https://doi.org/10.1140/epjc/s10052-014-2946-8
Regular Article - Theoretical Physics
Analyticity of 
isospin-violating form factors and the 
second-class decay
1
Laboratoire de Physique Théorique, CNRS/Univ. Paris-Sud 11 (UMR8627), 91405 , Orsay, France
2
Groupe de Physique Théorique, IPN, CNRS/IN2P3/Univ. Paris-Sud 11 (UMR8608), 91406 , Orsay, France
* e-mail: moussall@ipno.in2p3.fr
Received:
7
April
2014
Accepted:
17
June
2014
Published online:
5
July
2014
We consider the evaluation of the isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do hold (i.e. no anomalous thresholds are present) in spite of the instability of the 
meson in QCD. Unitarity relates the vector form factor to the 
amplitude: we exploit progress in formulating and solving the Khuri–Treiman equations for 
and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the 
-meson peak. Observing this peak in the energy distribution of the decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the elastic scattering 
-wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the 
scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the 
decay.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
