Abstract
Baryon chiral perturbation theory (BChPT), as an effective field theory of low-energy quantum chromodynamics (QCD), has played and is still playing an important role in our understanding of non-perturbative strong-interaction phenomena. In the past two decades, inspired by the rapid progress in lattice QCD simulations and the new experimental campaign to study the strangeness sector of low-energy QCD, many efforts have been made to develop a fully covariant BChPT and to test its validity in all scenarios. These new endeavours have not only deepened our understanding of some long-standing problems, such as the power-counting-breaking problem and the convergence problem, but also resulted in theoretical tools that can be confidently applied to make robust predictions. Particularly, the manifestly covariant BChPT supplemented with the extended-on-mass-shell (EOMS) renormalization scheme has been shown to satisfy all analyticity and symmetry constraints and converge relatively faster compared to its non-relativistic and infrared counterparts. In this article, we provide a brief review of the fully covariant BChPT and its latest applications in the u, d, and s three-flavor sector.
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References
D. Gross and F. Wilczek, Phys. Rev. Lett., 1973, 30(26): 1343
H. D. Politzer, Phys. Rev. Lett., 1973, 30(26): 1346
K. G. Wilson, Phys. Rev. D, 1974, 10(8): 2445
J. Donoghue, E. Golowich, and B. R. Holstein, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol., 1992, 2: 1
S. Weinberg, Physica A, 1979, 96(1–2): 327
J. Gasser and H. Leutwyler, Ann. Phys., 1984, 158(1): 142
J. Gasser and H. Leutwyler, Nucl. Phys. B, 1985, 250(1–4): 465
J. Gasser, M. Sainio, and A. Svarc, Nucl. Phys. B, 1988, 307(4): 779
E. E. Jenkins and A. V. Manohar, Phys. Lett. B, 1991, 255(4): 558
V. Bernard, N. Kaiser, and U. G. Meissner, Int. J. Mod. Phys. E, 1995, 04(02): 193, arXiv: hep-ph/9501384
M. E. Luke and A. V. Manohar, Phys. Lett. B, 1992, 286(3–4): 348, arXiv: hep-ph/9205228
G. Ecker and M. Mojzis, Phys. Lett. B, 1996, 365(1–4): 312, arXiv: hep-ph/9508204
G. Ecker and M. Mojzis, Phys. Lett. B, 1997, 410(2–4): 266, arXiv: hep-ph/9705216
H. B. Tang, arXiv: hep-ph/9607436, 1996
T. Becher and H. Leutwyler, Eur. Phys. J. C, 1999, 9: 643, arXiv: hep-ph/9901384
T. Fuchs, J. Gegelia, G. Japaridze, and S. Scherer, Phys. Rev. D, 2003, 68(5): 056005, arXiv: hep-ph/0302117
V. Pascalutsa, B. R. Holstein, and M. Vanderhaeghen, Phys. Lett. B, 2004, 600(3–4): 239, arXiv: hep-ph/0407313
L. S. Geng, J. Martin Camalich, L. Alvarez-Ruso, and M. Vicente Vacas, Phys. Rev. Lett., 2008, 101(22): 222002, arXiv: 0805.1419 [hep-ph]
J. Martin Camalich, L. S. Geng, and M. Vicente Vacas, Phys. Rev. D, 2010, 82(7): 074504, arXiv: 1003.1929 [hep-lat]
