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Low energy scattering with a nontrivial pion
Phys. Rev. D 76, 114001 – Published 4 December, 2007
DOI: https://doi.org/10.1103/PhysRevD.76.114001
Abstract
An earlier calculation in a generalized linear sigma model showed that the well-known current algebra formula for low energy pion-pion scattering held even though the massless Nambu Goldstone pion contained a small admixture of a two-quark two-antiquark field. Here we turn on the pion mass and note that the current algebra formula no longer holds exactly. We discuss this small deviation and also study the effects of a SU(3) symmetric quark mass type term on the masses and mixings of the eight SU(3) multiplets in the model. We calculate the s-wave scattering lengths, including the beyond current algebra theorem corrections due to the scalar mesons, and observe that the effect of the scalar mesons is to improve the agreement with experiment. In the process, we uncover the way in which linear sigma models give controlled corrections (due to the presence of scalar mesons) to the current algebra scattering formula. Such a feature is commonly thought to exist only in the nonlinear sigma model approach.
Article Text
References (19)
- A. H. Fariborz, R. Jora, and J. Schechter, arXiv:0707.0843. This “companion” paper contains the appropriate background references.
- S. Weinberg, Phys. Rev. Lett. 17, 616 (1966).
- W-M. Yao et al., J. Phys. G 33, 1 (2006).
- See Table V of D. Black, A. H. Fariborz, S. Moussa, S. Nasri, and J. Schechter, Phys. Rev. D 64, 014031 (2001).
- N. N. Achasov and G. N. Shestakov, Phys. Rev. D 49, 5779 (1994).
- S. L. Adler, Phys. Rev. 137, B1022 (1965); 139, B1638 (1965).
- J. R. Betley et al. (NA48/2 Collaboration), Phys. Lett. B 633, 173 (2006).
- S. Pislak et al. (E865 Collaboration), Phys. Rev. D 67, 072004 (2003).
- B. Adeva et al. (DIRAC Collaboration), Phys. Lett. B 619, 50 (2005).
- B. Ananthanarayan, Curr. Sci. 92, 886 (2007).
- J. Schechter and Y. Ueda, Phys. Rev. D 3, 2874 (1971); 8, 987(E) (1973). See Secs. V and VIB.
- M. D. Scadron, F. Kleefeld, and G. Rupp, arXiv: hep-ph/0601196.
- The Roy equation for the pion amplitude, S. M. Roy, Phys. Lett. 36B, 353 (1971), has been used by several authors to obtain information about the resonance. See T. Sawada, p. 67 of S. Ishida et al., KEK Proceedings of Possible Existence of the Sigma Meson and Its Implication to Hadron Physics, 2000-4 [Soryyushiron Kenkyu 102, No. 5 (2001)]; I. Caprini, G. Colangelo, and H. Leutwyler, Phys. Rev. Lett. 96, 132001 (2006). A similar approach has been employed to study the putative light kappa by S. Descotes-Genon and B. Moussallam, Eur. Phys. J. C 48, 553 (2006). Further discussion of the approach in Ref. [13] above is given in D. V. Bugg, J. Phys. G 34, 151 (2007). A detailed discussion of the chiral perturbation theory approach to pion-pion scattering is given in G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B603, 125 (2001).
- S. L. Adler and F. J. Yndurain, Phys. Rev. D 75, 116002 (2007).
- Y. T. Chiu and J. Schechter, Nuovo Cimento 46, 548 (1966). The Regge form for the high energy behavior used was also suggested by H. J. Schnitzer (private communication).
- A. H. Fariborz, R. Jora, and J. Schechter, Phys. Rev. D 72, 034001 (2005).
- G.’t Hooft, Nucl. Phys. B72, 461 (1974).
- F. Sannino and J. Schechter, Phys. Rev. D 76, 014014 (2007).
- E. Corrigan and P. Ramond, Phys. Lett. 87B, 73 (1979).