava, B. Fahy, B. Hörz, K.J. Juge, C. Morningstar, C.H. Wong, Nucl. Phys. B 910, 842 (2016) arXiv:1604.05593 D. Guo, A. Alexandru, R. Molina, M. Döring, Phys. Rev. D 94, 034501 (2016) arXiv:1605.03993 R.A. Briceño, J.J. Dudek, R.G. Edwards, D.J. Wilson, Phys. Rev. Lett. 118, 022002 (2017) arXiv:1607.05900 D. Guo, A. Alexandru, R. Molina, M. Mai, M. Döring, Phys. Rev. D 98, 014507 (2018) arXiv:1803.02897 C.B. Lang, L. Leskovec, D. Mohler, S. Prelovsek, Phys. Rev. D 86, 054508 (2012) arXiv:1207.3204 Z. Fu, K. Fu, Phys. Rev. D 86, 094507 (2012) arXiv:1209.0350 S. Prelovsek, L. Leskovec, C.B. Lang, D. Mohler, Phys. Rev. D 88, 054508 (2013) arXiv:1307.0736 R. Brett, J. Bulava, J. Fallica, A. Hanlon, B. Hörz, C. Morningstar, Nucl. Phys. B 932, 29 (2018) arXiv:1802.03100 C.W. Andersen, J. Bulava, B. Hörz, C. Morningstar, Phys. Rev. D 97, 014506 (2018) arXiv:1710.01557 M. Luscher, U. Wolff, Nucl. Phys. B 339, 222 (1990) X. Li, C. Liu, Phys. Lett. B 587, 100 (2004) arXiv:hep-lat/0311035 W. Detmold, M.J. Savage, Nucl. Phys. A 743, 170 (2004) arXiv:hep-lat/0403005 D. Mohler, S. Prelovsek, R. Woloshyn, Phys. Rev. D 87, 034501 (2013) arXiv:1208.4059 S. Prelovsek, L. Leskovec, Phys. Rev. Lett. 111, 192001 (2013) arXiv:1307.5172 C.B. Lang, L. Leskovec, D. Mohler, S. Prelovsek, R.M. Woloshyn, Phys. Rev. D 90, 034510 (2014) arXiv:1403.8103 C.B. Lang, L. Leskovec, D. Mohler, S. Prelovsek, JHEP 09, 089 (2015) arXiv:1503.05363 C.B. Lang, D. Mohler, S. Prelovsek, Phys. Rev. D 94, 074509 (2016) arXiv:1607.03185 Hadron Spectrum Collaboration (J.J. Dudek, R.G. Edwards, C.E. Thomas, D.J. Wilson), Phys. Rev. Lett. 113, 182001 (2014) arXiv:1406.4158 D.J. Wilson, J.J. Dudek, R.G. Edwards, C.E. Thomas, Phys. Rev. D 91, 054008 (2015) arXiv:1411.2004 G. Moir, M. Peardon, S.M. Ryan, C.E. Thomas, D.J. Wilson, JHEP 10, 011 (2016) arXiv:1607.07093 Hadron Spectrum Collaboration (J.J. Dudek, R.G. Edwards, D.J. Wilson), Phys. Rev. D 93, 094506 (2016) arXiv:1602.05122 R.A. Briceño, J.J. Dudek, R.G. Edwards, D.J. Wilson, Phys. Rev. D 97, 054513 (2018) arXiv:1708.06667 M. Doring, U.G. Meissner, E. Oset, A. Rusetsky, Eur. Phys. J. A 47, 139 (2011) arXiv:1107.3988 M. Albaladejo, P. Fernandez-Soler, F.K. Guo, J. Nieves, Phys. Lett. B 767, 465 (2017) arXiv:1610.06727 L. Lellouch, M. Lüscher, Commun. Math. Phys. 219, 31 (2001) arXiv:hep-lat/0003023 C.J.D. Lin, G. Martinelli, C.T. Sachrajda, M. Testa, Nucl. Phys. B 619, 467 (2001) arXiv:hep-lat/0104006 V. Bernard, D. Hoja, U.G. Meissner, A. Rusetsky, JHEP 