L. S. Geng, M. Altenbuchinger, and W. Weise, Phys. Lett. B, 2011, 696(4): 390, arXiv: 1012.0666 [hep-ph]
P. Hagler, Phys. Rep., 2010, 490(3—5): 49, arXiv: 0912.5483 [hep-lat]
A. Bazavov, D. Toussaint, C. Bernard, J. Laiho, C. DeTar, L. Levkova, M. B. Oktay, S. Gottlieb, U. M. Heller, J. E. Hetrick, P. B. Mackenzie, R. Sugar, and R. S. Van de Water, Rev. Mod. Phys., 2010, 82(2): 1349, arXiv: 0903.3598 [hep-lat]
G. Colangelo, S. Durr, A. Juttner, L. Lellouch, H. Leutwyler, V. Lubicz, S. Necco, C. T. Sachrajda, S. Simula, A. Vladikas, U. Wenger, and H. Wittig, Eur. Phys. J. C, 2011, 71(7): 1695, arXiv: 1011.4408 [hep-lat]
S. Beane, W. Detmold, K. Orginos, and M. Savage, Prog. Part. Nucl. Phys., 2011, 66(1): 1, arXiv: 1004.2935 [hep-lat]
S. Aoki, et al. [HAL QCD Collaboration], Prog. Theor. Exp. Phys., 2012, 2012(1): 01A102, arXiv: 1206.5088 [hep-lat]
Z. Fodor and C. Hoelbling, Rev. Mod. Phys., 2012, 84(2): 449, arXiv: 1203.4789 [hep-lat]
S. Durr, arXiv: 1301.1914 [hep-lat], 2013
S. Durr, Z. Fodor, C. Hoelbling, S. Katz, S. Krieg, et al., J. High Energy Phys., 2011, 1108: 148, arXiv: 1011.2711 [hep-lat]
S. Durr, Z. Fodor, C. Hoelbling, S. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, and G. Vulvert, Phys. Lett. B, 2011, 701(2): 265, arXiv: 1011.2403 [hep-lat]
A. Bazavov, et al. [MILC Collaboration], Phys. Rev. D, 2013, 87: 054505, arXiv: 1212.4768 [hep-lat]
M. Golterman, arXiv: 0912.4042 [hep-lat], 2009
X. L. Ren, L. S. Geng, J. M. Camalich, J. Meng, and H. Toki, J. High Energy Phys., 2012, 1212: 073, arXiv: 1209.3641 [nucl-th]
U. G. Meissner, Rep. Prog. Phys., 1993, 56(8): 903, arXiv: hep-ph/9302247
G. Ecker, Prog. Part. Nucl. Phys., 1995, 35: 1, arXiv: hepph/9501357
A. Pich, Rep. Prog. Phys., 1995, 58(6): 563, arXiv: hepph/9502366
J. Bijnens, Prog. Part. Nucl. Phys., 2007, 58(2): 521, arXiv: hep-ph/0604043
V. Bernard, Prog. Part. Nucl. Phys., 2008, 60(1): 82, arXiv: 0706.0312 [hep-ph]
S. Scherer, Prog. Part. Nucl. Phys., 2010, 64(1): 1, arXiv: 0908.3425 [hep-ph]
S. Scherer and M. Schindler, A Primer for Chiral Perturbation Theory, Lecture Notes in Physics, Berlin Heidelberg: Springer, 2012
J. A. Oller, M. Verbeni, and J. Prades, J. High Energy Phys., 2006, 0609: 079, arXiv: hep-ph/0608204
J. Bijnens, G. Colangelo, and G. Ecker, J. High Energy Phys., 1999, 9902: 020, arXiv: hep-ph/9902437
J. Bijnens and I. Jemos, Nucl. Phys. B, 2012, 854(3): 631, arXiv: 1103.5945 [hep-ph]
M. Frink and U. G. Meissner, Eur. Phys. J. A, 2006, 29(3): 255, arXiv: hep-ph/0701096
J. A. Oller, M. Verbeni, and J. Prades, arXiv: hepph/0701096, 2007
L. S. Geng, J. Martin Camalich, and M. Vicente Vacas, Phys. Rev. D, 2009, 79(9): 094022, arXiv: 0903.4869 [hep-ph]
