Η → 3Π at Two Loops in Chiral Perturbation Theory (original) (raw)

Abstract

Abstract: We calculate the decay η → 3π at next-to-next-to-leading order or order p 6 in Chiral Perturbation Theory. The corrections are somewhat larger than was indicated by dispersive estimates. We present numerical results for the Dalitz plot parameters, the ratio r of the neutral to charged decay and the total decay rate. In addition we derive an inequality between the slope parameters of the charged and neutral decay. The experimental charged decay rate leads to central values for the isospin breaking quantities R = 42.2 and Q = 23.2.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (66)

  1. J. Bijnens, G. Fäldt and B.M.K. Nefkens (eds.) Phys. Scripta T99 (2002) 1-282
  2. B. Höistad and P. Moskal (eds.), Acta Phys. Slov. 56 (2005) 193-409.
  3. D. G. Sutherland Phys. Lett. 23 (1966) 384
  4. J. S. Bell and D. G. Sutherland, Nucl. Phys. B 4 (1968) 315.
  5. J. A. Cronin, Phys. Rev. 161 (1967) 1483.
  6. H. Osborn and D. J. Wallace, Nucl. Phys. B 20 (1970) 23.
  7. S. Weinberg, Physica A 96 (1979) 327.
  8. J. Gasser and H. Leutwyler, Annals Phys. 158 (1984) 142.
  9. J. Gasser and H. Leutwyler, Nucl. Phys. B 250 (1985) 465.
  10. J. Gasser and H. Leutwyler, Nucl. Phys. B 250 (1985) 539.
  11. J. Bijnens and J. Gasser, Phys. Scripta T99 (2002) 34 [arXiv:hep-ph/0202242].
  12. R. F. Dashen, Phys. Rev. 183 (1969) 1245.
  13. W. M. Yao et al. [Particle Data Group], J. Phys. G 33 (2006) 1.
  14. J. F. Donoghue, B. R. Holstein and D. Wyler, Phys. Rev. D 47 (1993) 2089.
  15. J. Bijnens, Phys. Lett. B 306 (1993) 343 [arXiv:hep-ph/9302217].
  16. R. Baur, J. Kambor and D. Wyler, Nucl. Phys. B 460 (1996) 127 [arXiv:hep-ph/9510396].
  17. A. Neveu and J. Scherk, Annals Phys. 57 (1970) 39.
  18. C. Roiesnel and T. N. Truong, Nucl. Phys. B 187 (1981) 293;
  19. T. N. Truong, Nucl. Phys. Proc. Suppl. 24A (1991) 93.
  20. J. Kambor, C. Wiesendanger and D. Wyler, Nucl. Phys. B 465 (1996) 215 [arXiv:hep-ph/9509374].
  21. A. V. Anisovich and H. Leutwyler, Phys. Lett. B 375 (1996) 335 [arXiv:hep-ph/9601237].
  22. B. Borasoy and R. Nissler, Eur. Phys. J. A 26 (2005) 383 [arXiv:hep-ph/0510384].
  23. S. Descotes-Genon, N. H. Fuchs, L. Girlanda and J. Stern, Eur. Phys. J. C 34 (2004) 201 [arXiv:hep-ph/0311120].
  24. J. Bijnens, Prog. Part. Nucl. Phys. 58 (2007) 521 [arXiv:hep-ph/0604043].
  25. J. Bijnens, G. Colangelo and J. Gasser, Nucl. Phys. B 427 (1994) 427 [arXiv:hep-ph/9403390].
  26. G. Amorós, J. Bijnens and P. Talavera, Nucl. Phys. B 585 (2000) 293 [Erratum-ibid. B 598 (2001) 665] [arXiv:hep-ph/0003258].
  27. A. V. Manohar, arXiv:hep-ph/9606222.
  28. V. Bernard, N. Kaiser and U. G. Meissner, Int. J. Mod. Phys. E 4 (1995) 193 [arXiv:hep-ph/9501384].
  29. G. Ecker, Prog. Part. Nucl. Phys. 35 (1995) 1 [arXiv:hep-ph/9501357].
  30. V. Bernard and U. G. Meissner, arXiv:hep-ph/0611231, to be published in Ann. Rev. Nucl. Part. Sci.
  31. J. Bijnens, G. Colangelo and G. Ecker, JHEP 9902 (1999) 020 [arXiv:hep-ph/9902437].
  32. J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M. E. Sainio, Nucl. Phys. B 508 (1997) 263 [Erratum-ibid. B 517 (1998) 639] [arXiv:hep-ph/9707291].
