Scalar resonances in a unitary ππ S-wave model for D+→π+π-π+
Abstract
We propose a model for D+→π+π-π+ decays following experimental results which indicate that the two-pion interaction in the S wave is dominated by the scalar resonances f0(600)/σ and f0(980). The weak decay amplitude for D+→Rπ+, where R is a resonance that subsequently decays into π+π-, is constructed in a factorization approach. In the S wave, we implement the strong decay R→π+π- by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range mππ2 from threshold to about 3GeV2. In order to reproduce the experimental Dalitz plot for D+→π+π-π+, we include contributions beyond the S wave. For the P wave, dominated by the ρ(770)0, we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the f2(1270) and ρ(1450)0. The major achievement is a good reproduction of the experimental mππ2 distribution, and of the partial as well as the total D+→π+π-π+ branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a by-product, we predict a value for the poorly known D→σ transition form factor at q2=mπ2.
- Publication:
-
Physical Review D
- Pub Date:
- February 2009
- DOI:
- 10.1103/PhysRevD.79.034020
- arXiv:
- arXiv:0812.3843
- Bibcode:
- 2009PhRvD..79c4020B
- Keywords:
-
- 13.25.Ft;
- 13.20.Fc;
- 12.39.St;
- 13.30.Eg;
- Decays of charmed mesons;
- Factorization;
- Hadronic decays;
- High Energy Physics - Phenomenology
- E-Print:
- 23 pages, 2 figures. Two new equations. The value for the strength of the contribution of the scalar form factor now agrees with other results in the literature. Main results unchanged. Version to appear in Phys. Rev. D