https://doi.org/10.1140/epjc/s10052-021-09772-8
Regular Article - Theoretical Physics
Revisiting 
near the 
using analyticity and the left-cut structure
Laboratoire Irène Joliot-Curie (CNRS/IN2P3, UMR9012), Pôle Théorie, Université Paris-Saclay, 91406, Orsay, France
Received:
3
August
2021
Accepted:
25
October
2021
Published online:
12
November
2021
Amplitudes of the form 
appear as sub-processes in the computation of the muon 
. We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at 
. Starting from an exact, parameter-free dispersive representation for the S-wave satisfying QCD asymptotic constraints and Low’s soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of 
, we show that a very good fit of the KLOE data can be achieved with two real parameters, using a T-matrix previously determined from 
scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the T-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the 
scalar form factors and to the 
resonance complex pole are presented.
© The Author(s) 2021
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