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Lattice simulations for light nuclei: Chiral effective field theory at leading order

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Abstract.

We discuss lattice simulations of light nuclei at leading order in the chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.

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References

  1. Y. Kuramashi, M. Fukugita, H. Mino, M. Okawa, A. Ukawa, Phys. Rev. Lett. 71, 2387 (1993).

    Article  ADS  Google Scholar 

  2. CP-PACS Collaboration (S. Aoki), Phys. Rev. D 67, 014502 (2003) hep-lat/0209124.

    Article  MathSciNet  ADS  Google Scholar 

  3. C.J.D. Lin, G. Martinelli, E. Pallante, C.T. Sachrajda, G. Villadoro, Phys. Lett. B 553, 229 (2003) hep-lat/0211043.

    Article  ADS  Google Scholar 

  4. NPLQCD Collaboration (S.R. Beane, P.F. Bedaque, K. Orginos, M.J. Savage), Phys. Rev. D 73, 054503 (2006) hep-lat/0506013.

    Article  ADS  Google Scholar 

  5. M. Fukugita, Y. Kuramashi, M. Okawa, H. Mino, A. Ukawa, Phys. Rev. D 52, 3003 (1995) hep-lat/9501024.

    Article  ADS  Google Scholar 

  6. S.R. Beane, P.F. Bedaque, A. Parreno, M.J. Savage, Phys. Lett. B 585, 106 (2004) hep-lat/0312004.

    Article  ADS  Google Scholar 

  7. S.R. Beane, P.F. Bedaque, K. Orginos, M.J. Savage, Phys. Rev. Lett. 97, 012001 (2006) hep-lat/0602010.

    Article  ADS  Google Scholar 

  8. A. Nogga, H. Kamada, W. Glöckle, B.R. Barrett, Phys. Rev. C 65, 054003 (2002) nucl-th/0112026.

    Article  ADS  Google Scholar 

  9. R. Machleidt, F. Sammarruca, Y. Song, Phys. Rev. C 53, 1483 (1996) nucl-th/9510023.

    Article  ADS  Google Scholar 

  10. R. Machleidt, Phys. Rev. C 63, 024001 (2001) nucl-th/0006014.

    Article  ADS  Google Scholar 

  11. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995) nucl-th/9408016.

    Article  ADS  Google Scholar 

  12. 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.

    Article  ADS  Google Scholar 

  13. S.A. Coon, W. Glöckle, Phys. Rev. C 23, 1790 (1981).

    Article  ADS  Google Scholar 

  14. S.A. Coon, H.K. Han, Few Body Syst. 30, 131 (2001) nucl-th/0101003.

    Article  ADS  Google Scholar 

  15. B.S. Pudliner, V.R. Pandharipande, J. Carlson, S.C. Pieper, R.B. Wiringa, Phys. Rev. C 56, 1720 (1997) nucl-th/9705009.

