https://doi.org/10.1140/epja/i2017-12401-8
Regular Article - Theoretical Physics
The reactions
and
in
PT with an isosinglet scalar resonance
1
Department of Chemistry and Physics, Franklin College, 46131, Franklin, IN, USA
2
Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, 45701, Athens, OH, USA
* e-mail: phillid1@ohio.edu
Received:
16
June
2017
Accepted:
28
September
2017
Published online:
24
October
2017
The lowest-lying resonance in the QCD spectrum is the isoscalar
-meson, also known as the
. We augment SU(2) chiral perturbation theory (
PT) by including the
-meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarrús and others. In this effective field theory, denoted
PTS, the
-meson’s well-established mass and decay width are not sufficient to properly renormalize its self energy. At
another low-energy constant appears in the dressed
-meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the
and
reactions to data from threshold through the energies at which the
-meson resonance affects observables. The leading-order (LO)
amplitude reproduces the
-meson pole position, the isoscalar
scattering lengths and
scattering and
data up to
GeV. It also yields a
amplitude that obeys the Ward identity. The value obtained for the
polarizability is, however, only slightly larger than that obtained in standard
PT.
© SIF, Springer-Verlag GmbH Germany, 2017