Abstract.
We present improved nucleon-nucleon potentials derived in chiral effective field theory up to next-to-next-to-next-to-leading order. We argue that the nonlocal momentum-space regulator employed in the two-nucleon potentials of previous works (Nucl. Phys. A 747, 362 (2005) and Phys. Rev. C 68, 041001 (2003)) is not the most efficient choice, in particular since it affects the long-range part of the interaction. We are able to significantly reduce finite-cutoff artefacts by using an appropriate regularization in coordinate space which maintains the analytic structure of the amplitude. The new potentials do not require the additional spectral function regularization employed in (Nucl. Phys. A 747, 362 (2005)) to cut off the short-range components of the two-pion exchange and make use of the low-energy constants ci and di determined from pion-nucleon scattering without any fine tuning. We discuss in detail the construction of the new potentials and convergence of the chiral expansion for two-nucleon observables. We also employ a simple approach for estimating the theoretical uncertainty in few-nucleon calculations from the truncation of the chiral expansion that replaces previous reliance on cutoff variation.
Similar content being viewed by others
References
S.R. Beane, W. Detmold, K. Orginos, M.J. Savage, Prog. Part. Nucl. Phys. 66, 1 (2011) arXiv:1004.2935 [hep-lat]
S. Weinberg, Phys. Lett. B 251, 288 (1990)
U. van Kolck, Phys. Rev. C 49, 2932 (1994)
C. Ordonez, L. Ray, U. van Kolck, Phys. Rev. C 53, 2086 (1996) hep-ph/9511380
E. Epelbaum, H.W. Hammer, U.-G. Meißner, Rev. Mod. Phys. 81, 1773 (2009) arXiv:0811.1338 [nucl-th]
N. Kalantar-Nayestanaki, E. Epelbaum, J.G. Messchendorp, A. Nogga, Rep. Prog. Phys. 75, 016301 (2012) arXiv:1108.1227 [nucl-th]
H.W. Hammer, A. Nogga, A. Schwenk, Rev. Mod. Phys. 85, 197 (2013) arXiv:1210.4273 [nucl-th]
J.W. Holt, N. Kaiser, W. Weise, Prog. Part. Nucl. Phys. 73, 35 (2013) arXiv:1304.6350 [nucl-th]
J.P. Vary, Nucl. Phys. Proc. Suppl. 251, 155 (2014)
H. Krebs, A. Gasparyan, E. Epelbaum, Phys. Rev. C 87, 054007 (2013) arXiv:1302.2872 [nucl-th]
D.R. Phillips, C. Schat, Phys. Rev. C 88, 034002 (2013) arXiv:1307.6274 [nucl-th]
E. Epelbaum, A.M. Gasparyan, H. Krebs, C. Schat, arXiv:1411.3612 [nucl-th]
R. Machleidt, D.R. Entem, J. Phys. G 37, 064041 (2010) arXiv:1001.0966 [nucl-th]
E. Epelbaum, in Proceedings of the 10th Conference on Quark Confinement and the Hadron Spectrum (Confinement X) Munich, Germany, October 8--12, 2012, edited by Matthias Berwein, Nora Brambilla, Stephan Paul (2012) 014, arXiv:1302.3241 [nucl-th]
Low-Energy Nuclear Physics International Collaboration, http://www.lenpic.org
E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 747, 362 (2005) nucl-th/0405048
D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001 (2003) nucl-th/0304018
E. Epelbaum, W. Glöckle, U.-G. Meißner, Eur. Phys. J. A 19, 125 (2004) nucl-th/0304037
E. Epelbaum, W. Glöckle, U.-G. Meißner, Eur. Phys. J. A 19, 401 (2004) nucl-th/0308010
R. Machleidt, D.R. Entem, Phys. Rep. 503, 1 (2011) arXiv:1105.2919 [nucl-th]
V. Bernard, N. Kaiser, U.-G. Meißner, Nucl. Phys. A 615, 483 (1997) hep-ph/9611253