V. Pascalutsa, AIP Conf. Proc., 2011, 1388: 60, arXiv: 1105.2509 [hep-ph]
V. Bernard, N. Kaiser, J. Kambor, and U. G. Meissner, Nucl. Phys. B, 1992, 388(2): 315
N. Fettes, U. G. Meissner, M. Mojzis, and S. Steininger, Ann. Phys., 2000, 283(2): 273, arXiv: hep-ph/0001308
R. E. Stuckey and M. C. Birse, J. Phys. G, 1997, 23: 29, arXiv: hep-ph/9602312
J. F. Donoghue, B. R. Holstein, and B. Borasoy, Phys. Rev. D, 1999, 59(3): 036002, arXiv: hep-ph/9804281
R. D. Young, D. B. Leinweber, A. W. Thomas, and S. V. Wright, Phys. Rev. D, 2002, 66(9): 094507, arXiv: heplat/0205017
R. D. Young, D. B. Leinweber, and A. W. Thomas, Prog. Part. Nucl. Phys., 2003, 50(2): 399, arXiv: hep-lat/0212031
D. B. Leinweber, A. W. Thomas, and R. D. Young, Phys. Rev. Lett., 2004, 92(24): 242002, arXiv: hep-lat/0302020
P. Wang, D. Leinweber, A. Thomas, and R. Young, Phys. Rev. D, 2009, 79(9): 094001, arXiv: 0810.1021 [hep-ph]
R. Young and A. Thomas, Phys. Rev. D, 2010, 81(1): 014503, arXiv: 0901.3310 [hep-lat]
P. Wang and A. Thomas, Phys. Rev. D, 2010, 81(11): 114015, arXiv: 1003.0957 [hep-ph]
P. Shanahan, A. Thomas, and R. Young, Phys. Rev. Lett., 2011, 107(9): 092004, arXiv: 1106.2851 [nucl-th]
P. Shanahan, A. Thomas, and R. Young, arXiv: 1205.5365 [nucl-th], 2012
P. Wang, D. Leinweber, A. Thomas, and R. Young, Phys. Rev. D, 2012, 86(9): 094038, arXiv: 1210.5072 [hep-ph]
M. R. Schindler, J. Gegelia, and S. Scherer, Phys. Lett. B, 2004, 586(3–4): 258, arXiv: hep-ph/0309005
M. Schindler, D. Djukanovic, J. Gegelia, and S. Scherer, Phys. Lett. B, 2007, 649(5–6): 390, arXiv: hep-ph/0612164
M. R. Schindler, D. Djukanovic, J. Gegelia, and S. Scherer, Nucl. Phys. A, 2008, 803(1–2): 68, arXiv: 0707.4296 [hepph]
M. Schindler, T. Fuchs, J. Gegelia, and S. Scherer, Phys. Rev. C, 2007, 75(2): 025202, arXiv: nucl-th/0611083
M. R. Schindler, J. Gegelia, and S. Scherer, Eur. Phys. J. A, 2005, 26(1): 1, arXiv: nucl-th/0509005
M. Dorati, T. A. Gail, and T. R. Hemmert, Nucl. Phys. A, 2008, 798(3–4): 96, arXiv: nucl-th/0703073
L. Greil, T. R. Hemmert, and A. Schafer, Eur. Phys. J. A, 2012, 48(5): 53, arXiv: 1112.2539 [hep-ph]
S. Durr, Z. Fodor, T. Hemmert, C. Hoelbling, J. Frison, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, A. Portelli, A. Ramos, A. Schäfer, and K. K. Szabó, Phys. Rev. D, 2012, 85(1): 014509, arXiv: 1109.4265 [hep-lat
E. Epelbaum and J. Gegelia, Phys. Lett. B, 2012, 716(2): 338, arXiv: 1207.2420 [nucl-th]
P. Ellis and K. Torikoshi, Phys. Rev. C, 1999, 61(1): 015205, arXiv: nucl-th/9904017
M. Frink and U. G. Meissner, J. High Energy Phys., 2004, 0407: 028, arXiv: hep-lat/0404018
S. L. Zhu, S. Puglia, and M. Ramsey-Musolf, Phys. Rev. D, 2001, 63(3): 034002, arXiv: hep-ph/0009159
B. Kubis and U. G. Meissner, Eur. Phys. J. C, 2001, 18(4): 747, arXiv: hep-ph/0010283
