The reactions \(\pi\pi \rightarrow \pi\pi\) and \(\gamma\gamma \rightarrow \pi\pi\) in \(\chi\) PT with an isosinglet scalar resonance

Regular Article - Theoretical Physics
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Abstract.

The lowest-lying resonance in the QCD spectrum is the \( 0^{++}\) isoscalar \( \sigma\)-meson, also known as the \( f_{0}(500)\). We augment SU(2) chiral perturbation theory (\( \chi\) PT) by including the \( \sigma\)-meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarrús and others. In this effective field theory, denoted \( \chi\) PTS, the \( \sigma\)-meson’s well-established mass and decay width are not sufficient to properly renormalize its self energy. At \( O(p^{4})\) another low-energy constant appears in the dressed \( \sigma\)-meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the \( \pi\pi\rightarrow\pi\pi\) and \( \gamma\gamma\rightarrow\pi\pi\) reactions to data from threshold through the energies at which the \( \sigma\)-meson resonance affects observables. The leading-order (LO) \( \pi \pi\) amplitude reproduces the \( \sigma\)-meson pole position, the isoscalar \( \pi \pi\) scattering lengths and \( \pi \pi\) scattering and \( \gamma\gamma\rightarrow\pi\pi\) data up to \( \sqrt{s} \approx 0.5\) GeV. It also yields a \( \gamma\gamma\rightarrow\pi\pi\) amplitude that obeys the Ward identity. The value obtained for the \( \pi^{0}\) polarizability is, however, only slightly larger than that obtained in standard \( \chi\) PT.

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Copyright information

© SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Chemistry and PhysicsFranklin CollegeFranklinUSA
  2. 2.Institute of Nuclear and Particle Physics and Department of Physics and AstronomyOhio UniversityAthensUSA

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