Isobar Rescattering Model and Light Scalar Mesons

Abstract

We use a toy model to discuss the problem of parameterizing the possible contribution of a light scalar meson, sigma, to the final state interactions in the non leptonic decays of heavy mesons.

D Hadronic Decays (not related to extraction of angle \gamma )

“…The most recent result is by CLEO-c [42], using ∼ 2600 signal events. CLEO consider isobar models with different descriptions of the f 0 (980) and σ , and two models that respect unitarity and chirality, one according to Schechter [43] and another developed by Achasov [44]. All models considered agree with each other and the results are consistent with previous fits.…”

Dalitz plot analysis of theD+→π−π+π+decay

“…We tested other models of the low mass ππ S wave contributions and in each case obtain optimal parameters. In Table V we summarize results for the model suggested by J. Schechter and co-workers [9], [19]. All fits for this model show consistent values for the parameters.…”

“…[19], the tilde is used for all parameters relating to the second scalar resonance,σ, which in our case is associated with f 0 (980). Equation 9 can be re-written as…”

“…15 from Ref. [9]) for the case of two resonances σ and f 0 (980) we get the total production amplitude with relative weak interaction mixing factor a f 0 e iφ f 0…”

“…We use two other S wave models, both of which satisfy chiral constraints and respect unitarity. A model by Schechter and his collaborators (Schechter model) [9] is based on the linear sigma model of the chiral symmetric Lagrangian. It includes only the lowest lying ππ S wave resonances, the σ and the f 0 (980).…”