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

  • Regular Article - Theoretical Physics
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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.

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References

  1. Y. Nakahara, M. Asakawa, T. Hatsuda, Phys. Rev. D 60, 091503 (1999)

    Article  ADS  Google Scholar 

  2. K. Sasaki, S. Sasaki, T. Hatsuda, Phys. Lett. B 623, 208 (2005)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  7. J. Foley, J. Bulava, K.J. Juge, C. Morningstar, M. Peardon, C.H. Wong, AIP Conf. Proc. 1257, 789 (2010)

    Article  ADS  Google Scholar 

  8. M.G. Alford, R.L. Jaffe, Nucl. Phys. B 578, 367 (2000)

    Article  ADS  Google Scholar 

  9. SCALAR Collaboration (T. Kunihiro et al.), Phys. Rev. D 70, 034504 (2004)

    Article  ADS  Google Scholar 

  10. F. Okiharu, T. Doi, H. Ichie, H. Iida, N. Ishii, M. Oka, H. Suganuma, T.T. Takahashi, hep-ph/0507187

  11. H. Suganuma, K. Tsumura, N. Ishii, F. Okiharu, PoS LAT 2005, 070 (2006)

    Google Scholar 

  12. H. Suganuma, K. Tsumura, N. Ishii, F. Okiharu, Prog. Theor. Phys. Suppl. 168, 168 (2007)

    Article  ADS  Google Scholar 

  13. UKQCD Collaboration (C. McNeile, C. Michael), Phys. Rev. D 74, 014508 (2006)

    Article  ADS  Google Scholar 

  14. UKQCD Collaboration (A. Hart et al.), Phys. Rev. D 74, 114504 (2006)

    Article  ADS  Google Scholar 

  15. H. Wada, T. Kunihiro, S. Muroya, A. Nakamura, C. Nonaka, M. Sekiguchi, Phys. Lett. B 652, 250 (2007)

    Article  ADS  Google Scholar 

  16. S. Prelovsek, C. Dawson, T. Izubuchi, K. Orginos, A. Soni, Phys. Rev. D 70, 094503 (2004)

    Article  ADS  Google Scholar 

  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. S. Prelovsek, T. Draper, C.B. Lang, M. Limmer, K.-F. Liu, N. Mathur, D. Mohler, Phys. Rev. D 82, 094507 (2010)

    Article  ADS  Google Scholar 

  19. Hadron Spectrum Collaboration (H.-W. Lin et al.), Phys. Rev. D 79, 034502 (2009)

    Article  ADS  Google Scholar 

  20. C. Gattringer, C. Hagen, C.B. Lang, M. Limmer, D. Mohler, A. Schäfer, Phys. Rev. D 79, 054501 (2009)

    Article  ADS  Google Scholar 

  21. BGR (Bern-Graz-Regensburg) Collaboration (G.P. Engel et al.), Phys. Rev. D 82, 034505 (2010)

    Article  ADS  Google Scholar 

  22. M.S. Mahbub, W. Kamleh, D.B. Leinweber, A.O. Cais, A.G. Williams, Phys. Lett. B 693, 351 (2010)

    Article  ADS  Google Scholar 

  23. B.J. Menadue, W. Kamleh, D.B. Leinweber, M.S. Mahbub, Phys. Rev. Lett. 108, 112001 (2012)

    Article  ADS  Google Scholar 

  24. R.G. Edwards, J.J. Dudek, D.G. Richards, S.J. Wallace, Phys. Rev. D 84, 074508 (2011)

    Article  ADS  Google Scholar 

  25. S. Prelovsek, C.B. Lang, D. Mohler, M. Vidmar, PoS LATTICE 2011, 137 (2011)

    Google Scholar 

  26. Z. Fu, JHEP 01, 017 (2012)

    Article  ADS  Google Scholar 

  27. C.B. Lang, L. Leskovec, D. Mohler, S. Prelovsek, arXiv:1207.3204 [hep-lat]

  28. V. Bernard, U.-G. Meißner, A. Rusetsky, Nucl. Phys. B 788, 1 (2008)

    Article  ADS  Google Scholar 

  29. V. Bernard, M. Lage, U.-G. Meißner, A. Rusetsky, JHEP 08, 024 (2008)

    Article  ADS  Google Scholar 

  30. V. Bernard, D. Hoja, U.-G. Meißner, A. Rusetsky, JHEP 06, 2009 (061)

    Google Scholar 

  31. V. Bernard, M. Lage, U.-G. Meißner, A. Rusetsky, JHEP 01, 019 (2011)

    Article  ADS  Google Scholar 

  32. M. Döring, U.-G. Meißner, E. Oset, A. Rusetsky, Eur. Phys. J. A 47, 131 (2011)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. M. Lüscher, Nucl. Phys. B 354, 531 (1991)

    Article  ADS  Google Scholar 

  35. S. He, X. Feng, C. Liu, JHEP 07, 011 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  36. C. Liu, X. Feng, S. He, Int. J. Mod. Phys. A 21, 847 (2006)