09, 023 (2012) arXiv:1205.4642 A. Agadjanov, V. Bernard, U.G. Meißner, A. Rusetsky, Nucl. Phys. B 886, 1199 (2014) arXiv:1405.3476 R.A. Briceño, M.T. Hansen, A. Walker-Loud, Phys. Rev. D 91, 034501 (2015) arXiv:1406.5965 R.A. Briceño, M.T. Hansen, Phys. Rev. D 92, 074509 (2015) arXiv:1502.04314 R.A. Briceño, M.T. Hansen, Phys. Rev. D 94, 013008 (2016) arXiv:1509.08507 A. Agadjanov, V. Bernard, U.G. Meißner, A. Rusetsky, Nucl. Phys. B 910, 387 (2016) arXiv:1605.03386 R.A. Briceño, J.J. Dudek, R.G. Edwards, C.J. Shultz, C.E. Thomas, D.J. Wilson, Phys. Rev. Lett. 115, 242001 (2015) arXiv:1507.06622 R.A. Briceño, J.J. Dudek, R.G. Edwards, C.J. Shultz, C.E. Thomas, D.J. Wilson, Phys. Rev. D 93, 114508 (2016) arXiv:1604.03530 C. Alexandrou, L. Leskovec, S. Meinel, J. Negele, S. Paul, M. Petschlies, A. Pochinsky, G. Rendon, S. Syritsyn, Phys. Rev. D 98, 074502 (2018) arXiv:1807.08357 X. Feng, S. Aoki, S. Hashimoto, T. Kaneko, Phys. Rev. D 91, 054504 (2015) arXiv:1412.6319 Hadron Spectrum Collaboration (M. Peardon, J. Bulava, J. Foley, C. Morningstar, J. Dudek, R.G. Edwards, B. Joo, H.W. Lin, D.G. Richards, K.J. Juge), Phys. Rev. D 80, 054506 (2009) arXiv:0905.2160 C. Morningstar, J. Bulava, J. Foley, K.J. Juge, D. Lenkner, M. Peardon, C.H. Wong, Phys. Rev. D 83, 114505 (2011) arXiv:1104.3870 A. Woss, C.E. Thomas, J.J. Dudek, R.G. Edwards, D.J. Wilson, JHEP 07, 043 (2018) arXiv:1802.05580 K. Polejaeva, A. Rusetsky, Eur. Phys. J. A 48, 67 (2012) arXiv:1203.1241 M.T. Hansen, S.R. Sharpe, Phys. Rev. D 92, 114509 (2015) arXiv:1504.04248 M.T. Hansen, S.R. Sharpe, Phys. Rev. D 90, 116003 (2014) arXiv:1408.5933 R.A. Briceño, M.T. Hansen, S.R. Sharpe, Phys. Rev. D 99, 014516 (2019) arXiv:1810.01429 M. Döring, H.W. Hammer, M. Mai, J.Y. Pang, A. Rusetsky, J. Wu, Phys. Rev. D 97, 114508 (2018) arXiv:1802.03362 M. Mai, M. Döring, Eur. Phys. J. A 53, 240 (2017) arXiv:1709.08222 M. Mai, M. Doring, Phys. Rev. Lett. 122, 062503 (2019) arXiv:1807.04746 H.W. Hammer, J.Y. Pang, A. Rusetsky, JHEP 10, 115 (2017) arXiv:1707.02176 H.W. Hammer, J.Y. Pang, A. Rusetsky, JHEP 09, 109 (2017) arXiv:1706.07700 Belle Collaboration (S.K. Choi et al.), Phys. Rev. Lett. 91, 262001 (2003) arXiv:hep-ex/0309032 F.K. Guo, U.G. Meißner, W. Wang, Z. Yang, Phys. Rev. D 92, 071502 (2015) arXiv:1507.04950 A.P. Szczepaniak, Phys. Lett. B 747, 410 (2015) arXiv:1501.01691 Hadron Spectrum Collaboration (G.K.C. Cheung, C.E. Thomas, J.J. Dudek, R.G. Edwards), JHEP 