Skip to main content
SpringerLink
Log in

Uncertainties in constraining low-energy constants from 3H \( \beta\) decay

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

An Erratum to this article was published on 15 May 2018

This article has been updated

Abstract.

We discuss the uncertainties in constraining low-energy constants of chiral effective field theory from 3H \( \beta\) decay. The half-life is very precisely known, so that the Gamow-Teller matrix element has been used to fit the coupling \( c_D\) of the axial-vector current to a short-range two-nucleon pair. Because the same coupling also describes the leading one-pion-exchange three-nucleon force, this in principle provides a very constraining fit, uncorrelated with the 3H binding energy fit used to constrain another low-energy coupling in three-nucleon forces. However, so far such 3H half-life fits have only been performed at a fixed cutoff value. We show that the cutoff dependence due to the regulators in the axial-vector two-body current can significantly affect the Gamow-Teller matrix elements and consequently also the extracted values for the \( c_D\) coupling constant. The degree of the cutoff dependence is correlated with the softness of the employed NN interaction. As a result, present three-nucleon forces based on a fit to 3H \( \beta\) decay underestimate the uncertainty in \( c_D\) . We explore a range of \( c_D\) values that is compatible within cutoff variation with the experimental 3H half-life and estimate the resulting uncertainties for many-body systems by performing calculations of symmetric nuclear matter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Change history

  • 15 May 2018

    This erratum fixes an error in the use of the low-energy constant in the two-body currents. The corrected version of one of the equations and of some of the figures is reported.

References

  1. A. Gezerlis, I. Tews, E. Epelbaum, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. Lett. 111, 032501 (2013)

    Article  ADS  Google Scholar 

  2. A. Ekström, G.R. Jansen, K.A. Wendt, G. Hagen, T. Papenbrock, B.D. Carlsson, C. Forssén, M. Hjorth-Jensen, P. Navrátil, W. Nazarewicz, Phys. Rev. C 91, 051301(R) (2015)

    Article  ADS  Google Scholar 

  3. E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. Lett. 115, 122301 (2015)

    Article  ADS  Google Scholar 

  4. B.D. Carlsson, A. Ekström, C. Forssén, D.F. Strömberg, G.R. Jansen, O. Lilja, M. Lindby, B.A. Mattsson, K.A. Wendt, Phys. Rev. X 6, 011019 (2016)

    Google Scholar 

  5. E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Rev. Mod. Phys. 81, 1773 (2009)

    Article  ADS  Google Scholar 

  6. R. Machleidt, D.R. Entem, Phys. Rep. 503, 1 (2011)

    Article  ADS  Google Scholar 

  7. H.-W. Hammer, A. Nogga, A. Schwenk, Rev. Mod. Phys. 85, 197 (2013)

    Article  ADS  Google Scholar 

  8. S. Bacca, S. Pastore, J. Phys. G 41, 123002 (2014)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. D.R. Entem, N. Kaiser, R. Machleidt, Y. Nosyk, Phys. Rev. C 91, 014002 (2015)

