Scalar resonances in a unitary {pi}{pi} S-wave model for D{sup +} {r_arrow} {pi}{sup+}{pi}{sup-}{pi}{sup+}.
We propose a model for D{sup +} {yields} {pi}{sup +}{pi}{sup -}{pi}{sup +} decays following experimental results which indicate that the two-pion interaction in the S wave is dominated by the scalar resonances f{sub 0}(600)/{sigma} and f{sub 0}(980). The weak decay amplitude for D{sup +} {yields} R{pi}{sup +}, where R is a resonance that subsequently decays into {pi}{sup +}{pi}{sup -}, is constructed in a factorization approach. In the S wave, we implement the strong decay R {yields} {pi}{sup +}{pi}{sup -} by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range m{sub {pi}{pi}}{sup 2} from threshold to about 3 GeV{sup 2}. In order to reproduce the experimental Dalitz plot for D{sup +} {yields} {pi}{sup +}{pi}{sup -}{pi}{sup +}, we include contributions beyond the S wave. For the P wave, dominated by the {rho}(770){sup 0}, we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the f{sub 2}(1270) and {rho}(1450){sup 0}. The major achievement is a good reproduction of the experimental m{sub {pi}{pi}}{sup 2} distribution, and of the partial as well as the total D{sup +} {yields} {pi}{sup +}{pi}{sup -}{pi}{sup +} 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 {yields} {sigma} transition form factor at q{sup 2} = m{sub {pi}}{sup 2}.
- Research Organization:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-AC02-06CH11357
- OSTI ID:
- 1006254
- Report Number(s):
- ANL/PHY/JA-63357; TRN: US1101211
- Journal Information:
- Phys. Rev. D, Vol. 79, Issue 2/19/2009
- Country of Publication:
- United States
- Language:
- ENGLISH
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