11, 033 (2017) arXiv:1709.01417 S. Prelovsek, C.B. Lang, L. Leskovec, D. Mohler, Phys. Rev. D 91, 014504 (2015) arXiv:1405.7623 A. Francis, R.J. Hudspith, R. Lewis, K. Maltman, Phys. Rev. Lett. 118, 142001 (2017) arXiv:1607.05214 P. Junnarkar, N. Mathur, M. Padmanath, Phys. Rev. D 99, 034507 (2019) arXiv:1810.12285 L. Leskovec, S. Meinel, M. Pflaumer, M. Wagner, Phys. Rev. D 100, 014503 (2019) arXiv:1904.04197 C. Hughes, E. Eichten, C.T.H. Davies, Phys. Rev. D 97, 054505 (2018) arXiv:1710.03236 A. Francis, R.J. Hudspith, R. Lewis, K. Maltman, Phys. Rev. D 99, 054505 (2019) arXiv:1810.10550 J.G. Korner, M. Kramer, D. Pirjol, Prog. Part. Nucl. Phys. 33, 787 (1994) arXiv:hep-ph/9406359 A.V. Manohar, M.B. Wise, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 10, 1 (2000) J. Carlson, L. Heller, J.A. Tjon, Phys. Rev. D 37, 744 (1988) M.J. Savage, M.B. Wise, Phys. Lett. B 248, 177 (1990) A.V. Manohar, M.B. Wise, Nucl. Phys. B 399, 17 (1993) arXiv:hep-ph/9212236 N. Brambilla, A. Vairo, T. Rosch, Phys. Rev. D 72, 034021 (2005) arXiv:hep-ph/0506065 E.J. Eichten, C. Quigg, Phys. Rev. Lett. 119, 202002 (2017) arXiv:1707.09575 CMS Collaboration (S. Chatrchyan et al.), Phys. Rev. Lett. 108, 252002 (2012) arXiv:1204.5955 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 109, 172003 (2012) arXiv:1205.3452 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 114, 062004 (2015) arXiv:1411.4849 LHCb Collaboration (R. Aaij et al.), JHEP 05, 161 (2016) arXiv:1604.03896 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 119, 112001 (2017) arXiv:1707.01621 LHCb Collaboration (R. Aaij et al.), JHEP 05, 030 (2017) arXiv:1701.07873 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 118, 182001 (2017) arXiv:1703.04639 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 121, 072002 (2018) arXiv:1805.09418 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 122, 012001 (2019) arXiv:1809.07752 Z.S. Brown, W. Detmold, S. Meinel, K. Orginos, Phys. Rev. D 90, 094507 (2014) arXiv:1409.0497 M. Padmanath, R.G. Edwards, N. Mathur, M. Peardon, Phys. Rev. D 91, 094502 (2015) arXiv:1502.01845 P. Perez-Rubio, S. Collins, G.S. Bali, Phys. Rev. D 92, 034504 (2015) arXiv:1503.08440 K.U. Can, G. Erkol, M. Oka, T.T. Takahashi, Phys. Rev. D 92, 114515 (2015) arXiv:1508.03048 C. Alexandrou, K. Hadjiyiannakou, C. Kallidonis, Phys. Rev. D 94, 034502 (2016) arXiv:1606.01650 H. Bahtiyar, K.U. Can, G. Erkol, M. Oka, T.T. Takahashi, Phys. Rev. D 98, 114505 (2018) arXiv:1807.06795 