A. Lacour, B. Kubis, and U. G. Meissner, J. High Energy Phys., 2007, 0710: 083, arXiv: 0708.3957 [hep-ph]
M. Mai, P. C. Bruns, B. Kubis, and U. G. Meissner, Phys. Rev. D, 2009, 80(9): 094006, arXiv: 0905.2810 [hep-ph]
P. Bruns, L. Greil, and A. Schafer, Eur. Phys. J. A, 2012, 48(2): 16, arXiv: 1105.6000 [hep-ph]
F. K. Guo and U. G. Meissner, J. High Energy Phys., 2012, 1212: 097, arXiv: 1210.5887 [hep-ph]
S. R. Coleman and S. L. Glashow, Phys. Rev. Lett., 1961, 6(8): 423
D. Caldi and H. Pagels, Phys. Rev. D, 1974, 10(11): 3739
E. E. Jenkins, M. E. Luke, A. V. Manohar, and M. J. Savage, Phys. Lett. B, 1993, 302(4): 482, arXiv: hep-ph/9212226
L. Durand and P. Ha, Phys. Rev. D, 1998, 58(1): 013010, arXiv: hep-ph/9712492
U. G. Meissner and S. Steininger, Nucl. Phys. B, 1997, 499: 349, arXiv: hep-ph/9701260
J. F. Donoghue, B. R. Holstein, T. Huber, and A. Ross, Fizika B, 2005, 14: 217, arXiv: hep-ph/0412035
S. Puglia and M. Ramsey-Musolf, Phys. Rev. D, 2000, 62(3): 034010, arXiv: hep-ph/9911542
L. S. Geng, J. Martin Camalich, and M. Vicente Vacas, Phys. Lett. B, 2009, 676(1–3): 63, arXiv: 0903.0779 [hep-ph]
W. Rarita and J. Schwinger, Phys. Rev., 1941, 60(1): 61
K. Johnson and E. Sudarshan, Ann. Phys., 1961, 13(1): 126
G. Velo and D. Zwanziger, Phys. Rev., 1969, 186(5): 1337
S. Deser, V. Pascalutsa, and A. Waldron, Phys. Rev. D, 2000, 62(10): 105031, arXiv: hep-th/0003011
L. Nath, B. Etemadi, and J. Kimel, Phys. Rev. D, 1971, 3(9): 2153
C. Hagen, Phys. Rev. D, 1971, 4(8): 2204
L. Singh, Phys. Rev. D, 1973, 7(4): 1256
V. Pascalutsa, Phys. Rev. D, 1998, 58(9): 096002, arXiv: hep-ph/9802288
V. Pascalutsa and R. Timmermans, Phys. Rev. C, 1999, 60(4): 042201, arXiv: nucl-th/9905065
V. Pascalutsa, Phys. Lett. B, 2001, 503(1–2): 85, arXiv: hepph/0008026
V. Pascalutsa, M. Vanderhaeghen, and S. N. Yang, Phys. Rep., 2007, 437(5–6): 125, arXiv: hep-ph/0609004
H. Krebs, E. Epelbaum, and U. G. Meissner, Phys. Rev. C, 2009, 80(2): 028201, arXiv: 0812.0132 [hep-th]
H. B. Tang and P. J. Ellis, Phys. Lett. B, 1996, 387(1): 9, arXiv: hep-ph/9606432
T. R. Hemmert, B. R. Holstein, and J. Kambor, J. Phys. G, 1998, 24: 1831, arXiv: hep-ph/9712496
C. Hacker, N. Wies, J. Gegelia, and S. Scherer, Phys. Rev. C, 2005, 72(5): 055203, arXiv: hep-ph/0505043
N. Wies, J. Gegelia, and S. Scherer, Phys. Rev. D, 2006, 73(9): 094012, arXiv: hep-ph/0602073
M. Benmerrouche, R. Davidson, and N. Mukhopadhyay, Phys. Rev. C, 1989, 39(6): 2339
C. Amsler, et al. [Particle Data Group], Phys. Lett. B, 2008, 667(1–5): 1
H. Krebs, E. Epelbaum, and U. G. Meissner, Phys. Lett. B, 2010, 683(2–3): 222, arXiv: 0905.2744 [hep-th]
L. S. Geng, J. Martin Camalich, and M. Vicente Vacas, Phys. Rev. D, 2009, 80(3): 034027, arXiv: 0907.0631 [hep-ph]
