https://doi.org/10.1140/epjc/s10052-017-5052-x
Regular Article - Theoretical Physics
Extended chiral Khuri–Treiman formalism for 
and the role of the 
, 
resonances
1
Instituto de Física Corpuscular (IFIC), Centro Mixto CSIC-Universidad de Valencia, Valencia, Spain
2
Departamento de Física, Facultad de Química, Universidad de Murcia, E-30071, Murcia, Spain
3
Groupe de Physique Théorique, IPN (UMR8608), Université Paris-Sud 11, Orsay, France
* e-mail: moussall@ipno.in2p3.fr
Received:
23
February
2017
Accepted:
7
July
2017
Published online:
1
August
2017
Recent experiments on decays have provided an extremely precise knowledge of the amplitudes across the Dalitz region which represent stringent constraints on theoretical descriptions. We reconsider an approach in which the low-energy chiral expansion is assumed to be optimally convergent in an unphysical region surrounding the Adler zero, and the amplitude in the physical region is uniquely deduced by an analyticity-based extrapolation using the Khuri–Treiman dispersive formalism. We present an extension of the usual formalism which implements the leading inelastic effects from the 
channel in the final-state 
interaction as well as in the initial-state 
interaction. The constructed amplitude has an enlarged region of validity and accounts in a realistic way for the influence of the two light scalar resonances and in the dispersive integrals. It is shown that the effect of these resonances in the low-energy region of the decay is not negligible, in particular for the 
mode, and improves the description of the energy variation across the Dalitz plot. Some remarks are made on the scale dependence and the value of the double quark mass ratio Q.
© The Author(s), 2017