R.M. Woloshyn, Eur. Phys. J. A 52, 273 (2016) arXiv:1605.09043 C. Alexandrou, C. Kallidonis, Phys. Rev. D 96, 034511 (2017) arXiv:1704.02647 N. Mathur, M. Padmanath, S. Mondal, Phys. Rev. Lett. 121, 202002 (2018) arXiv:1806.04151 N. Mathur, M. Padmanath, Phys. Rev. D 99, 031501 (2019) arXiv:1807.00174 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 115, 072001 (2015) arXiv:1507.03414 LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 122, 222001 (2019) arXiv:1904.03947 K. Yokokawa, S. Sasaki, T. Hatsuda, A. Hayashigaki, Phys. Rev. D 74, 034504 (2006) arXiv:hep-lat/0605009 L. Liu, H.W. Lin, K. Orginos, PoS LATTICE2008, 112 (2008) arXiv:0810.5412 T. Kawanai, S. Sasaki, Phys. Rev. D 82, 091501 (2010) arXiv:1009.3332 S.R. Beane, E. Chang, S.D. Cohen, W. Detmold, H.W. Lin, K. Orginos, A. Parreño, M.J. Savage, Phys. Rev. D 91, 114503 (2015) arXiv:1410.7069 U. Skerbis, S. Prelovsek, Phys. Rev. D 99, 094505 (2019) arXiv:1811.02285 PACS-CS Collaboration (T. Yamazaki, Y. Kuramashi, A. Ukawa), Phys. Rev. D 81, 111504 (2010) arXiv:0912.1383 NPLQCD Collaboration (S.R. Beane, P.F. Bedaque, T.C. Luu, K. Orginos, E. Pallante, A. Parreno, M.J. Savage), Nucl. Phys. A 794, 62 (2007) arXiv:hep-lat/0612026 S.R. Beane, P.F. Bedaque, K. Orginos, M.J. Savage, Phys. Rev. Lett. 97, 012001 (2006) arXiv:hep-lat/0602010 S.R. Beane, W. Detmold, T.C. Luu, K. Orginos, A. Parreno, M.J. Savage, A. Torok, A. Walker-Loud, Phys. Rev. D 80, 074501 (2009) arXiv:0905.0466 S.R. Beane, W. Detmold, T.C. Luu, K. Orginos, A. Parreno, M.J. Savage, A. Torok, A. Walker-Loud, Phys. Rev. D 79, 114502 (2009) arXiv:0903.2990 NPLQCD Collaboration (S.R. Beane et al.), Phys. Rev. Lett. 106, 162001 (2011) arXiv:1012.3812 HAL QCD Collaboration (T. Inoue, N. Ishii, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, K. Murano, H. Nemura, K. Sasaki), Phys. Rev. Lett. 106, 162002 (2011) arXiv:1012.5928 S.R. Beane et al., Mod. Phys. Lett. A 26, 2587 (2011) arXiv:1103.2821 NPLQCD Collaboration (S.R. Beane, E. Chang, W. Detmold, H.W. Lin, T.C. Luu, K. Orginos, A. Parreno, M.J. Savage, A. Torok, A. Walker-Loud), Phys. Rev. D 85, 054511 (2012) arXiv:1109.2889 E. Berkowitz, T. Kurth, A. Nicholson, B. Joo, E. Rinaldi, M. Strother, P.M. Vranas, A. Walker-Loud, Phys. Lett. B 765, 285 (2017) arXiv:1508.00886 A. Francis, J.R. Green, P.M. Junnarkar, C. Miao, T.D. Rae, H. Wittig, Phys. Rev. D 99, 074505 (2019) arXiv:1805.03966 M.L. Wagman, F. Winter, E. Chang, Z. Davoudi, W. Detmold, K. Orginos, M.J. Savage, P.E. Shanahan, Phys. Rev. D 