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K→3π final state interactions at NLO in CHPT and Cabibbo’s proposal to measure a0-a2

  • Regular Article - Theoretical Physics
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Abstract

We present the analytical results for the K→3π final state interaction phases at next-to-leading order (NLO) in CHPT. We also study the recent proposal of Cabibbo to measure the ππ scattering lengths combination a0-a2 from the cusp effect in the π0π0 energy spectrum at threshold for K+→π0π0π+ and KL→π0π0π0, and we give the relevant formulas to describe it at NLO. We estimate the theoretical uncertainty of the a0-a2 determination at NLO in our approach and obtain the result that it is not smaller than 5% if added quadratically and 7% if added linearly, for K+→π0π0π+. One gets similar theoretical uncertainties if the neutral KL→π0π0π0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations, and data above threshold cannot be used to get the scattering lengths. We do not include isospin corrections apart from two-pion phase space factors which are physical. We compare our results for the cusp effect with those due to Cabibbo and Isidori.

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References

  1. G. Ecker, hep-ph/0011026

  2. A. Pich, hep-ph/9806303

  3. G. Ecker, Prog. Part. Nucl. Phys. 35, 1 (1995)

    Article  Google Scholar 

  4. E. de Rafael, hep-ph/9502254

  5. A. Pich, Rep. Prog. Phys. 58, 563 (1995)

    Article  ADS  Google Scholar 

  6. S. Weinberg, Physica A 96, 327 (1979)

    ADS  Google Scholar 

  7. J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  8. J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)

    Article  ADS  Google Scholar 

  9. E. Gámiz, J. Prades, I. Scimemi, J. High Energ. Phys. 10, 042 (2003)

    Article  Google Scholar 

  10. E. Gámiz, J. Prades, I. Scimemi, hep-ph/0410150

  11. E. Gámiz, J. Prades, I. Scimemi, hep-ph/0305164

  12. I. Scimemi, E. Gámiz, J. Prades, in: Proc. of the 39th Rencontres de Moriond on Electroweak Interactions and Unified Theories (The Gioi Publishers, 2005) p. 355 [hep-ph/0405204]

  13. J. Prades, E. Gámiz, I. Scimemi, Nucl. Phys. B Proc. Suppl. 164, 79 (2007)

    Article  ADS  Google Scholar 

  14. V. Bernard, N. Kaiser, U.G. Meißner, Nucl. Phys. B 357, 129 (1991)

    Article  ADS  Google Scholar 

  15. J. Bijnens, P. Dhonte, F. Persson, Nucl. Phys. B 648, 317 (2003)

    Article  ADS  Google Scholar 

  16. J. Kambor, J. Missimer, D. Wyler, Nucl. Phys. B 346, 17 (1990)

    Article  ADS  Google Scholar 

  17. J. Kambor, J. Missimer, D. Wyler, Phys. Lett. B 261, 496 (1991)

    Article  ADS  Google Scholar 

  18. J. Kambor, J.F. Donoghue, B.R. Holstein, J. Missimer, D. Wyler, Phys. Rev. Lett. 68, 1818 (1992)

    Article  ADS  Google Scholar 

  19. J. Bijnens, F. Borg, Nucl. Phys. B 697, 319 (2004)

    Article  ADS  Google Scholar 

  20. J. Bijnens, F. Borg, Eur. Phys. J. C 39, 347 (2005)

    Article  ADS  Google Scholar 

  21. A. Nehme, Phys. Rev. D 70, 094025 (2004)

    Article  ADS  Google Scholar 

  22. J. Bijnens, F. Borg, Eur. Phys. J. C 40, 383 (2005)

    Article  ADS  Google Scholar 

  23. N. Cabibbo, Phys. Rev. Lett. 93, 121801 (2004)

    Article  ADS  Google Scholar 

  24. U.-G. Meißner, G. Müller, S. Steininger, Phys. Lett. B 406, 154 (1997) [Erratum-ibid. B 407, 454 (1997)]

    Article  ADS  Google Scholar 

  25. M. Knecht, R. Urech, Nucl. Phys. B 519, 329 (1998)

    Article  ADS  Google Scholar 

  26. N. Cabibbo, G. Isidori, J. High Energ. Phys. 03, 021 (2005)

    Article  ADS  Google Scholar 

  27. G. D’Ambrosio, G. Isidori, A. Pugliese, N. Paver, Phys. Rev. D 50, 5767 (1994) [Erratum-ibid. D 51, 3975 (1995)]

    Article  ADS  Google Scholar 

  28. NA48/2 Collaboration, J.R. Batley et al., Phys. Lett. B 633, 173 (2006)

    Article  ADS  Google Scholar 

  29. NA48/2 Collaboration, S. Giudici, hep-ex/0505032

  30. J. Gasser, Talk at IV EURIDICE Collaboration Meeting, Marseille 8–11 February 2006

  31. G. Colangelo, J. Gasser, H. Leutwyler, Phys. Lett. B 488, 261 (2000)

    Article  ADS  Google Scholar 

  32. G. Colangelo, J. Gasser, H. Leutwyler, Nucl. Phys. B 603, 125 (2001)

    Article  ADS  Google Scholar 

  33. J.R. Peláez, F.J. Ynduráin, Phys. Rev. D 71, 074016 (2005)

    Article  ADS  Google Scholar 

  34. J.R. Peláez, F.J. Ynduráin, hep-ph/0412320

  35. J. Gasser, private communication

  36. G. Colangelo, J. Gasser, B. Kubis, A. Rusetsky, Phys. Lett. B 638, 187 (2006)

    Article  ADS  Google Scholar 

  37. A.V. Anisovich, Phys. Atom. Nucl. 66, 172 (2003) [Yad. Fiz. 66, 175 (2003)]

    Article  Google Scholar 

  38. V.V. Anisovich, A.A. Ansel’m, Usp. Fiz. Nauk. 88, 287 (1966) [Sov. Phys. Usp. 9, 117 (1966)]

    Google Scholar 

  39. R. Unterdorfer, G. Ecker, J. High Energ. Phys. 10, 017 (2005)

    Article  ADS  Google Scholar 

  40. Particle Data Group, S. Eidelman et al., Phys. Lett. B 592, 1 (2004)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, The University of Glasgow, Glasgow, G12 8QQ, UK

    E. Gámiz

  2. CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, Campus de Fuente Nueva, 18002, Granada, Spain

    J. Prades

  3. Departament de Física Teòrica, IFIC, CSIC-Universitat de València, Apt. de Correus 22085, 46071, València, Spain

    I. Scimemi

Authors
  1. E. Gámiz
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  2. J. Prades
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  3. I. Scimemi
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Correspondence to J. Prades.

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PACS

13.25.Es; 12.39.Fe; 13.75.Lb

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Gámiz, E., Prades, J. & Scimemi, I. K→3π final state interactions at NLO in CHPT and Cabibbo’s proposal to measure a0-a2 . Eur. Phys. J. C 50, 405–422 (2007). https://doi.org/10.1140/epjc/s10052-006-0201-7

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  • DOI: https://doi.org/10.1140/epjc/s10052-006-0201-7

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