A. Manohar, H. Georgi, Nucl. Phys. B 234, 189 (1984)
G.P. Lepage, nucl-th/9706029
S.R. Beane, P.F. Bedaque, M.J. Savage, U. van Kolck, Nucl. Phys. A 700, 377 (2002) nucl-th/0104030
A. Nogga, R.G.E. Timmermans, U. van Kolck, Phys. Rev. C 72, 054006 (2005) nucl-th/0506005
B. Long, C.J. Yang, Phys. Rev. C 85, 034002 (2012) arXiv:1111.3993 [nucl-th]
M.C. Birse, Philos. Trans. R. Soc. London A 369, 2662 (2011) arXiv:1012.4914 [nucl-th]
M. Pavon Valderrama, Phys. Rev. C 84, 064002 (2011) arXiv:1108.0872 [nucl-th]
E. Epelbaum, U.-G. Meißner, Few-Body Syst. 54, 2175 (2013) nucl-th/0609037
E. Epelbaum, J. Gegelia, Eur. Phys. J. A 41, 341 (2009) arXiv:0906.3822 [nucl-th]
E. Epelbaum, J. Gegelia, Phys. Lett. B 716, 338 (2012) arXiv:1207.2420 [nucl-th]
E. Epelbaum, A.M. Gasparyan, J. Gegelia, H. Krebs, arXiv:1501.01191 [nucl-th]
N. Kaiser, R. Brockmann, W. Weise, Nucl. Phys. A 625, 758 (1997) nucl-th/9706045
E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 637, 107 (1998) nucl-th/9801064
E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006) nucl-th/0509032
E. Epelbaum, Eur. Phys. J. A 34, 197 (2007) arXiv:0710.4250 [nucl-th]
E. Epelbaum, arXiv:1001.3229 [nucl-th]
U. van Kolck, M.C.M. Rentmeester, J.L. Friar, J.T. Goldman, J.J. de Swart, Phys. Rev. Lett. 80, 4386 (1998) nucl-th/9710067
J.L. Friar, U. van Kolck, Phys. Rev. C 60, 034006 (1999) nucl-th/9906048
M. Walzl, U.-G. Meißner, E. Epelbaum, Nucl. Phys. A 693, 663 (2001) nucl-th/0010019
J.L. Friar, U. van Kolck, G.L. Payne, S.A. Coon, Phys. Rev. C 68, 024003 (2003) nucl-th/0303058
E. Epelbaum, U.-G. Meißner, Phys. Rev. C 72, 044001 (2005) nucl-th/0502052
N. Kaiser, Phys. Rev. C 73, 064003 (2006) nucl-th/0605040
J.J. de Swart, M.C.M. Rentmeester, R.G.E. Timmermans, PiN Newslett. 13, 96 (1997) nucl-th/9802084
V.G.J. Stoks, R.A.M. Klomp, M.C.M. Rentmeester, J.J. de Swart, Phys. Rev. C 48, 792 (1993) Nijmegen NN on-line program, http://nn-online.org/
N. Kaiser, Phys. Rev. C 64, 057001 (2001) nucl-th/0107064
N. Fettes, U.-G. Meißner, S. Steininger, Nucl. Phys. A 640, 199 (1998) hep-ph/9803266
S. Weinberg, Nucl. Phys. B 363, 3 (1991)
J.L. Friar, Phys. Rev. C 60, 034002 (1999) nucl-th/9901082
V. Bernard, E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. C 84, 054001 (2011) arXiv:1108.3816 [nucl-th]
E. Epelbaum, J. Gegelia, PoS CD 12, 090 (2013) arXiv:1301.6134 [nucl-th]
E. Epelbaum, A.M. Gasparyan, J. Gegelia, M.R. Schindler, Eur. Phys. J. A 50, 51 (2014) arXiv:1311.7164 [nucl-th]
E. Marji, A. Canul, Q. MacPherson, R. Winzer, C. Zeoli, D.R. Entem, R. Machleidt, Phys. Rev. C 88, 054002 (2013) arXiv:1309.5114 [nucl-th]
B. Borasoy, E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner, Eur. Phys. J. A 31, 105 (2007) nucl-th/0611087
E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner, Phys. Rev. Lett. 104, 142501 (2010) arXiv:0912.4195 [nucl-th]
E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner, Phys. Rev. Lett. 106, 192501 (2011) arXiv:1101.2547 [nucl-th]
E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.-G. Meißner, Phys. Rev. Lett. 109, 252501 (2012) arXiv:1208.1328 [nucl-th]
T.A. Lähde, E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner, G. Rupak, Phys. Lett. B 732, 110 (2014) arXiv:1311.0477 [nucl-th]