96, 114510 (2017) arXiv:1706.06550 N. Ishii, S. Aoki, T. Hatsuda, Phys. Rev. Lett. 99, 022001 (2007) arXiv:nucl-th/0611096 W. Detmold, K. Orginos, M.J. Savage, Phys. Rev. D 76, 114503 (2007) arXiv:hep-lat/0703009 M.C. Birse, Eur. Phys. J. A 53, 223 (2017) arXiv:1208.4807 T. Yamazaki, Y. Kuramashi, Phys. Rev. D 98, 038502 (2018) arXiv:1808.06299 T. Yamazaki, Y. Kuramashi, Phys. Rev. D 96, 114511 (2017) arXiv:1709.09779 Y. Namekawa, T. Yamazaki, Phys. Rev. D 98, 011501 (2018) arXiv:1712.10141 HAL QCD Collaboration (D. Kawai, S. Aoki, T. Doi, Y. Ikeda, T. Inoue, T. Iritani, N. Ishii, T. Miyamoto, H. Nemura, K. Sasaki), Prog. Theor. Exp. Phys. 2018, 043B04 (2018) arXiv:1711.01883 S.R. Beane, W. Detmold, T.C. Luu, K. Orginos, M.J. Savage, A. Torok, Phys. Rev. Lett. 100, 082004 (2008) arXiv:0710.1827 W. Detmold, K. Orginos, M.J. Savage, A. Walker-Loud, Phys. Rev. D 78, 054514 (2008) arXiv:0807.1856 W. Detmold, B. Smigielski, Phys. Rev. D 84, 014508 (2011) arXiv:1103.4362 NPLQCD Collaboration (S.R. Beane, E. Chang, S.D. Cohen, W. Detmold, H.W. Lin, T.C. Luu, K. Orginos, A. Parreno, M.J. Savage, A. Walker-Loud), Phys. Rev. D 87, 034506 (2013) arXiv:1206.5219 T. Yamazaki, K.i. Ishikawa, Y. Kuramashi, A. Ukawa, Phys. Rev. D 86, 074514 (2012) arXiv:1207.4277 T. Yamazaki, K.i. Ishikawa, Y. Kuramashi, A. Ukawa, Phys. Rev. D 92, 014501 (2015) arXiv:1502.04182 HAL QCD Collaboration (T. Iritani, S. Aoki, T. Doi, S. Gongyo, T. Hatsuda, Y. Ikeda, T. Inoue, N. Ishii, H. Nemura, K. Sasaki), Phys. Rev. D 99, 014514 (2019) arXiv:1805.02365 S.R. Beane, arXiv:1705.09239 (2017) PACS Collaboration (T. Yamazaki, K.i. Ishikawa, Y. Kuramashi), EPJ Web of Conferences 175, 05019 (2018) arXiv:1710.08066 G.P. Lepage, The analysis of algorithms for lattice field theory, lectures given at TASI’89 Summer School, Boulder, CO, Jun 4--30, 1989 G. Parisi, Phys. Rep. 103, 203 (1984) H.W. Hamber, E. Marinari, G. Parisi, C. Rebbi, Nucl. Phys. B 225, 475 (1983) S.R. Beane, W. Detmold, K. Orginos, M.J. Savage, J. Phys. G 42, 034022 (2015) arXiv:1410.2937 M.L. Wagman, PhD Thesis, Washington U., Seattle, arXiv:1711.00062 (2017) M.L. Wagman, M.J. Savage, arXiv:1704.07356 (2017) M.L. Wagman, M.J. Savage, Phys. Rev. D 96, 114508 (2017) arXiv:1611.07643 W. Detmold, G. Kanwar, M.L. Wagman, Phys. Rev. D 98, 074511 (2018) arXiv:1806.01832 W. Detmold, M.G. Endres, Phys. Rev. D 90, 034503 (2014) arXiv:1404.6816 T. Doi, M.G. Endres, Comput. Phys. Commun. 