Scalar mesons moving in a finite volume and the role of partial wave mixing

  • M. Döring
  • U. -G. Meißner
  • E. Oset
  • A. Rusetsky
Regular Article - Theoretical Physics

Abstract

Phase shifts and resonance parameters can be obtained from finite-volume lattice spectra for interacting pairs of particles, moving with non-zero total momentum. We present a simple derivation of the method that is subsequently applied to obtain the ππ and πK phase shifts in the sectors with total isospin I = 0 and I = 1/2 , respectively. Considering different total momenta, one obtains extra data points for a given volume that allow for a very efficient extraction of the resonance parameters in the infinite-volume limit. Corrections due to the mixing of partial waves are provided. We expect that our results will help to optimize the strategies in lattice simulations, which aim at an accurate determination of the scattering and resonance properties.

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, S.J. Dong, T. Draper, I. Horvath, F.X. Lee, K.F. Liu et al., Phys. Rev. D 76, 114505 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    S. Basak, R.G. Edwards, G.T. Fleming, K.J. Juge, A. Lichtl, C. Morningstar, D.G. Richards, I. Sato et al., Phys. Rev. D 76, 074504 (2007)ADSCrossRefGoogle Scholar
  5. 5.
    J. Bulava, R.G. Edwards, E. Engelson, B. Joo, H-W. Lin, C. Morningstar, D.G. Richards, S.J. Wallace, Phys. Rev. D 82, 014507 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    C. Morningstar, A. Bell, J. Bulava, E. Engelson, J. Foley, K.J. Juge, D. Lenkner, M. Peardon et al., AIP Conf. Proc. 1257, 779 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    J. Foley, J. Bulava, K.J. Juge, C. Morningstar, M. Peardon, C.H. Wong, 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 et al.), Phys. Rev. D 70, 034504 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    F. Okiharu, T. Doi, H. Ichie, H. Iida, N. Ishii, M. Oka, H. Suganuma, T.T. Takahashi, hep-ph/0507187Google Scholar
  11. 11.
    H. Suganuma, K. Tsumura, N. Ishii, F. Okiharu, PoS LAT 2005, 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 et al.), 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. Schäfer, 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.
    B.J. Menadue, W. Kamleh, D.B. Leinweber, M.S. Mahbub, Phys. Rev. Lett. 108, 112001 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    R.G. Edwards, J.J. Dudek, D.G. Richards, S.J. Wallace, Phys. Rev. D 84, 074508 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    S. Prelovsek, C.B. Lang, D. Mohler, M. Vidmar, PoS LATTICE 2011, 137 (2011)Google Scholar
  26. 26.
    Z. Fu, JHEP 01, 017 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    C.B. Lang, L. Leskovec, D. Mohler, S. Prelovsek, arXiv:1207.3204 [hep-lat]
  28. 28.
    V. Bernard, U.-G. Meißner, A. Rusetsky, Nucl. Phys. B 788, 1 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    V. Bernard, M. Lage, U.-G. Meißner, A. Rusetsky, JHEP 08, 024 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    V. Bernard, D. Hoja, U.-G. Meißner, A. Rusetsky, JHEP 06, 2009 (061)Google Scholar
  31. 31.
    V. Bernard, M. Lage, U.-G. Meißner, A. Rusetsky, JHEP 01, 019 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    M. Döring, U.-G. Meißner, E. Oset, A. Rusetsky, Eur. Phys. J. A 47, 131 (2011)CrossRefGoogle Scholar
  33. 33.
    M. Lüscher, Commun. Math. Phys. 105, 153 (1986)ADSCrossRefGoogle Scholar
  34. 34.
    M. Lüscher, Nucl. Phys. B 354, 531 (1991)ADSCrossRefGoogle Scholar
  35. 35.
    S. He, X. Feng, C. Liu, JHEP 07, 011 (2005)MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    C. Liu, X. Feng, S. He, Int. J. Mod. Phys. A 21, 847 (2006)ADSCrossRefMATHGoogle Scholar
  37. 37.
    M. Lage, U.-G. Meißner, A. Rusetsky, Phys. Lett. B 681, 439 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    K. Polejaeva, A. Rusetsky, arXiv:1203.1241 [hep-lat]
  39. 39.
    S. Kreuzer, H.W. Grießhammer, Eur. Phys. J. A 48, 93 (2012)ADSCrossRefGoogle Scholar
  40. 40.
    M. Döring, J. Haidenbauer, U.-G. Meißner, A. Rusetsky, Eur. Phys. J. A 47, 163 (2011)ADSCrossRefGoogle Scholar
  41. 41.
    M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, Phys. Lett. B 681, 26 (2009)ADSCrossRefGoogle Scholar
  42. 42.
    M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, Nucl. Phys. A 829, 170 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, D. Rönchen, Nucl. Phys. A 851, 58 (2011)ADSCrossRefGoogle Scholar