S. Nozawa and D. Leinweber, Phys. Rev. D, 1990, 42(10): 3567
K. Hikasa, et al. [Particle Data Group], Phys. Rev. D, 1992, 45: S1
F. Schlumpf, Phys. Rev. D, 1993, 48(9): 4478, arXiv: hepph/9305293
G. Wagner, A. Buchmann, and A. Faessler, J. Phys. G, 2000, 26: 267
T. Ledwig, A. Silva, and M. Vanderhaeghen, Phys. Rev. D, 2009, 79(9): 094025, arXiv: 0811.3086 [hep-ph]
F. X. Lee, Phys. Rev. D, 1998, 57(3): 1801, arXiv: hepph/9708323
D. B. Leinweber, T. Draper, and R. Woloshyn, Phys. Rev. D, 1992, 46(7): 3067, arXiv: hep-lat/9208025
F. Lee, R. Kelly, L. Zhou, and W. Wilcox, Phys. Lett. B, 2005, 627(1–4): 71, arXiv: hep-lat/0509067
M. A. Luty, J. March-Russell, and M. J. White, Phys. Rev. D, 1995, 51(5): 2332, arXiv: hep-ph/9405272
M. N. Butler, M. J. Savage, and R. P. Springer, Phys. Rev. D, 1994, 49(7): 3459, arXiv: hep-ph/9308317
W. Yao, et al. [Particle Data Group], J. Phys. G, 2006, 33: 1
C. Alexandrou, et al. [ETM Collaboration], Phys. Rev. D, 2009, 80: 114503, arXiv: 0910.2419 [hep-lat]
S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, and G. Vulvert, Science, 2008, 322(5905): 1224, arXiv: 0906.3599 [hep-lat]
S. Aoki, et al. [PACS-CS Collaboration], Phys. Rev. D, 2009, 79: 034503, arXiv: 0807.1661 [hep-lat]
S. Aoki, et al. [PACS-CS Collaboration], Phys. Rev. D, 2010, 81: 074503, arXiv: 0911.2561 [hep-lat]
A. Walker-Loud, H. W. Lin, D. Richards, R. Edwards, M. Engelhardt, G. Fleming, P. Hägler, B. Musch, M. Lin, H. Meyer, J. Negele, A. Pochinsky, M. Procura, S. Syritsyn, C. Morningstar, K. Orginos, D. Renner, and W. Schroers, Phys. Rev. D, 2009, 79(5): 054502, arXiv: 0806.4549 [hep-lat]
H. W. Lin, et al. [Hadron Spectrum Collaboration], Phys. Rev. D, 2009, 79: 034502, arXiv: 0810.3588 [hep-lat]
W. Bietenholz, V. Bornyakov, N. Cundy, M. Gockeler, R. Horsley, A. D. Kennedy, W. G. Lockhart, Y. Nakamura, H. Perlt, D. Pleiter, P. E. L. Rakow, A. Schäfer, G. Schierholz, A. Schiller, H. Stüben, and J. M. Zanotti, Phys. Lett. B, 2010, 690(4): 436, arXiv: 1003.1114 [hep-lat]
W. Bietenholz, V. Bornyakov, M. Gockeler, R. Horsley, W. Lockhart, Y. Nakamura, H. Perlt, D. Pleiter, P. E. L. Rakow, G. Schierholz, A. Schiller, T. Streuer, H. Stüben, F. Winter, and J. M. Zanotti,, Phys. Rev. D, 2011, 84(5): 054509, arXiv: 1102.5300 [hep-lat]
S. Beane, E. Chang, W. Detmold, H. Lin, T. Luu, K. Orginos, A. Parreño, M. J. Savage, A. Torok, and A. Walker-Loud, Phys. Rev. D, 2011, 84(1): 014507, arXiv: 1104.4101 [hep-lat]
F. Wilczek, Central Eur. J. Phys., 2012, 10: 1021, arXiv: 1206.7114 [hep-ph]
J. Beringer, et al. [Particle Data Group], Phys. Rev. D, 2012, 86(1): 010001
E. E. Jenkins, Nucl. Phys. B, 1992, 368(1): 190
V. Bernard, N. Kaiser, and U. G. Meissner, Z. Phys. C, 1993, 60(1): 111, arXiv: hep-ph/9303311