    Article  ADS  Google Scholar 

  11. S. Ishikawa, M.R. Robilotta, Phys. Rev. C 76, 014006 (2007)

    Article  ADS  Google Scholar 

  12. V. Bernard, E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. C 77, 064004 (2008)

    Article  ADS  Google Scholar 

  13. V. Bernard, E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. C 84, 054001 (2011)

    Article  ADS  Google Scholar 

  14. E. Epelbaum, Phys. Lett. B 639, 456 (2006)

    Article  ADS  Google Scholar 

  15. H. Krebs, E. Epelbaum, U.G. Meißner, Ann. Phys. 378, 317 (2017)

    Article  ADS  Google Scholar 

  16. A. Baroni, L. Girlanda, S. Pastore, R. Schiavilla, M. Viviani, Phys. Rev. C 93, 015501 (2016)

    Article  ADS  Google Scholar 

  17. S. Kölling, E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. C 80, 045502 (2009)

    Article  ADS  Google Scholar 

  18. S. Kölling, E. Epelbaum, H. Krebs, U.-G. Meißner, Phys. Rev. C 84, 054008 (2011)

    Article  ADS  Google Scholar 

  19. S. Pastore, L. Girlanda, R. Schiavilla, M. Viviani, R.B. Wiringa, Phys. Rev. C 80, 034004 (2009)

    Article  ADS  Google Scholar 

  20. S. Pastore, L. Girlanda, R. Schiavilla, M. Viviani, Phys. Rev. C 84, 024001 (2011)

    Article  ADS  Google Scholar 

  21. M. Piarulli, L. Girlanda, L.E. Marcucci, S. Pastore, R. Schiavilla, M. Viviani, Phys. Rev. C 87, 014006 (2013)

    Article  ADS  Google Scholar 

  22. D. Gazit, S. Quaglioni, P. Navrá, Phys. Rev. Lett. 103, 102502 (2009)

    Article  ADS  Google Scholar 

  23. L.E. Marcucci, A. Kievsky, S. Rosati, R. Schiavilla, M. Viviani, Phys. Rev. Lett. 108, 052502 (2012)

    Article  ADS  Google Scholar 

  24. A. Ekström, G.R. Jansen, K.A. Wendt, G. Hagen, T. Papenbrock et al., Phys. Rev. Lett. 113, 262504 (2014)

    Article  ADS  Google Scholar 

  25. A. Baroni, L. Girlanda, A. Kievsky, L.E. Marcucci, R. Schiavilla, M. Viviani, Phys. Rev. C 94, 024003 (2016)

    Article  ADS  Google Scholar 

  26. K. Hebeler, S.K. Bogner, R.J. Furnstahl, A. Nogga, A. Schwenk, Phys. Rev. C 83, 031301(R) (2011)

    Article  ADS  Google Scholar 

  27. E. Epelbaum, A. Nogga, W. Glöckle, H. Kamada, U.-G. Meißner, H. Witała, Phys. Rev. C 66, 064001 (2002)

    Article  ADS  Google Scholar 

  28. J.E. Lynn, I. Tews, J. Carlson, S. Gandolfi, A. Gezerlis, K.E. Schmidt, A. Schwenk, Phys. Rev. Lett. 116, 062501 (2016)