E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.-G. Meißner, G. Rupak, Phys. Rev. Lett. 112, 102501 (2014) arXiv:1312.7703 [nucl-th]
B.N. Lu, T.A. Lähde, D. Lee, U.-G. Meißner, Phys. Rev. D 90, 034507 (2014) arXiv:1403.8056 [nucl-th]
A. Gezerlis, I. Tews, E. Epelbaum, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. Lett. 111, 032501 (2013) arXiv:1303.6243 [nucl-th]
A. Gezerlis, I. Tews, E. Epelbaum, M. Freunek, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, arXiv:1406.0454 [nucl-th]
T.D. Cohen, J.M. Hansen, Phys. Rev. C 59, 13 (1999) nucl-th/9808038
A.M. Gasparyan, M.F.M. Lutz, E. Epelbaum, Eur. Phys. J. A 49, 115 (2013) arXiv:1212.3057 [nucl-th]
J.A. Oller, arXiv:1402.2449 [nucl-th]
V. Baru, E. Epelbaum, C. Hanhart, M. Hoferichter, A.E. Kudryavtsev, D.R. Phillips, Eur. Phys. J. A 48, 69 (2012) arXiv:1202.0208 [nucl-th]
S. Ishikawa, M.R. Robilotta, Phys. Rev. C 76, 014006 (2007) arXiv:0704.0711 [nucl-th]
V. Bernard, E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. C 77, 064004 (2008) arXiv:0712.1967 [nucl-th]
H. Krebs, A. Gasparyan, E. Epelbaum, Phys. Rev. C 85, 054006 (2012) arXiv:1203.0067 [nucl-th]
V. Baru, C. Hanhart, M. Hoferichter, B. Kubis, A. Nogga, D.R. Phillips, Phys. Lett. B 694, 473 (2011) arXiv:1003.4444 [nucl-th]
R.A. Arndt, R.L. Workman, M.M. Pavan, Phys. Rev. C 49, 2729 (1994)
P. Büttiker, U.-G. Meißner, Nucl. Phys. A 668, 97 (2000) hep-ph/9908247
N. Fettes, U.-G. Meißner, Nucl. Phys. A 676, 311 (2000) hep-ph/0002162
J.M. Alarcon, J. Martin Camalich, J.A. Oller, Ann. Phys. 336, 413 (2013) arXiv:1210.4450 [hep-ph]
Y.H. Chen, D.L. Yao, H.Q. Zheng, Phys. Rev. D 87, 054019 (2013) arXiv:1212.1893 [hep-ph]
K.A. Wendt, B.D. Carlsson, A. Ekström, arXiv:1410.0646 [nucl-th]
M.C.M. Rentmeester, R.G.E. Timmermans, J.L. Friar, J.J. de Swart, Phys. Rev. Lett. 82, 4992 (1999) nucl-th/9901054
D.R. Entem, R. Machleidt, Phys. Rev. C 66, 014002 (2002) nucl-th/0202039
M.C.M. Rentmeester, R.G.E. Timmermans, J.J. de Swart, Phys. Rev. C 67, 044001 (2003) nucl-th/0302080
D.R. Entem, R. Machleidt, nucl-th/0303017
A. Ekström, B.D. Carlsson, K.A. Wendt, C. Forssén, M. Hjorth-Jensen, R. Machleidt, S.M. Wild, J. Phys. G 42, 034003 (2015) arXiv:1406.6895 [nucl-th]
R.N. Perez, J.E. Amaro, E.R. Arriola, arXiv:1411.1212 [nucl-th]
A. Ekstrom, G. Baardsen, C. Forssen, G. Hagen, M. Hjorth-Jensen, G.R. Jansen, R. Machleidt, W. Nazarewicz et al., Phys. Rev. Lett. 110, 192502 (2013) arXiv:1303.4674 [nucl-th]
J.R. Bergervoet, P.C. van Campen, W.A. van der Sanden, J.J. de Swart, Phys. Rev. C 38, 15 (1988)
R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995) nucl-th/9408016
R. Machleidt, Phys. Rev. C 63, 024001 (2001) nucl-th/0006014
T. Mehen, I.W. Stewart, M.B. Wise, Phys. Rev. Lett. 83, 931 (1999) hep-ph/9902370
E. Epelbaum, U.-G. Meißner, W. Glöckle, C. Elster, Phys. Rev. C 65, 044001 (2002) nucl-th/0106007
J.L. Friar, Phys. Rev. C 20, 325 (1979)
V.G.J. Stoks, R.A.M. Klomp, C.P.F. Terheggen, J.J. de Swart, Phys. Rev. C 49, 2950 (1994) nucl-th/9406039
J.L. Forest, Phys. Rev. C 61, 034007 (2000) nucl-th/9905063
R. Machleidt, P. Liu, D.R. Entem, E. Ruiz Arriola, Phys. Rev. C 81, 024001 (2010) arXiv:0910.3942 [nucl-th]
