Advertisement

The European Physical Journal C

, 71:1732 | Cite as

Integrating out the heaviest quark in N-flavour χPT

  • Mikhail A. IvanovEmail author
  • Martin Schmid
Regular Article - Theoretical Physics

Abstract

We extend a known method to integrate out the strange quark in three flavour chiral perturbation theory to the context of an arbitrary number of flavours. As an application, we present the explicit formulæ to one-loop accuracy for the heavy quark mass dependency of the low-energy constants after decreasing the number of flavours by one while integrating out the heaviest quark in N-flavour chiral perturbation theory.

Keywords

Quark Mass Heavy Quark High Energy Phys Strange Quark Chiral Perturbation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    S. Weinberg, Phenomenological Lagrangians. Physica A 96, 327 (1979) ADSCrossRefGoogle Scholar
  2. 2.
    J. Gasser, H. Leutwyler, Chiral perturbation theory to one loop. Ann. Phys. 158, 142 (1984) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    J. Gasser, H. Leutwyler, Chiral perturbation theory: Expansions in the mass of the strange quark. Nucl. Phys. B 250, 465 (1985) ADSCrossRefGoogle Scholar
  4. 4.
    B. Moussallam, Flavor stability of the chiral vacuum and scalar meson dynamics. J. High Energy Phys. 08, 005 (2000). hep-ph/0005245 ADSCrossRefGoogle Scholar
  5. 5.
    R. Kaiser, J. Schweizer, The expansion by regions in πK scattering. J. High Energy Phys. 06, 9 (2006). hep-ph/0603153 ADSCrossRefGoogle Scholar
  6. 6.
    J. Gasser, C. Haefeli, M.A. Ivanov et al., Integrating out strange quarks in ChPT. Phys. Lett. B 652, 21 (2007). arXiv:0706.0955 [hep-ph] ADSCrossRefGoogle Scholar
  7. 7.
    J. Gasser, C. Haefeli, M.A. Ivanov et al., Integrating out strange quarks in ChPT: terms at order p 6. Phys. Lett. B 675, 49 (2009). 0903.0801 [hep-ph] ADSCrossRefGoogle Scholar
  8. 8.
    J. Gasser, V.E. Lyubovitskij, A. Rusetsky et al., Decays of the π + π atom. Phys. Rev. D 64, 16008 (2001). hep-ph/0103157 ADSCrossRefGoogle Scholar
  9. 9.
    H. Jallouli, H. Sazdjian, Relativistic effects in the pionium lifetime. Phys. Rev. D 58, 014011 (1998). hep-ph/9706450 ADSCrossRefGoogle Scholar
  10. 10.
    C. Haefeli, M.A. Ivanov, M. Schmid, Electromagnetic low-energy constants in ChPT. Eur. Phys. J. C 53, 549 (2008). 0710.5432 [hep-ph] ADSCrossRefGoogle Scholar
  11. 11.
    K. Kampf, B. Moussallam, Chiral expansions of the π 0 lifetime. 0901.4688 [hep-th]
  12. 12.
    M. Schmid, Strangeless χ PT at large m s. Ph.D. thesis, University of Bern, 2007 Google Scholar
  13. 13.
    J. Bijnens, G. Colangelo, G. Ecker, Renormalization of chiral perturbation theory to order p 6. Ann. Phys. 280, 100 (2000) hep-ph/9907333 MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. 14.
    S. Descotes-Genon, L. Girlanda, J. Stern, Paramagnetic effect of light quark loops on chiral symmetry breaking. J. High Energy Phys. 01, 041 (2000). hep-ph/9910537 ADSCrossRefGoogle Scholar
  15. 15.
    S. Descotes-Genon, L. Girlanda, J. Stern, Chiral order and fluctuations in multi-flavour QCD. Eur. Phys. J. C 27, 115 (2003). hep-ph/0207337 ADSCrossRefGoogle Scholar
  16. 16.
    S. Descotes-Genon, N.H. Fuchs, L. Girlanda et al., Resumming QCD vacuum fluctuations in three-flavour chiral perturbation theory. Eur. Phys. J. C 34, 201 (2004). hep-ph/0311120 ADSCrossRefGoogle Scholar
  17. 17.
    S. Descotes-Genon, π-π and π-K scatterings in three-flavour resummed chiral perturbation theory. J. Phys. Conf. Ser. 110, 052012 (2008). 0710.1696 [hep-ph] ADSCrossRefGoogle Scholar
  18. 18.
    D.G. Boulware, L.S. Brown, Tree graphs and classical fields. Phys. Rev. 172(5), 1628 (1968) ADSCrossRefGoogle Scholar
  19. 19.
    A. Nyffeler, A. Schenk, Effective field theory of the linear O(N) sigma model. Ann. Phys. 241, 301 (1995). hep-ph/9409436 MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    P. Hernandez, M. Laine, Charm mass dependence of the weak Hamiltonian in chiral perturbation theory. J. High Energy Phys. 0409, 018 (2004). hep-ph/0407086 ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2011

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Basler VersicherungenBaselSwitzerland

Personalised recommendations