    Article  ADS  Google Scholar 

  16. W. Glöckle, H. Witała, D. Hüber, H. Kamada, J. Golak, Phys. Rep. 274, 107 (1996).

    Article  ADS  Google Scholar 

  17. E. Epelbaum, Phys. Rev. Lett. 86, 4787 (2001) nucl-th/0007057.

    Article  ADS  Google Scholar 

  18. E. Epelbaum, Phys. Rev. C 66, 064001 (2002) nucl-th/0208023.

    Article  ADS  Google Scholar 

  19. E. Epelbaum, W. Glöckle, U.-G. Meißner, Phys. Lett. B 439, 1 (1998) nucl-th/9804005.

    Article  ADS  Google Scholar 

  20. S.K. Bogner, T.T.S. Kuo, A. Schwenk, D.R. Entem, R. Machleidt, Phys. Lett. B 576, 265 (2003) nucl-th/0108041.

    Article  ADS  Google Scholar 

  21. S.K. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386, 1 (2003) nucl-th/0305035.

    Article  ADS  Google Scholar 

  22. S. Fujii, Phys. Rev. C 70, 024003 (2004) nucl-th/0404049.

    Article  ADS  Google Scholar 

  23. A. Nogga, S.K. Bogner, A. Schwenk, Phys. Rev. C 70, 061002 (2004) nucl-th/0405016.

    Article  ADS  Google Scholar 

  24. A. Kievsky, S. Rosati, M. Viviani, Nucl. Phys. A 551, 241 (1993).

    Article  ADS  Google Scholar 

  25. V.D. Efros, W. Leidemann, G. Orlandini, Phys. Lett. B 338, 130 (1994) nucl-th/9409004.

    Article  ADS  Google Scholar 

  26. K. Varga, Y. Suzuki, Phys. Rev. C 52, 2885 (1995) nucl-th/9508023.

    Article  ADS  Google Scholar 

  27. A. Kievsky, Nucl. Phys. A 624, 125 (1997) nucl-th/9706061.

    Article  ADS  Google Scholar 

  28. R.B. Wiringa, S.C. Pieper, J. Carlson, V.R. Pandharipande, Phys. Rev. C 62, 014001 (2000) nucl-th/0002022.

    Article  ADS  Google Scholar 

  29. S.C. Pieper, R.B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53 (2001) nucl-th/0103005.

    Article  ADS  Google Scholar 

  30. S.C. Pieper, V.R. Pandharipande, R.B. Wiringa, J. Carlson, Phys. Rev. C 64, 014001 (2001) nucl-th/0102004.

    Article  ADS  Google Scholar 

  31. S.C. Pieper, K. Varga, R.B. Wiringa, Phys. Rev. C 66, 044310 (2002) nucl-th/0206061.

    Article  ADS  Google Scholar 

  32. R.B. Wiringa, S.C. Pieper, Phys. Rev. Lett. 89, 182501 (2002) nucl-th/0207050.

    Article  ADS  Google Scholar 

  33. S.C. Pieper, R.B. Wiringa, J. Carlson, Phys. Rev. C 70, 054325 (2004) nucl-th/0409012.

    Article  ADS  Google Scholar 

  34. S. Fantoni, A. Sarsa, K.E. Schmidt, Phys. Rev. Lett. 87, 181101 (2001) nucl-th/0106026.

    Article  ADS  Google Scholar 

  35. A. Sarsa, S. Fantoni, K.E. Schmidt, F. Pederiva, Phys. Rev. C 68, 024308 (2003) nucl-th/0303035.