184, 117 (2013) arXiv:1205.0585 J. Günther, B.C. Toth, L. Varnhorst, Phys. Rev. D 87, 094513 (2013) arXiv:1301.4895 W. Detmold, M.J. Savage, Phys. Rev. D 82, 014511 (2010) arXiv:1001.2768 W. Detmold, K. Orginos, Phys. Rev. D 87, 114512 (2013) arXiv:1207.1452 K. Orginos, A. Parreno, M.J. Savage, S.R. Beane, E. Chang, W. Detmold, Phys. Rev. D 92, 114512 (2015) arXiv:1508.07583 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, Phys. Rev. Lett. 110, 112502 (2013) arXiv:1212.4181 J.C. Berengut, E. Epelbaum, V.V. Flambaum, C. Hanhart, U.G. Meissner, J. Nebreda, J.R. Pelaez, Phys. Rev. D 87, 085018 (2013) arXiv:1301.1738 M.E. Carrillo-Serrano, I.C. Cloët, K. Tsushima, A.W. Thomas, I.R. Afnan, Phys. Rev. C 87, 015801 (2013) arXiv:1208.3009 W. Detmold, M. McCullough, A. Pochinsky, Phys. Rev. D 90, 115013 (2014) arXiv:1406.2276 W. Detmold, M. McCullough, A. Pochinsky, Phys. Rev. D 90, 114506 (2014) arXiv:1406.4116 V. Ayyar, T. DeGrand, M. Golterman, D.C. Hackett, W.I. Jay, E.T. Neil, Y. Shamir, B. Svetitsky, Phys. Rev. D 97, 074505 (2018) arXiv:1710.00806 European Muon Collaboration (J.J. Aubert et al.), Phys. Lett. B 123, 275 (1983) S.R. Beane, E. Chang, S. Cohen, W. Detmold, H.W. Lin, K. Orginos, A. Parreno, M.J. Savage, B.C. Tiburzi, Phys. Rev. Lett. 113, 252001 (2014) arXiv:1409.3556 NPLQCD Collaboration (S.R. Beane, E. Chang, W. Detmold, K. Orginos, A. Parreño, M.J. Savage, B.C. Tiburzi), Phys. Rev. Lett. 115, 132001 (2015) arXiv:1505.02422 W. Detmold, K. Orginos, A. Parreno, M.J. Savage, B.C. Tiburzi, S.R. Beane, E. Chang, Phys. Rev. Lett. 116, 112301 (2016) arXiv:1508.05884 M.J. Savage, P.E. Shanahan, B.C. Tiburzi, M.L. Wagman, F. Winter, S.R. Beane, E. Chang, Z. Davoudi, W. Detmold, K. Orginos, Phys. Rev. Lett. 119, 062002 (2017) arXiv:1610.04545 NPLQCD Collaboration (E. Chang, Z. Davoudi, W. Detmold, A.S. Gambhir, K. Orginos, M.J. Savage, P.E. Shanahan, M.L. Wagman, F. Winter), Phys. Rev. Lett. 120, 152002 (2018) arXiv:1712.03221 T. Marrodán Undagoitia, L. Rauch, J. Phys. G 43, 013001 (2016) arXiv:1509.08767 C. Delaunay, R. Ozeri, G. Perez, Y. Soreq, Phys. Rev. D 96, 093001 (2017) arXiv:1601.05087 C. Delaunay, C. Frugiuele, E. Fuchs, Y. Soreq, Phys. Rev. D 96, 115002 (2017) arXiv:1709.02817 J. Engel, M.J. Ramsey-Musolf, U. van Kolck, Prog. Part. Nucl. Phys. 71, 21 (2013) arXiv:1303.2371 N. Yamanaka, Int. J. Mod. Phys. E 26, 1730002 (2017) arXiv:1609.04759 T. Chupp, P. Fierlinger, M. Ramsey-Musolf, J. Singh, Rev. Mod. Phys. 