DOI 10.1007/s100520000497
VMD, the WZW Lagrangian and ChPT: The third mixing angle
M. Benayoun1 - L. DelBuono1 - H.B. O'Connell2
1 LPNHE des Universités Paris VI et VII-IN2P3, Paris,
France
2 Stanford Linear Accelerator Center, Stanford University, Stanford CA 94309, USA
Received: 20 June 2000 / Published online: 23 October 2000 - © Springer-Verlag 2000
Abstract
We show that the Hidden Local Symmetry Model, supplemented with
well-known
procedures for breaking flavor SU(3) and nonet symmetry, provides all
the information contained in the standard Chiral Perturbation Theory
(ChPT) Lagrangian
.
This allows to
rely on radiative decays of light mesons (
and
)
in order to extract some numerical information of
relevance to ChPT: a
value for
,
a quark mass ratio of
,
and a negligible departure from the Gell-Mann-Okubo
mass formula. The mixing angles are
and
.
We also give
the values of all decay constants. It is shown that the common mixing
pattern with one mixing angle
is actually quite appropriate
and algebraically related to the
mixing pattern presently
preferred by the ChPT community. For instance the traditional
is
functionally related to the ChPT
and fulfills
.
The vanishing of
,
supported by all data
on radiative decays, gives a novel relation between mixing angles and
the violation of nonet symmetry in the pseudoscalar sector. Finally,
it is shown that the interplay of nonet symmetry breaking through U(3)
SU(3)
U(1) satisfies all requirements of the physics of
radiative decays without any need for additional glueballs.
Copyright Società Italiana di Fisica, Springer-Verlag 2000