    Article  ADS  Google Scholar 

  36. F. Pederiva, A. Sarsa, K.E. Schmidt, S. Fantoni, Nucl. Phys. A 742, 255 (2004) nucl-th/0403069.

    Article  ADS  Google Scholar 

  37. S.Y. Chang, Nucl. Phys. A 746, 215 (2004) nucl-th/0401016.

    Article  ADS  Google Scholar 

  38. P. Navratil, J.P. Vary, B.R. Barrett, Phys. Rev. Lett. 84, 5728 (2000) nucl-th/0004058.

    Article  ADS  Google Scholar 

  39. M.S. Fayache, J.P. Vary, B.R. Barrett, P. Navratil, S. Aroua, nucl-th/0112066 (2001).

  40. P. Navratil, W.E. Ormand, Phys. Rev. C 68, 034305 (2003) nucl-th/0305090.

    Article  ADS  Google Scholar 

  41. E. Caurier, P. Navratil, Phys. Rev. C 73, 021302 (2006) nucl-th/0512015.

    Article  ADS  Google Scholar 

  42. C. Forssen, P. Navratil, W.E. Ormand, E. Caurier, Phys. Rev. C 71, 044312 (2005) nucl-th/0412049.

    Article  ADS  Google Scholar 

  43. A. Nogga, P. Navratil, B.R. Barrett, J.P. Vary, Phys. Rev. C 73, 064002 (2006) nucl-th/0511082.

    Article  ADS  Google Scholar 

  44. I. Stetcu, B.R. Barrett, U. van Kolck, nucl-th/0609023 (2006).

  45. H. Kamada, Phys. Rev. C 64, 044001 (2001) nucl-th/0104057.

    Article  ADS  Google Scholar 

  46. J. Carlson, R. Schiavilla, Rev. Mod. Phys. 70, 743 (1998).

    Article  ADS  Google Scholar 

  47. H.M. Müller, S.E. Koonin, R. Seki, U. van Kolck, Phys. Rev. C 61, 044320 (2000) nucl-th/9910038.

    Article  ADS  Google Scholar 

  48. D. Lee, B. Borasoy, T. Schäfer, Phys. Rev. C 70, 014007 (2004) nucl-th/0402072.

    Article  ADS  Google Scholar 

  49. J. Hubbard, Phys. Rev. Lett. 3, 77 (1959).

    Article  ADS  Google Scholar 

  50. R.L. Stratonovich, Sov. Phys. Dokl. 2, 416 (1958).

    ADS  Google Scholar 

  51. S. Duane, A.D. Kennedy, B.J. Pendleton, D. Roweth, Phys. Lett. B 195, 216 (1987).

    Article  ADS  Google Scholar 

  52. B. Borasoy, H. Krebs, D. Lee, U.-G. Meißner, Nucl. Phys. A 768, 179 (2006) nucl-th/0510047.

    Article  MathSciNet  ADS  Google Scholar 

  53. E. Jenkins, A.V. Manohar, Phys. Lett. B 255, 558 (1991).

    Article  ADS  Google Scholar 

  54. V. Bernard, N. Kaiser, J. Kambor, U.G. Meißner, Nucl. Phys. B 388, 315 (1992).

    Article  ADS  Google Scholar 

  55. T. Becher, H. Leutwyler, Eur. Phys. J. C 9, 643 (1999) hep-ph/9901384.

    Article  ADS  Google Scholar 

  56. S. Weinberg, Phys. Lett. B 251, 288 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  57. S. Weinberg, Nucl. Phys. B 363, 3 (1991).