91, 015001 (2019) arXiv:1710.02504 R.J. Hill, EPJ Web of Conferences 137, 01023 (2017) arXiv:1702.01189 J.W. Chen, W. Detmold, Phys. Lett. B 625, 165 (2005) arXiv:hep-ph/0412119 J.W. Chen, W. Detmold, J.E. Lynn, A. Schwenk, Phys. Rev. Lett. 119, 262502 (2017) arXiv:1607.03065 O. Hen, G.A. Miller, E. Piasetzky, L.B. Weinstein, Rev. Mod. Phys. 89, 045002 (2017) arXiv:1611.09748 J.M. Lattimer, M. Prakash, Astrophys. J. 550, 426 (2001) arXiv:astro-ph/0002232 S.R. Beane, E. Chang, S.D. Cohen, W. Detmold, H.W. Lin, T.C. Luu, K. Orginos, A. Parreno, M.J. Savage, A. Walker-Loud, Phys. Rev. Lett. 109, 172001 (2012) arXiv:1204.3606 LIGO Scientific, Virgo Collaborations (B. Abbott et al.), Phys. Rev. Lett. 119, 161101 (2017) arXiv:1710.05832 LIGO Scientific, Virgo, Fermi GBM, INTEGRAL, IceCube, AstroSat Cadmium Zinc Telluride Imager Team, IPN, Insight-Hxmt, ANTARES, Swift, AGILE Team, 1M2H Team, Dark Energy Camera GW-EM, DES, DLT40, GRAWITA, Fermi-LAT, ATCA, ASKAP, Las Cumbres Observatory Group, OzGrav, DWF (Deeper Wider Faster Program), AST3, CAASTRO, VINROUGE, MASTER, J-GEM, GROWTH, JAGWAR, CaltechNRAO, TTU-NRAO, NuSTAR, Pan-STARRS, MAXI Team, TZAC Consortium, KU, Nordic Optical Telescope, ePESSTO, GROND, Texas Tech University, SALT Group, TOROS, BOOTES, MWA, CALET, IKI-GW Follow-up, H.E.S.S., LOFAR, LWA, HAWC, Pierre Auger, ALMA, Euro VLBI Team, Pi of Sky, Chandra Team at McGill University, DFN, ATLAS Telescopes, High Time Resolution Universe Survey, RIMAS, RATIR, SKA South Africa/MeerKAT Collaborations (B.P. Abbott et al.), Astrophys. J. 848, L12 (2017) arXiv:1710.05833 F. Ozel, D. Psaltis, Z. Arzoumanian, S. Morsink, M. Baubock, Astrophys. J. 832, 92 (2016) arXiv:1512.03067 S.R. Beane, M.J. Savage, Phys. Rev. D 90, 074511 (2014) arXiv:1407.4846 S.R. Beane, W. Detmold, M.J. Savage, Phys. Rev. D 76, 074507 (2007) arXiv:0707.1670 W. Detmold, M.J. Savage, Phys. Rev. D 77, 057502 (2008) arXiv:0801.0763 S. Tan, Phys. Rev. A 78, 013636 (2008) arXiv:0709.2530 S. Kreuzer, H.W. Hammer, Phys. Lett. B 694, 424 (2011) arXiv:1008.4499 R.A. Briceño, Z. Davoudi, Phys. Rev. D 87, 094507 (2013) arXiv:1212.3398 W. Detmold, PoS ConfinementX, 016 (2012) W. Detmold, Eur. Phys. J. A 49, 83 (2013) W. Detmold, Lect. Notes Phys. 889, 153 (2015) J. Kirscher, Int. J. Mod. Phys. E 25, 1641001 (2016) arXiv:1509.07697 Z. Davoudi, EPJ Web of Conferences 175, 01022 (2018) arXiv:1711.02020 M.J. Savage, PoS LATTICE2016, 021 (2016) arXiv:1611.02078 