The European Physical Journal A

, Volume 44, Issue 2, pp 175–179 | Cite as

Stringent constraints on the scalar K\( \pi\) form factor from analyticity, unitarity and low-energy theorems

  • Gauhar Abbas
  • B. Ananthanarayan
  • I. Caprini
  • I. Sentitemsu Imsong
  • S. Ramanan
Open Access
Letter

Abstract

We investigate the scalar K\( \pi\) form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t = 0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher-order ChPT corrections at the second Callan-Treiman point.

References

  1. 1.
    J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)CrossRefADSGoogle Scholar
  2. 2.
    J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 517 (1985)CrossRefADSGoogle Scholar
  3. 3.
    J. Bijnens, P. Talavera, Nucl. Phys. B 669, 341 (2003) [arXiv:hep-ph/0303103]CrossRefADSGoogle Scholar
  4. 4.
    L. Lellouch, PoS (LATTICE2008) 015 (2009) [arXiv: 0902.4545 [hep-lat]]Google Scholar
  5. 5.
    H. Leutwyler, arXiv:0911.1416 [hep-ph]
  6. 6.
    C.G. Callan, S.B. Treiman, Phys. Rev. Lett. 16, 153 (1966)CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    R. Oehme, Phys. Rev. Lett. 16, 215 (1966)CrossRefADSGoogle Scholar
  8. 8.
    A. Kastner, H. Neufeld, Eur. Phys. J. C 57, 541 (2008) [arXiv:0805.2222 [hep-ph]]CrossRefADSGoogle Scholar
  9. 9.
    M. Jamin, J.A. Oller, A. Pich, Nucl. Phys. B 622, 279 (2002) [arXiv:hep-ph/0110193]CrossRefADSGoogle Scholar
  10. 10.
    B. El-Bennich, A. Furman, R. Kaminski, L. Lesniak, B. Loiseau, B. Moussallam, Phys. Rev. D 79, 094005 (2009) [arXiv:0902.3645 [hep-ph]]CrossRefADSGoogle Scholar
  11. 11.
    V. Bernard, M. Oertel, E. Passemar, J. Stern, Phys. Rev. D 80, 034034 (2009) [arXiv:0903.1654 [hep-ph]]CrossRefADSGoogle Scholar
  12. 12.
    S. Okubo, Phys. Rev. D 3, 2807 (1971)CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    V. Singh, A. K. Raina, Fortschr. Phys. 27, 561 (1979)CrossRefMathSciNetGoogle Scholar
  14. 14.
    C. Bourrely, I. Caprini, L. Lellouch, Phys. Rev. D 79, 013008 (2009) [arXiv:0807.2722 [hep-ph]]CrossRefADSGoogle Scholar
  15. 15.
    C. Bourrely, B. Machet, E. de Rafael, Nucl. Phys. B 189, 157 (1981)CrossRefADSGoogle Scholar
  16. 16.
    C. Bourrely, I. Caprini, Nucl. Phys. B 722, 149 (2005) [arXiv:hep-ph/0504016]ADSGoogle Scholar
  17. 17.
    Gauhar Abbas, B. Ananthanarayan, Eur. Phys. J. A 41, 7 (2009) [arXiv:0905.0951 [hep-ph]]CrossRefADSGoogle Scholar
  18. 18.
    I. Caprini, Eur. Phys. J. C 13, 471 (2000) [arXiv:hep-ph/9907227]CrossRefADSGoogle Scholar
  19. 19.
    Belle Collaboration (D. Epifanov et al.), Phys. Lett. B 654, 65 (2007) [arXiv:0706.2231 [hep-ex]]CrossRefADSGoogle Scholar
  20. 20.
    Gauhar Abbas, B. Ananthanarayan, I. Caprini, I. Sentitemsu Imsong, S. Ramanan, in preparationGoogle Scholar
  21. 21.
    R.J. Hill, Phys. Rev. D 74, 096006 (2006) [arXiv:hep-ph/0607108]CrossRefADSGoogle Scholar
  22. 22.
    S.C. Generalis, D.J. Broadhurst, Phys. Lett. B 139, 85 (1984)CrossRefADSGoogle Scholar
  23. 23.
    P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, Phys. Rev. Lett. 96, 012003 (2006) [arXiv:hep-ph/0511063]CrossRefADSGoogle Scholar
  24. 24.
    M. Jamin, J.A. Oller, A. Pich, Phys. Rev. D 74, 074009 (2006) [arXiv:hep-ph/0605095]CrossRefADSGoogle Scholar
  25. 25.
    M. Beneke, M. Jamin, JHEP 0809, 044 (2008) [arXiv: 0806.3156 [hep-ph]]CrossRefADSGoogle Scholar
  26. 26.
    M. Davier, S. Descotes-Genon, A. Hocker, B. Malaescu, Z. Zhang, Eur. Phys. J. C 56, 305 (2008) [arXiv:0803.0979 [hep-ph]]CrossRefGoogle Scholar
  27. 27.
    S. Bethke, Eur. Phys. J. C 64, 689 (2009) [arXiv:0908.1135 [hep-ph]]CrossRefADSGoogle Scholar
  28. 28.
    I. Caprini, J. Fischer, Eur. Phys. J. C 64, 35 (2009) [arXiv:0906.5211 [hep-ph]]CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2010

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Gauhar Abbas
    • 1
  • B. Ananthanarayan
    • 1
  • I. Caprini
    • 2
  • I. Sentitemsu Imsong
    • 1
  • S. Ramanan
    • 1
  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia
  2. 2.National Institute of Physics and Nuclear EngineeringBucharestRomania

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