    Article  ADS  Google Scholar 

  58. E. Epelbaum, Dissertation Jülich (2000).

  59. D. Lee, Phys. Rev. C 70, 064002 (2004) nucl-th/0407088.

    Article  ADS  Google Scholar 

  60. E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 637, 107 (1998) nucl-th/9801064.

    Article  ADS  Google Scholar 

  61. H. Krebs, V. Bernard, U.-G. Meißner, Ann. Phys. 316, 160 (2005) nucl-th/0407078.

    Article  ADS  Google Scholar 

  62. C. Ordonez, L. Ray, U. van Kolck, Phys. Rev. C 53, 2086 (1996) hep-ph/9511380.

    Article  ADS  Google Scholar 

  63. N. Kaiser, R. Brockmann, W. Weise, Nucl. Phys. A 625, 758 (1997) nucl-th/9706045.

    Article  ADS  Google Scholar 

  64. M. Creutz, Phys. Rev. D 38, 1228 (1988).

    Article  ADS  Google Scholar 

  65. M. Creutz, Found. Phys. 30, 487 (2000) hep-lat/9905024.

    Article  MathSciNet  Google Scholar 

  66. C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950).

    MathSciNet  Google Scholar 

  67. M. Lüscher, Commun. Math. Phys. 105, 153 (1986).

    Article  ADS  Google Scholar 

  68. R. Seki, U. van Kolck, Phys. Rev. C 73, 044006 (2006) nucl-th/0509094.

    Article  ADS  Google Scholar 

  69. E. Epelbaum, U.G. Meißner, W. Glöckle, C. Elster, Phys. Rev. C 65, 044001 (2002) nucl-th/0106007.

    Article  ADS  Google Scholar 

  70. D. Lee, Phys. Rev. A 73, 063204 (2006) physics/0512085.

    Article  ADS  Google Scholar 

  71. C. Wu, J. Hu, S.-C. Zhang, Phys. Rev. Lett. 91, 186402 (2003) cond-mat/0302165.

    Article  ADS  Google Scholar 

  72. C. Wu, Phys. Rev. Lett. 95, 266404 (2005) cond-mat/0409247.

    Article  ADS  Google Scholar 

  73. D. Lee, T. Schäfer, Phys. Rev. C 73, 015202 (2006) nucl-th/0509018.

    Article  ADS  Google Scholar 

  74. L.H. Thomas, Phys. Rev. 47, 903 (1935).

    Article  ADS  Google Scholar 

  75. V.N. Efimov, Sov. J. Nucl. Phys. 12, 589 (1971).

    Google Scholar 

  76. V.N. Efimov, Phys. Rev. C 47, 1876 (1993).

    Article  ADS  Google Scholar 

  77. P.F. Bedaque, H.-W. Hammer, U. van Kolck, Phys. Rev. Lett. 82, 463 (1999) nucl-th/9809025.

    Article  ADS  Google Scholar 

  78. P.F. Bedaque, H.-W. Hammer, U. van Kolck, Nucl. Phys. A 646, 444 (1999) nucl-th/9811046.

    Article  ADS  Google Scholar 

  79. P.F. Bedaque, H.-W. Hammer, U. van Kolck, Nucl. Phys. A 676, 357 (2000) nucl-th/9906032.

    Article  ADS  Google Scholar 

  80. E. Braaten, H.-W. Hammer, Phys. Rep. 428, 259 (2006).

    Article  MathSciNet  ADS  Google Scholar 

  81. L. Platter, Phys. Rev. C 74, 037001 (2006) nucl-th/ 0606006.

    Article  ADS  Google Scholar 

  82. L. Platter, H.-W. Hammer, U.-G. Meißner, Phys. Rev. A 70, 052101 (2004) cond-mat/0404313.

    Article  ADS  Google Scholar 

  83. L. Platter, H.-W. Hammer, U.-G. Meißner, Phys. Lett. B 607, 254 (2005) nucl-th/0409040.

    Article  ADS  Google Scholar 

  84. D. Lee, Phys. Rev. B 73, 115112 (2006) cond-mat/ 0511332.

    Article  ADS  Google Scholar 

  85. D. Lee, Phys. Rev. C 71, 044001 (2005) nucl-th/0407101.

    Article  ADS  Google Scholar 

  86. J.-W. Chen, D. Lee, T. Schäfer, Phys. Rev. Lett. 93, 242302 (2004) nucl-th/0408043.

    Article  ADS  Google Scholar 

  87. D. Lee, cond-mat/0606706.

  88. A. Amroun, Nucl. Phys. A 579, 596 (1994).

    Article  ADS  Google Scholar 

  89. L. Platter, H.W. Hammer, Nucl. Phys. A 766, 132 (2006) nucl-th/0509045.

    Article  ADS  Google Scholar 

  90. E. Borie, G.A. Rinker, Phys. Rev. A 18, 324 (1978).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Universität Bonn, Nußallee 14-16, D-53115, Bonn, Germany

    B. Borasoy, E. Epelbaum, H. Krebs & U. -G. Meißner

  2. Institut für Kernphysik (Theorie), Forschungszentrum Jülich, D-52425, Jülich, Germany

    E. Epelbaum, H. Krebs & U. -G. Meißner

  3. Department of Physics, North Carolina State University, 27603, Raleigh, NC, USA

    D. Lee

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  1. B. Borasoy
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  2. E. Epelbaum
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  3. H. Krebs
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  4. D. Lee
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  5. U. -G. Meißner
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Correspondence to B. Borasoy.

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A. Schäfer

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Borasoy, B., Epelbaum, E., Krebs, H. et al. Lattice simulations for light nuclei: Chiral effective field theory at leading order. Eur. Phys. J. A 31, 105–123 (2007). https://doi.org/10.1140/epja/i2006-10154-1

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