The DN, πΣc interaction in finite volume and the Λc(2595) resonance

Regular Article - Theoretical Physics

Abstract

In this work the interaction of the coupled channels DN and πΣc in an SU(4) extrapolation of the chiral unitary theory, where the Λc(2595) resonance appears as dynamically generated from that interaction, is extended to produce results in finite volume. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the phase shifts in the infinite volume from the lattice results is solved. We observe that it is possible to obtain accurate πΣc phase shifts and the position of the Λc(2595) resonance, but it requires the explicit consideration of the two coupled channels. We also observe that some of the energy levels in the box are attached to the closed DN channel, such that their use to induce the πΣc phase shifts via Lüscher's formula leads to incorrect results.

References

  1. 1.
    Y. Nakahara, M. Asakawa, T. Hatsuda, Phys. Rev. D 60, 091503 (1999).ADSCrossRefGoogle Scholar
  2. 2.
    K. Sasaki, S. Sasaki, T. Hatsuda, Phys. Lett. B 623, 208 (2005).ADSCrossRefGoogle Scholar
  3. 3.
    N. Mathur, A. Alexandru, Y. Chen et al., Phys. Rev. D 76, 114505 (2007).ADSCrossRefGoogle Scholar
  4. 4.
    S. Basak, R.G. Edwards, G.T. Fleming et al., Phys. Rev. D 76, 074504 (2007).ADSCrossRefGoogle Scholar
  5. 5.
    J. Bulava, R.G. Edwards, E. Engelson et al., Phys. Rev. D 82, 014507 (2010).ADSCrossRefGoogle Scholar
  6. 6.
    C. Morningstar, A. Bell, J. Bulava et al., AIP Conf. Proc. 1257, 779 (2010).ADSCrossRefGoogle Scholar
  7. 7.
    J. Foley, J. Bulava, K.J. Juge et al., AIP Conf. Proc. 1257, 789 (2010).ADSCrossRefGoogle Scholar
  8. 8.
    M.G. Alford, R.L. Jaffe, Nucl. Phys. B 578, 367 (2000).ADSCrossRefGoogle Scholar
  9. 9.
    SCALAR Collaboration (T. Kunihiro, S. Muroya, A. Nakamura, C. Nonaka, M. Sekiguchi, H. Wada), Phys. Rev. D 70, 034504 (2004).ADSCrossRefGoogle Scholar
  10. 10.
  11. 11.
    H. Suganuma, K. Tsumura, N. Ishii, F. Okiharu, PoS LAT2005, 070 (2006).Google Scholar
  12. 12.
    H. Suganuma, K. Tsumura, N. Ishii, F. Okiharu, Prog. Theor. Phys. Suppl. 168, 168 (2007).ADSCrossRefGoogle Scholar
  13. 13.
    UKQCD Collaboration (C. McNeile, C. Michael), Phys. Rev. D 74, 014508 (2006).ADSCrossRefGoogle Scholar
  14. 14.
    UKQCD Collaboration (A. Hart, C. McNeile, C. Michael, J. Pickavance), Phys. Rev. D 74, 114504 (2006).ADSCrossRefGoogle Scholar
  15. 15.
    H. Wada, T. Kunihiro, S. Muroya, A. Nakamura, C. Nonaka, M. Sekiguchi, Phys. Lett. B 652, 250 (2007).ADSCrossRefGoogle Scholar
  16. 16.
    S. Prelovsek, C. Dawson, T. Izubuchi, K. Orginos, A. Soni, Phys. Rev. D 70, 094503 (2004).ADSCrossRefGoogle Scholar
  17. 17.
    S. Prelovsek, T. Draper, C.B. Lang, M. Limmer, K.F. Liu, N. Mathur, D. Mohler, Conf. Proc. C 0908171, 508 (2009).Google Scholar
  18. 18.
    S. Prelovsek, T. Draper, C.B. Lang, M. Limmer, K.F. Liu, N. Mathur, D. Mohler, Phys. Rev. D 82, 094507 (2010).ADSCrossRefGoogle Scholar
  19. 19.
    Hadron Spectrum Collaboration (H.-W. Lin et al.), Phys. Rev. D 79, 034502 (2009).ADSCrossRefGoogle Scholar
  20. 20.
    C. Gattringer, C. Hagen, C.B. Lang, M. Limmer, D. Mohler, A. Schafer, Phys. Rev. D 79, 054501 (2009).ADSCrossRefGoogle Scholar
  21. 21.
    BGR (Bern-Graz-Regensburg) Collaboration (G.P. Engel et al.), Phys. Rev. D 82, 034505 (2010).ADSCrossRefGoogle Scholar
  22. 22.
    M.S. Mahbub, W. Kamleh, D.B. Leinweber, A.O Cais, A.G. Williams, Phys. Lett. B 693, 351 (2010).ADSCrossRefGoogle Scholar
  23. 23.
    R.G. Edwards, J.J. Dudek, D.G. Richards, S.J. Wallace, Phys. Rev. D 84, 074508 (2011).ADSCrossRefGoogle Scholar
  24. 24.