    Article  ADS  Google Scholar 

  29. A. Gardestig, D.R. Phillips, Phys. Rev. Lett. 96, 232301 (2006)

    Article  ADS  Google Scholar 

  30. B.R. Barrett, P. Navrá, Prog. Part. Nucl. Phys. 69, 131 (2013)

    Article  ADS  Google Scholar 

  31. K. Hebeler, J.D. Holt, J. Menendez, A. Schwenk, Annu. Rev. Nucl. Part. Sci. 65, 457 (2015)

    Article  ADS  Google Scholar 

  32. P. Navrátil, S. Quaglioni, G. Hupin, C. Romero-Redondo, A. Calci, Phys. Scr. 91, 053002 (2016)

    Article  ADS  Google Scholar 

  33. H. Hergert, S.K. Bogner, S. Binder, A. Calci, J. Langhammer et al., Phys. Rev. C 87, 034307 (2013)

    Article  ADS  Google Scholar 

  34. S. Binder, J. Langhammer, A. Calci, R. Roth, Phys. Lett. B 736, 119 (2014)

    Article  ADS  Google Scholar 

  35. H. Hergert, S.K. Bogner, T.D. Morris, S. Binder, A. Calci, J. Langhammer, R. Roth, Phys. Rev. C 90, 041302(R) (2014)

    Article  ADS  Google Scholar 

  36. J. Hu, Y. Zhang, E. Epelbaum, U.-G. Meißner, J. Meng, arXiv:1612.05433

  37. G. Hagen et al., Nat. Phys. 12, 186 (2016)

    Article  Google Scholar 

  38. J. Simonis, K. Hebeler, J.D. Holt, J. Menéndez, A. Schwenk, Phys. Rev. C 93, 011302(R) (2016)

    Article  ADS  Google Scholar 

  39. J. Simonis, S.R. Stroberg, K. Hebeler, J.D. Holt, A. Schwenk, Phys. Rev. C 96, 014303 (2017)

    Article  ADS  Google Scholar 

  40. C. Drischler, K. Hebeler, A. Schwenk, Phys. Rev. C 93, 054314 (2016)

    Article  ADS  Google Scholar 

  41. R.F. Garcia Ruiz et al., Nat. Phys. 12, 594 (2016)

    Article  Google Scholar 

  42. G. Hagen, G.R. Jansen, T. Papenbrock, Phys. Rev. Lett. 117, 172501 (2016)

    Article  ADS  Google Scholar 

  43. J. Birkhan et al., Phys. Rev. Lett. 118, 252501 (2017)

    Article  ADS  Google Scholar 

  44. D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001(R) (2003)

    Article  ADS  Google Scholar 

  45. P. Navrátil, Few Body Syst. 41, 117 (2007)

    Article  ADS  Google Scholar 

  46. I. Tews, S. Gandolfi, A. Gezerlis, A. Schwenk, Phys. Rev. C 93, 024305 (2016)

    Article  ADS  Google Scholar 

  47. A. Dyhdalo, R.J. Furnstahl, K. Hebeler, I. Tews, Phys. Rev. C 94, 034001 (2016)

    Article  ADS  Google Scholar 

  48. L. Coraggio, J.W. Holt, N. Itaco, R. Machleidt, L.E. Marcucci, F. Sammarruca, Phys. Rev. C 89, 044321 (2014)

    Article  ADS  Google Scholar 

  49. F. Sammarruca, L. Coraggio, J.W. Holt, N. Itaco, R. Machleidt, L.E. Marcucci, Phys. Rev. C 91, 054311 (2015)

    Article  ADS  Google Scholar 

  50. R. Schiavilla et al., Phys. Rev. C 58, 1263 (1998)

    Article  ADS  Google Scholar 

  51. S. Raman, C.A. Houser, T.A. Walkiewicz, At. Data Nucl. Data Tables 21, 567 (1978)

    Article  ADS  Google Scholar 

  52. T.S. Park, L.E. Marcucci, R. Schiavilla, M. Viviani, A. Kievsky, S. Rosati, K. Kubodera, D.P. Min, M. Rho, Phys. Rev. C 67, 055206 (2003)

    Article  ADS  Google Scholar 

  53. S. Ando, T.S. Park, K. Kubodera, F. Myhrer, Phys. Lett. B 533, 25 (2002)

    Article  ADS  Google Scholar 

  54. M. Hoferichter, P. Klos, A. Schwenk, Phys. Lett. B 746, 410 (2015)

    Article  ADS  Google Scholar 

  55. A. Nogga, A. Kievsky, H. Kamada, W. Glöckle, L.E. Marcucci, S. Rosati, M. Viviani, Phys. Rev. C 67, 034004 (2003)

    Article  ADS  Google Scholar 

  56. D.R. Entem, R. Machleidt, Y. Nosyk, Phys. Rev. C 96, 024004 (2017)

    Article  ADS  Google Scholar 

  57. E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 747, 362 (2005)

    Article  ADS  Google Scholar 

  58. J. Hoppe, C. Drischler, R.J. Furnstahl, K. Hebeler, A. Schwenk, arXiv:1707.06438 (2017)

  59. E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006)

    Article  ADS  Google Scholar 

  60. A. Carbone, A. Rios, A. Polls, Phys. Rev. C 90, 054322 (2014)

    Article  ADS  Google Scholar 

  61. M. Dutra, O. Lourenço, J.S. Sá Martins, A. Delfino, J.R. Stone, P.D. Stevenson, Phys. Rev. C 85, 035201 (2012)

    Article  ADS  Google Scholar 

  62. E. Epelbaum, H. Krebs, U.-G. Meißner, Eur. Phys. J. A 51, 53 (2015)

    Article  ADS  Google Scholar 

  63. S. Binder et al., Phys. Rev. C 93, 044002 (2016)

    Article  ADS  Google Scholar 

  64. A. Carbone, A. Cipollone, C. Barbieri, A. Rios, A. Polls, Phys. Rev. C 88, 054326 (2013)

    Article  ADS  Google Scholar 

  65. M.P. Valderrama, D.R. Phillips, Phys. Rev. Lett. 114, 082502 (2015)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Kernphysik, Technische Universität Darmstadt, 64289, Darmstadt, Germany

    P. Klos, A. Carbone, K. Hebeler & A. Schwenk

  2. ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291, Darmstadt, Germany

    P. Klos, A. Carbone, K. Hebeler & A. Schwenk

  3. Department of Physics, University of Tokyo, Hongo, 113-0033, Tokyo, Japan

    J. Menéndez

  4. Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117, Heidelberg, Germany

    A. Schwenk

Authors
  1. P. Klos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Carbone
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Hebeler
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Menéndez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Schwenk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Klos.

Additional information

Communicated by U.-G. Meißner

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klos, P., Carbone, A., Hebeler, K. et al. Uncertainties in constraining low-energy constants from 3H \( \beta\) decay. Eur. Phys. J. A 53, 168 (2017). https://doi.org/10.1140/epja/i2017-12357-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/i2017-12357-7

Search

Navigation