M. Banerjee and J. Milana, Phys. Rev. D, 1995, 52(11): 6451, arXiv: hep-ph/9410398
B. Borasoy and U. G. Meissner, Ann. Phys., 1997, 254(1): 192, arXiv: hep-ph/9607432
A. Walker-Loud, Nucl. Phys. A., 2005, 747(2–4): 476, arXiv: hep-lat/0405007
M. Frink, U. G. Meissner, and I. Scheller, Eur. Phys. J. A, 2005, 24(3): 395, arXiv: hep-lat/0501024
B. Lehnhart, J. Gegelia, and S. Scherer, J. Phys. G, 2005, 31: 89, arXiv: hep-ph/0412092
A. Semke and M. Lutz, Nucl. Phys. A, 2006, 778(3-4): 153, arXiv: nucl-th/0511061
A. Semke and M. Lutz, Nucl. Phys. A, 2007, 789(1-4): 251
A. Semke and M. Lutz, Phys. Rev. D, 2012, 85(3): 034001, arXiv: 1111.0238 [hep-ph]
P. C. Bruns, L. Greil, and A. Schafer, Phys. Rev. D, 2013, 87: 054021, arXiv: 1209.0980 [hep-ph]
M. Lutz and A. Semke, Phys. Rev. D, 2012, 86(9): 091502, arXiv: 1209.2791 [hep-lat]
K. I. Ishikawa, et al., Phys. Rev. D, 2009, 80: 054502, arXiv: 0905.0962 [hep-lat]
E. E. Jenkins, A. V. Manohar, J. W. Negele, and A. Walker-Loud, Phys. Rev. D, 2010, 81(1): 014502, arXiv: 0907.0529 [hep-lat]
A. Walker-Loud, Phys. Rev. D, 2012, 86(7): 074509, arXiv: 1112.2658 [hep-lat]
A. Semke and M. Lutz, Phys. Lett. B, 2012, 717(1–3): 242, arXiv: 1202.3556 [hep-ph]
L. S. Geng, X. Ren, J. Martin-Camalich, and W. Weise, Phys. Rev. D, 2011, 84(7): 074024, arXiv: 1108.2231 [hepph]
A. Bottino, F. Donato, N. Fornengo, and S. Scopel, Astropart. Phys., 2000, 13(2–3): 215, arXiv: hep-ph/9909228
J. R. Ellis, K. A. Olive, and C. Savage, Phys. Rev. D, 2008, 77(6): 065026, arXiv: 0801.3656 [hep-ph]
J. Gasser, H. Leutwyler, and M. Sainio, Phys. Lett. B, 1991, 253(1–2): 252
J. Alarcon, J. Martin Camalich, and J. Oller, Phys. Rev. D, 2012, 85(5): 051503, arXiv: 1110.3797 [hep-ph]
G. S. Bali, et al. [QCDSF Collaboration], Phys. Rev. D, 2012, 85: 054502, arXiv: 1111.1600 [hep-lat]
G. Bali, P. Bruns, S. Collins, M. Deka, B. Glasle, et al, Nucl. Phys. B, 2013, 866(1): 1, arXiv: 1206.7034 [hep-lat]
R. Horsley, Y. Nakamura, H. Perlt, D. Pleiter, P. Rakow, G. Schierholz, A. Schiller, H. Stüben, F. Winter, and J.M. Zanotti,, Phys. Rev. D, 2012, 85(3): 034506, arXiv: 1110.4971 [hep-lat]
H. Ohki, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko, et al., PoS, 2009, LAT 2009: 124, arXiv: 0910.3271 [hep-lat]
J. Alarcon, L. S. Geng, J. M. Camalich, and J. Oller, arXiv: 1209.2870 [hep-ph], 2012
P. Shanahan, A. Thomas, and R. Young, PoS, 2012, LAT 2012: 165, arXiv: 1301.3231 [hep-lat]
N. Cabibbo, E. C. Swallow, and R. Winston, Ann. Rev. Nucl. Part. Sci., 2003, 53: 39, arXiv: hep-ph/0307298
N. Cabibbo, E. C. Swallow, and R. Winston, Phys. Rev. Lett., 2004, 92(25): 251803, arXiv: hep-ph/0307214
R. Flores-Mendieta, Phys. Rev. D, 2004, 70(11): 114036, arXiv: hep-ph/0410171