N. Barnea, L. Contessi, D. Gazit, F. Pederiva, U. van Kolck, Phys. Rev. Lett. 114, 052501 (2015) arXiv:1311.4966 A. Bansal, S. Binder, A. Ekström, G. Hagen, G.R. Jansen, T. Papenbrock, Phys. Rev. C 98, 054301 (2018) arXiv:1712.10246 L. Contessi, A. Lovato, F. Pederiva, A. Roggero, J. Kirscher, U. van Kolck, Phys. Lett. B 772, 839 (2017) arXiv:1701.06516 S. Gandolfi, J. Carlson, A. Roggero, J. Lynn, S. Reddy, Phys. Lett. B 785, 232 (2018) arXiv:1712.10236 J. Kirscher, E. Pazy, J. Drachman, N. Barnea, Phys. Rev. C 96, 024001 (2017) arXiv:1702.07268 T.A. Lähde, U.G. Meißner, Lect. Notes Phys. 957, 1 (2019) T.A. Lähde, U.G. Meißner, E. Epelbaum, arXiv:1906.00607 (2019) A. Nicholson et al., Phys. Rev. Lett. 121, 172501 (2018) arXiv:1805.02634 X. Feng, L.C. Jin, X.Y. Tuo, S.C. Xia, Phys. Rev. Lett. 122, 022001 (2019) arXiv:1809.10511 W. Detmold, D. Murphy, PoS LATTICE2018, 262 (2019) arXiv:1811.05554 Intensity Frontier Charged Lepton Working Group (J. Albrecht), Working Group Report: Charged Leptons, in Proceedings, 2013 Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi (CSS2013): Minneapolis, MN, USA, July 29-August 6, 2013 (2013) arXiv:1311.5278 S. Dell’Oro, S. Marcocci, M. Viel, F. Vissani, Adv. High Energy Phys. 2016, 2162659 (2016) arXiv:1601.07512 J. Engel, J. Menendez, Rep. Prog. Phys. 80, 046301 (2017) arXiv:1610.06548 A. Antognini et al., Science 339, 417 (2013) M.A. Belushkin, H.W. Hammer, U.G. Meissner, Phys. Rev. C 75, 035202 (2007) arXiv:hep-ph/0608337 M. Hoferichter, B. Kubis, J. Ruiz de Elvira, H.W. Hammer, U.G. Meißner, Eur. Phys. J. A 52, 331 (2016) arXiv:1609.06722 J.M. Alarcón, C. Weiss, Phys. Lett. B 784, 373 (2018) arXiv:1803.09748 C. Bouchard, C.C. Chang, K. Orginos, D. Richards, PoS LATTICE2016, 170 (2016) arXiv:1610.02354 M. Burkardt, Int. J. Mod. Phys. A 18, 173 (2003) arXiv:hep-ph/0207047 G.A. Miller, Phys. Rev. Lett. 99, 112001 (2007) arXiv:0705.2409 C.E. Carlson, M. Vanderhaeghen, Phys. Rev. Lett. 100, 032004 (2008) arXiv:0710.0835 R. Hofstadter, R.W. McAllister, Phys. Rev. 98, 217 (1955) E.E. Chambers, R. Hofstadter, Phys. Rev. 103, 1454 (1956) G.S. Bali, B. Lang, B.U. Musch, A. Schäfer, Phys. Rev. D 93, 094515 (2016) arXiv:1602.05525 S. Syritsyn, A.S. Gambhir, B. Musch, K. Orginos, PoS LATTICE2016, 176 (2017) A. Baroni, R.A. Briceño, M.T. Hansen, F.G. Ortega-Gama, Phys. Rev. D 100, 034511 (2019) arXiv:1812.10504 C. Michael, Nucl. Phys. B 259, 58 (1985) P. Vachaspati, W. Detmold, PoS LATTICE2014, 041 (2014) arXiv:1411.3691