M.R. Schindler, D.R. Phillips, Ann. Phys. 324, 682 (2009) 324
R.A. Arndt, I.I. Strakovsky, R.L. Workman, Phys. Rev. C 50, 2731 (1994)
D.R. Entem, N. Kaiser, R. Machleidt, Y. Nosyk, arXiv:1411.5335 [nucl-th]
M.C. Birse, J.A. McGovern, Phys. Rev. C 70, 054002 (2004) nucl-th/0307050
H.W. Grießhammer, Nucl. Phys. A 744, 192 (2004) nucl-th/0404073
H.W. Grießhammer, talk given at the Workshop on Bound states and resonances in effective field theories and lattice QCD calculations, Benasque, Spain, July 20 - August 1, 2014
R.J. Furnstahl, D.R. Phillips, S. Wesolowski, J. Phys. G 42, 034028 (2015) arXiv:1407.0657 [nucl-th]
C. van der Leun, C. Alderlisten, Nucl. Phys. A 380, 261 (1982)
T.E.O. Ericson, M. Rosa-Clot, Nucl. Phys. A 405, 497 (1983)
N.L. Rodning, L.D. Knutson, Phys. Rev. C 41, 898 (1990)
A. Huber, T. Udem, B. Gross, J. Reichert, M. Kourogi, K. Pachucki, M. Weitz, T.W. Hansch, Phys. Rev. Lett. 80, 468 (1998)
J. Martorell, D.W.L. Sprung, D.C. Zheng, Phys. Rev. C 51, 1127 (1995)
D.M. Bishop, L.M. Cheung, Phys. Rev. A 20, 381 (1979)
M. Kohno, J. Phys. G 9, L85 (1983)
D.R. Phillips, J. Phys. G 34, 365 (2007) nucl-th/0608036
M. Piarulli, L. Girlanda, L.E. Marcucci, S. Pastore, R. Schiavilla, M. Viviani, Phys. Rev. C 87, 014006 (2013) arXiv:1212.1105 [nucl-th]
H. Witala, J. Golak, R. Skibinski, K. Topolnicki, J. Phys. G 41, 094011 (2014) arXiv:1310.0198 [nucl-th]
N. Fettes, V. Bernard, U.-G. Meißner, Nucl. Phys. A 669, 269 (2000) hep-ph/9907276
D. Siemens, V. Bernard, E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. C 89, 065211 (2014) arXiv:1403.2510 [nucl-th]
R. Navarro Perez, J.E. Amaro, E. Ruiz Arriola, Phys. Rev. C 88, 064002 (2013) arXiv:1310.2536 [nucl-th]
W.P. Abfalterer, F.B. Bateman, F.S. Dietrich, R.W. Finlay, R.C. Haight, G.L. Morgan, Phys. Rev. C 63, 044608 (2001)
G. Fink et al., Nucl. Phys. A 518, 561 (1990)
T.C. Montgomery et al., Phys. Rev. C 16, 499 (1977)
D.H. Fitzgerald et al., Phys. Rev. C 21, 1190 (1980)
R. Garrett et al., Phys. Rev. C 21, 1149 (1980)
A. Langsford et al., Nucl. Phys. 74, 241 (1965)
J.L. Romero et al., Phys. Rev. C 17, 468 (1978)
J. Wilczynski et al., Nucl. Phys. A 425, 458 (1984)
T.C. Griffith et al., Proc. Phys. Soc. London Sect. A 71, 305 (1958)
J. Rahm et al., Phys. Rev. C 63, 044001 (2001)
T. Rönnqvist et al., Phys. Rev. C 45, R496 (1992)
G.H. Stafford et al., Lett. Nuovo Cimento 5, 1589 (1957)
A.J. Bersbach et al., Phys. Rev. D 13, 535 (1976)
A.F. Kuckes et al., Phys. Rev. 121, 1226 (1961)
A.R. Thomas, D. Spalding, E.H. Thorndike, Phys. Rev. 167, 1240 (1968)
Yu.M. Kazarinov et al., SPJETP 16, 24 (1963)
H.P. Stapp, T.J. Ypsilantis, N. Metropolis, Phys. Rev. 105, 302 (1957)
J.M. Blatt, L.C. Biedenharn, Phys. Rev. 86, 399 (1952)
J.M. Blatt, L.C. Biedenharn, Rev. Mod, Phys. 24, 258 (1952)
C.M. Vincent, S.C. Phatak, Phys. Rev. C 10, 391 (1974)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by H. Wittig
Rights and permissions
About this article
Cite this article
Epelbaum, E., Krebs, H. & Meißner, U.G. Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order. Eur. Phys. J. A 51, 53 (2015). https://doi.org/10.1140/epja/i2015-15053-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/i2015-15053-8