  44. 44.
    A. Martinez Torres, L.R. Dai, C. Koren, D. Jido, E. Oset, Phys. Rev. D 85, 014027 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    M. Döring, U.-G. Meißner, JHEP 01, 009 (2012)CrossRefGoogle Scholar
  46. 46.
    L. Roca, E. Oset, Phys. Rev. D 85, 054507 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    J.-J. Xie, E. Oset, arXiv:1201.0149 [hep-ph]
  48. 48.
    H.-X. Chen, E. Oset, arXiv:1202.2787 [hep-lat]
  49. 49.
    A. Martinez Torres, M. Bayar, D. Jido, E. Oset, arXiv:1202.4297 [hep-lat]
  50. 50.
    V. Bernard, D. Hoja, U.-G. Meißner, A. Rusetsky, arXiv:1205.4642 [hep-lat]
  51. 51.
    K. Rummukainen, S.A. Gottlieb, Nucl. Phys. B 450, 397 (1995)ADSCrossRefGoogle Scholar
  52. 52.
    C.H. Kim, C.T. Sachrajda, S.R. Sharpe, Nucl. Phys. B 727, 218 (2005)ADSCrossRefGoogle Scholar
  53. 53.
    S. Bour, S. König, D. Lee, H.-W. Hammer, U.-G. Meißner, Phys. Rev. D 84, 091503 (2011)ADSCrossRefGoogle Scholar
  54. 54.
    NPLQCD Collaboration (S.R. Beane et al.), Phys. Rev. D 85, 034505 (2012)ADSCrossRefGoogle Scholar
  55. 55.
    Z. Davoudi, M.J. Savage, Phys. Rev. D 84, 114502 (2011)ADSCrossRefGoogle Scholar
  56. 56.
    Z. Fu, Phys. Rev. D 85, 014506 (2012)ADSCrossRefGoogle Scholar
  57. 57.
    L. Leskovec, S. Prelovsek, arXiv:1202.2145 [hep-lat]
  58. 58.
    J.J. Dudek, R.G. Edwards, C.E. Thomas, arXiv:1203.6041 [hep-ph]
  59. 59.
    M.T. Hansen, S.R. Sharpe, arXiv:1204.0826 [hep-lat]
  60. 60.
    R.A. Briceño, Z. Davoudi, arXiv:1204.1110 [hep-lat]
  61. 61.
    J.A. Oller, U.-G. Meißner, Phys. Lett. B 500, 263 (2001)ADSCrossRefGoogle Scholar
  62. 62.
    J.A. Oller, E. Oset, J.R. Pelaez, Phys. Rev. D 59, 074001 (1999) 60ADSCrossRefGoogle Scholar
  63. 63.
    J.A. Oller, E. Oset, Nucl. Phys. A 620, 438 (1997) 652ADSCrossRefGoogle Scholar
  64. 64.
    M. Döring, in preparationGoogle Scholar
  65. 65.
    J. Nieves, E. Ruiz Arriola, Phys. Rev. D 64, 116008 (2001)ADSCrossRefGoogle Scholar
  66. 66.
    B. Borasoy, P.C. Bruns, U.-G. Meißner, R. Nißler, Eur. Phys. J. A 34, 161 (2007)ADSCrossRefGoogle Scholar
  67. 67.
    P. C. Bruns, M. Mai, U.-G. Meißner, Phys. Lett. B 697, 254 (2011)ADSCrossRefGoogle Scholar
  68. 68.
    A. Dobado, J.R. Pelaez, Phys. Rev. D 56, 3057 (1997)ADSCrossRefGoogle Scholar
  69. 69.
    J. Nieves, M. Pavon Valderrama, E. Ruiz Arriola, Phys. Rev. D 65, 036002 (2002)ADSCrossRefGoogle Scholar
  70. 70.
    A. Gomez Nicola, J.R. Pelaez, Phys. Rev. D 65, 054009 (2002)ADSCrossRefGoogle Scholar
  71. 71.
    C. Hanhart, J.R. Pelaez, G. Rios, Phys. Rev. Lett. 100, 152001 (2008)ADSCrossRefGoogle Scholar
  72. 72.
    J. Nebreda, J.R. Pelaez, Phys. Rev. D 81, 054035 (2010)ADSCrossRefGoogle Scholar
  73. 73.
    M. Göckeler, R. Horsley, M. Lage, U.-G. Meißner, P.E.L. Rakow, A. Rusetsky, G. Schierholz, J.M. Zanotti, arXiv:1206.4141 [hep-lat]
  74. 74.
    T. Luu, M.J. Savage, Phys. Rev. D 83, 114508 (2011)ADSCrossRefGoogle Scholar
  75. 75.
    D. Aston, N. Awaji, T. Bienz, F. Bird, J. D’Amore, W.M. Dunwoodie, R. Endorf, K. Fujii et al., Nucl. Phys. B 296, 493 (1988)ADSCrossRefGoogle Scholar
  76. 76.
    J.A. Oller, E. Oset, Phys. Rev. D 60, 074023 (1999)ADSCrossRefGoogle Scholar
  77. 77.
    R. Mercer, P. Antich, A. Callahan, C.Y. Chien, B. Cox, R. Carson, D. Denegri, L. Ettlinger et al., Nucl. Phys. B 32, 381 (1971)ADSCrossRefGoogle Scholar
  78. 78.
    P. Estabrooks, R.K. Carnegie, A.D. Martin, W.M. Dunwoodie, T.A. Lasinski, D.W.G.S. Leith, Nucl. Phys. B 133, 490 (1978)ADSCrossRefGoogle Scholar
  79. 79.
    R. Garcia-Martin, R. Kaminski, J.R. Pelaez, J. Ruiz de Elvira, F.J. Yndurain, Phys. Rev. D 83, 074004 (2011)ADSCrossRefGoogle Scholar
  80. 80.
    I. Caprini, G. Colangelo, J. Gasser, H. Leutwyler, Phys. Rev. D 68, 074006 (2003)ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • M. Döring
    • 1
  • U. -G. Meißner
    • 1
    • 2
  • E. Oset
    • 3
  • A. Rusetsky
    • 1
  1. 1.Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  2. 2.Forschungszentrum Jülich, Jülich Center for Hadron PhysicsInstitut für Kernphysik (IKP-3) and Institute for Advanced Simulation (IAS-4)JülichGermany
  3. 3.Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSICInstitutos de Investigación de PaternaValenciaSpain

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