  33. J. Bijnens, G. Colangelo and G. Ecker, Annals Phys. 280 (2000) 100 [arXiv:hep-ph/9907333].
  34. C. Aubin et al. [MILC Collaboration], Phys. Rev. D 70 (2004) 114501 [arXiv:hep-lat/0407028].
  35. G. Amorós, J. Bijnens and P. Talavera, Nucl. Phys. B 602 (2001) 87 [arXiv:hep-ph/0101127].
  36. G. Ecker, J. Gasser, A. Pich and E. de Rafael, Nucl. Phys. B 321 (1989) 311.
  37. V. Cirigliano, G. Ecker, M. Eidemuller, R. Kaiser, A. Pich and J. Portoles, Nucl. Phys. B 753 (2006) 139 [arXiv:hep-ph/0603205].
  38. G. Ecker, J. Gasser, H. Leutwyler, A. Pich and E. de Rafael, Phys. Lett. B 223 (1989) 425.
  39. J. Bijnens, E. Gamiz, E. Lipartia and J. Prades, JHEP 0304 (2003) 055 [arXiv:hep-ph/0304222].
  40. H. Leutwyler, Phys. Lett. B 378 (1996) 313 [arXiv:hep-ph/9602366].
  41. M. Knecht, B. Moussallam, J. Stern and N. H. Fuchs, Nucl. Phys. B 457 (1995) 513 [arXiv:hep-ph/9507319].
  42. J. Bijnens, P. Dhonte and F. Persson, Nucl. Phys. B 648 (2003) 317 [arXiv:hep-ph/0205341].
  43. G. Amorós, J. Bijnens and P. Talavera, Nucl. Phys. B 568 (2000) 319 [arXiv:hep-ph/9907264].
  44. J. Bijnens and P. Talavera, JHEP 0203, 046 (2002) [arXiv:hep-ph/0203049].
  45. S. Necco, talk at Lattice 2007
  46. H. Leutwyler, Phys. Lett. B 374 (1996) 181 [arXiv:hep-ph/9601236].
  47. R. Kaiser and H. Leutwyler, Eur. Phys. J. C 17 (2000) 623 [arXiv:hep-ph/0007101].
  48. R. Kaiser, talk presented at EuroFlavour06, 2-4 November 2006, Barcelona, Spain.
  49. K. Kampf, J. Novotny and J. Trnka, Eur. Phys. J. C 50 (2007) 385 [arXiv:hep-ph/0608051].
  50. J. Bijnens, Acta Phys. Slov. 56 (2005) 305 [arXiv:hep-ph/0511076].
  51. F. Ambrosino et al. [KLOE Collaboration], arXiv:0707.2355 [hep-ex].
  52. A. Abele et al. [Crystal Barrel Collaboration], Phys. Lett. B 417 (1998) 197.
  53. J. G. Layter, J. A. Appel, A. Kotlewski, W. Y. Lee, S. Stein and J. J. Thaler, Phys. Rev. D 7 (1973) 2565.
  54. M. Gormley, E. Hyman, W. Y. Lee, T. Nash, J. Peoples, C. Schultz and S. Stein, Phys. Rev. D 2 (1970) 501.
  55. F. Ambrosino et al. [KLOE collaboration], arXiv:0707.4137 [hep-ex].
  56. T. Capussela [KLOE Collaboration], Acta Phys. Slov. 56 (2005) 341;
  57. S. Giovannella et al. [KLOE Collaboration], 40th Rencontres de Moriond on QCD and High Energy Hadronic Interactions, La Thuile, Aosta Valley, Italy, 12-19 Mar 2005 arXiv:hep-ex/0505074.
  58. W. B. Tippens et al. [Crystal Ball Collaboration], Phys. Rev. Lett. 87 (2001) 192001.
  59. M. Bashkanov et al., arXiv:0708.2014 [nucl-ex].
  60. A. Abele et al. [Crystal Barrel Collaboration], Phys. Lett. B 417 (1998) 193.
  61. D. Alde et al. [Serpukhov-Brussels-Annecy(LAPP) Collaboration], Z. Phys. C 25 (1984) 225 [Yad. Fiz. 40 (1984) 1447].
  62. M. N. Achasov et al., JETP Lett. 73 (2001) 451 [Pisma Zh. Eksp. Teor. Fiz. 73 (2001) 511.
  63. B. V. Martemyanov and V. S. Sopov, Phys. Rev. D 71 (2005) 017501 [arXiv:hep-ph/0502023].
  64. J. Bijnens, P. Dhonte and P. Talavera, JHEP 0401 (2004) 050 [arXiv:hep-ph/0401039].
  65. D. B. Kaplan and A. V. Manohar, Phys. Rev. Lett. 56 (1986) 2004.
  66. J. Bijnens and J. Prades, Nucl. Phys. B 490 (1997) 239 [arXiv:hep-ph/9610360].