    Article  ADS  MATH  Google Scholar 

  37. M. Lage, U.-G. Meißner, A. Rusetsky, Phys. Lett. B 681, 439 (2009)

    Article  ADS  Google Scholar 

  38. K. Polejaeva, A. Rusetsky, arXiv:1203.1241 [hep-lat]

  39. S. Kreuzer, H.W. Grießhammer, Eur. Phys. J. A 48, 93 (2012)

    Article  ADS  Google Scholar 

  40. M. Döring, J. Haidenbauer, U.-G. Meißner, A. Rusetsky, Eur. Phys. J. A 47, 163 (2011)

    Article  ADS  Google Scholar 

  41. M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, Phys. Lett. B 681, 26 (2009)

    Article  ADS  Google Scholar 

  42. M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, Nucl. Phys. A 829, 170 (2009)

    Article  ADS  Google Scholar 

  43. M. Döring, C. Hanhart, F. Huang, S. Krewald, U.-G. Meißner, D. Rönchen, Nucl. Phys. A 851, 58 (2011)

    Article  ADS  Google Scholar 

  44. A. Martinez Torres, L.R. Dai, C. Koren, D. Jido, E. Oset, Phys. Rev. D 85, 014027 (2012)

    Article  ADS  Google Scholar 

  45. M. Döring, U.-G. Meißner, JHEP 01, 009 (2012)

    Article  Google Scholar 

  46. L. Roca, E. Oset, Phys. Rev. D 85, 054507 (2012)

    Article  ADS  Google Scholar 

  47. J.-J. Xie, E. Oset, arXiv:1201.0149 [hep-ph]

  48. H.-X. Chen, E. Oset, arXiv:1202.2787 [hep-lat]

  49. A. Martinez Torres, M. Bayar, D. Jido, E. Oset, arXiv:1202.4297 [hep-lat]

  50. V. Bernard, D. Hoja, U.-G. Meißner, A. Rusetsky, arXiv:1205.4642 [hep-lat]

  51. K. Rummukainen, S.A. Gottlieb, Nucl. Phys. B 450, 397 (1995)

    Article  ADS  Google Scholar 

  52. C.H. Kim, C.T. Sachrajda, S.R. Sharpe, Nucl. Phys. B 727, 218 (2005)

    Article  ADS  Google Scholar 

  53. S. Bour, S. König, D. Lee, H.-W. Hammer, U.-G. Meißner, Phys. Rev. D 84, 091503 (2011)

    Article  ADS  Google Scholar 

  54. NPLQCD Collaboration (S.R. Beane et al.), Phys. Rev. D 85, 034505 (2012)

    Article  ADS  Google Scholar 

  55. Z. Davoudi, M.J. Savage, Phys. Rev. D 84, 114502 (2011)

    Article  ADS  Google Scholar 

  56. Z. Fu, Phys. Rev. D 85, 014506 (2012)

    Article  ADS  Google Scholar 

  57. L. Leskovec, S. Prelovsek, arXiv:1202.2145 [hep-lat]

  58. J.J. Dudek, R.G. Edwards, C.E. Thomas, arXiv:1203.6041 [hep-ph]

  59. M.T. Hansen, S.R. Sharpe, arXiv:1204.0826 [hep-lat]

  60. R.A. Briceño, Z. Davoudi, arXiv:1204.1110 [hep-lat]

  61. J.A. Oller, U.-G. Meißner, Phys. Lett. B 500, 263 (2001)

    Article  ADS  Google Scholar 

  62. J.A. Oller, E. Oset, J.R. Pelaez, Phys. Rev. D 59, 074001 (1999) 60

    Article  ADS  Google Scholar 

  63. J.A. Oller, E. Oset, Nucl. Phys. A 620, 438 (1997) 652

    Article  ADS  Google Scholar 

  64. M. Döring, in preparation

  65. J. Nieves, E. Ruiz Arriola, Phys. Rev. D 64, 116008 (2001)

    Article  ADS  Google Scholar 

  66. B. Borasoy, P.C. Bruns, U.-G. Meißner, R. Nißler, Eur. Phys. J. A 34, 161 (2007)

    Article  ADS  Google Scholar 

  67. P. C. Bruns, M. Mai, U.-G. Meißner, Phys. Lett. B 697, 254 (2011)

    Article  ADS  Google Scholar 

  68. A. Dobado, J.R. Pelaez, Phys. Rev. D 56, 3057 (1997)

    Article  ADS  Google Scholar 

  69. J. Nieves, M. Pavon Valderrama, E. Ruiz Arriola, Phys. Rev. D 65, 036002 (2002)

    Article  ADS  Google Scholar 

  70. A. Gomez Nicola, J.R. Pelaez, Phys. Rev. D 65, 054009 (2002)

    Article  ADS  Google Scholar 

  71. C. Hanhart, J.R. Pelaez, G. Rios, Phys. Rev. Lett. 100, 152001 (2008)

    Article  ADS  Google Scholar 

  72. J. Nebreda, J.R. Pelaez, Phys. Rev. D 81, 054035 (2010)

    Article  ADS  Google Scholar 

  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. T. Luu, M.J. Savage, Phys. Rev. D 83, 114508 (2011)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  76. J.A. Oller, E. Oset, Phys. Rev. D 60, 074023 (1999)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  79. R. Garcia-Martin, R. Kaminski, J.R. Pelaez, J. Ruiz de Elvira, F.J. Yndurain, Phys. Rev. D 83, 074004 (2011)

    Article  ADS  Google Scholar 

  80. I. Caprini, G. Colangelo, J. Gasser, H. Leutwyler, Phys. Rev. D 68, 074006 (2003)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, Nußallee 14-16, D-53115, Bonn, Germany

    M. Döring, U. -G. Meißner & A. Rusetsky

  2. Forschungszentrum Jülich, Jülich Center for Hadron Physics, Institut für Kernphysik (IKP-3) and Institute for Advanced Simulation (IAS-4), D-52425, Jülich, Germany

    U. -G. Meißner

  3. Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigación de Paterna, Aptdo. 22085, 46071, Valencia, Spain

    E. Oset

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  1. M. Döring
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  2. U. -G. Meißner
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  3. E. Oset
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Communicated by H. Wittig

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Döring, M., Meißner, U.G., Oset, E. et al. Scalar mesons moving in a finite volume and the role of partial wave mixing. Eur. Phys. J. A 48, 114 (2012). https://doi.org/10.1140/epja/i2012-12114-6

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