V. Mateu and A. Pich, J. High Energy Phys., 2005, 0510: 041, arXiv: hep-ph/0509045
N. Cabibbo, Phys. Rev. Lett., 1963, 10(12): 531
M. Kobayashi and T. Maskawa, Prog. Theor. Phys., 1973, 49(2): 652
E. Blucher, E. De Lucia, G. Isidori, V. Lubicz, H. Abele, et al., arXiv: hep-ph/0512039, 2005
E. Gamiz, M. Jamin, A. Pich, J. Prades, and F. Schwab, PoS, 2008, KAON: 008, arXiv: 0709.0282 [hep-ph]
W. J. Marciano, Phys. Rev. Lett., 2004, 93(23): 231803, arXiv: hep-ph/0402299
M. Ademollo and R. Gatto, Phys. Rev. Lett., 1964, 13(7): 264
J. F. Donoghue, B. R. Holstein, and S. W. Klimt, Phys. Rev. D, 1987, 35(3): 934
F. Schlumpf, Phys. Rev. D, 1995, 51(5): 2262, arXiv: hepph/9409272
A. Faessler, T. Gutsche, B. R. Holstein, M. A. Ivanov, J. G. Korner, and V. Lyubovitskij, Phys. Rev. D, 2008, 78(9): 094005, arXiv: 0809.4159 [hep-ph]
A. Krause, Helv. Phys. Acta, 1990, 63: 3
J. Anderson and M. A. Luty, Phys. Rev. D, 1993, 47(11): 4975, arXiv: hep-ph/9301219
N. Kaiser, Phys. Rev. C, 2001, 64(2): 028201, arXiv: nuclth/0105043
G. Villadoro, Phys. Rev. D, 2006, 74(1): 014018, arXiv: hepph/0603226
D. Guadagnoli, V. Lubicz, M. Papinutto, and S. Simula, Nucl. Phys. B, 2007, 761(1–2): 63, arXiv: hep-ph/0606181
S. Sasaki and T. Yamazaki, Phys. Rev. D, 2009, 79(7): 074508, arXiv: 0811.1406 [hep-ph]
S. Sasaki, Phys. Rev. D, 2012, 86(11): 114502, arXiv: 1209.6115 [hep-lat]
J. Alarcon, J. M. Camalich, and J. Oller, arXiv: 1210.4450 [hep-ph], 2012
Y. H. Chen, D. L. Yao, and H. Zheng, Phys. Rev. D, 2013, 87: 054019, arXiv: 1212.1893 [hep-ph]
V. Lensky and V. Pascalutsa, Eur. Phys. J. C, 2010, 65(1–2): 195, arXiv: 0907.0451 [hep-ph]
T. Ledwig, J. Martin-Camalich, V. Pascalutsa, and M. Vanderhaeghen, Phys. Rev. D, 2012, 85(3): 034013, arXiv: 1108.2523 [hep-ph]
L. S. Geng, J. Martin Camalich, L. Alvarez-Ruso, and M. Vicente Vacas, Phys. Rev. D, 2008, 78(1): 014011, arXiv: 0801.4495 [hep-ph]
S. I. Ando and H. W. Fearing, Phys. Rev. D, 2007, 75(1): 014025, arXiv: hep-ph/0608195
M. Altenbuchinger, L. S. Geng, and W. Weise, Phys. Lett. B, 2012, 713(4–5): 453, arXiv: 1109.0460 [hep-ph]
L. S. Geng, N. Kaiser, J. Martin-Camalich, and W. Weise, Phys. Rev. D, 2010, 82(5): 054022, arXiv: 1008.0383 [hepph]
Z. W. Liu, Y. R. Liu, X. Liu, and S. L. Zhu, Phys. Rev. D, 2011, 84(3): 034002, arXiv: 1104.2726 [hep-ph]
E. Follana, C. Davies, G. Lepage, and J. Shigemitsu [HPQCD Collaboration, UKQCD Collaboration], Phys. Rev. Lett., 2008, 100: 062002, arXiv: 0706.1726 [hep-lat]
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Geng, LS. Recent development in SU(3) covariant baryon chiral perturbation theory. Front. Phys. 8, 328–348 (2013). https://doi.org/10.1007/s11467-013-0327-7
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DOI: https://doi.org/10.1007/s11467-013-0327-7