    V. Bernard, U.-G. Meissner, A. Rusetsky, Nucl. Phys. B 788, 1 (2008).ADSCrossRefGoogle Scholar
  25. 25.
    V. Bernard, M. Lage, U.-G. Meissner, A. Rusetsky, JHEP 08, 024 (2008).ADSCrossRefGoogle Scholar
  26. 26.
    M. Döring, U.-G. Meissner, E. Oset, A. Rusetsky, Eur. Phys. J. A 47, 139 (2011).ADSCrossRefGoogle Scholar
  27. 27.
    M. Lüscher, Commun. Math. Phys. 105, 153 (1986).ADSCrossRefGoogle Scholar
  28. 28.
    M. Lüscher, Nucl. Phys. B 354, 531 (1991).ADSCrossRefGoogle Scholar
  29. 29.
    C. Liu, X. Feng, S. He, Int. J. Mod. Phys. A 21, 847 (2006).ADSCrossRefMATHGoogle Scholar
  30. 30.
    M. Lage, U.-G. Meissner, A. Rusetsky, Phys. Lett. B 681, 439 (2009).ADSCrossRefGoogle Scholar
  31. 31.
    V. Bernard, M. Lage, U.-G. Meissner, A. Rusetsky, JHEP 01, 019 (2011).ADSCrossRefGoogle Scholar
  32. 32.
    M.T. Hansen, S.R. Sharpe, Phys. Rev. D 86, 016007 (2012).ADSCrossRefGoogle Scholar
  33. 33.
    R.A. Briceno, Z. Davoudi, arXiv: 1204.1110 [hep-lat].Google Scholar
  34. 34.
    M. Doring, J. Haidenbauer, U.-G. Meissner, A. Rusetsky, Eur. Phys. J. A 47, 163 (2011).ADSCrossRefGoogle Scholar
  35. 35.
    A. Martinez Torres, L.R. Dai, C. Koren, D. Jido, E. Oset, Phys. Rev. D 85, 014027 (2012).ADSCrossRefGoogle Scholar
  36. 36.
    E.E. Kolomeitsev, M.F.M. Lutz, Phys. Lett. B 582, 39 (2004).ADSCrossRefGoogle Scholar
  37. 37.
    J. Hofmann, M.F.M. Lutz, Nucl. Phys. A 733, 142 (2004).ADSCrossRefGoogle Scholar
  38. 38.
    F.-K. Guo, P.-N. Shen, H.-C. Chiang, R.-G. Ping, B.-S. Zou, Phys. Lett. B 641, 278 (2006).ADSCrossRefGoogle Scholar
  39. 39.
    D. Gamermann, E. Oset, D. Strottman, M.J. Vicente Vacas, Phys. Rev. D 76, 074016 (2007).ADSCrossRefGoogle Scholar
  40. 40.
    M. Doring, U.G. Meissner, JHEP 01, 009 (2012).ADSCrossRefGoogle Scholar
  41. 41.
    J. Hofmann, M.F.M. Lutz, Nucl. Phys. A 763, 90 (2005).ADSCrossRefGoogle Scholar
  42. 42.
    T. Mizutani, A. Ramos, Phys. Rev. C 74, 065201 (2006).ADSCrossRefGoogle Scholar
  43. 43.
    L. Tolos, A. Ramos, T. Mizutani, Phys. Rev. C 77, 015207 (2008).ADSCrossRefGoogle Scholar
  44. 44.
    C. Garcia-Recio, V.K. Magas, T. Mizutani, J. Nieves, A. Ramos, L.L. Salcedo, L. Tolos, Phys. Rev. D 79, 054004 (2009).ADSCrossRefGoogle Scholar
  45. 45.
  46. 46.
    Jia-Jun Wu, R. Molina, E. Oset, Bing-Song Zou, Phys. Rev. Lett. 105, 232001 (2010).ADSCrossRefGoogle Scholar
  47. 47.
    D. Gamermann, J. Nieves, E. Oset, E. Ruiz Arriola, Phys. Rev. D 81, 014029 (2010).ADSCrossRefGoogle Scholar
  48. 48.
    S. Weinberg, Phys. Rev. 137, B677 (1965).MathSciNetCrossRefGoogle Scholar
  49. 49.
    T. Sekihara, T. Hyodo, D. Jido, Phys. Rev. C 83, 055202 (2011).ADSCrossRefGoogle Scholar
  50. 50.
    J.A. Oller, E. Oset, Nucl. Phys. A 620, 438 (1997).ADSCrossRefGoogle Scholar
  51. 51.
    J.A. Oller, U.G. Meissner, Phys. Lett. B 500, 263 (2001).ADSCrossRefGoogle Scholar
  52. 52.
    For tabulated numbers and further references see, e.g., the On-Line Encyclopedia of Integer Sequences, http://oeis.org/A005875.
  53. 53.
    J.A. Oller, E. Oset, J.R. Pelaez, Phys. Rev. D 59, 074001 (1999) 60.ADSCrossRefGoogle Scholar
  54. 54.
    K. Polejaeva, A. Rusetsky, Eur. Phys. J. A 48, 67 (2012).ADSCrossRefGoogle Scholar
  55. 55.
    Particle Data Group (J. Beringer et al.), Phys. Rev. D 86, 010001 (2012).ADSCrossRefGoogle Scholar
  56. 56.
    L. Castillejo, R.H. Dalitz, F.J. Dyson, Phys. Rev. 101, 453 (1956).ADSCrossRefMATHGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of PhysicsZhengzhou UniversityHenanChina
  2. 2.Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSICInstitutos de Investigación de PaternaValenciaSpain

Personalised recommendations