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Register a new userDecay $D^+ to K^- pi^+ pi^+$: chiral symmetry and scalar resonances
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The low-energy S-wave component of the decay $D^+ to K^- pi^+ pi^+$ is studied by means of a chiral SU(3)XSU(3) effective theory. As far as the primary vertex is concerned, we allow for the possibility of either direct production of three pseudoscalar mesons or a meson and a scalar resonance. Special attention is paid to final state interactions associated with elastic meson-meson scattering. The corresponding two-body amplitude is unitarized by ressumming s-channel diagrams and can be expressed in terms of the usal phase shifts $delta$. This procedure preserves the chiral properties of the amplitude at low-energies. Final state interactions also involve another phase $omega$, which describes intermediate two-meson propagation and is theoretically unambiguous. This phase is absent in the K-matrix approximation. Partial contributions to the decay amplitude involve a real term, another one with phase $delta$ and several others with phases $delta+omega$. Our main result is a simple and almost model independent chiral generalization of the usual Breit-Wigner expression, suited to be used in analyses of production data involving scalar resonances.
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We propose a model for $D^+ to pi^+ pi^- pi^+$ decays following experimental results which indicate that the two-pion interaction in the $S$-wave is dominated by the scalar resonances $f_0(600)/sigma$ and $f_0(980)$. The weak decay amplitude for $D^+to R pi^+$, where $R$ is a resonance that subsequently decays into $pi^+pi^-$, is constructed in a factorization approach. In the $S$-wave, we implement the strong decay $Rto pi^-pi^+$ by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range $m_{pipi}^2$ from threshold to about 3 GeV$^2$. In order to reproduce the experimental Dalitz plot for $Dppp$, we include contributions beyond the $S$-wave. For the $P$-wave, dominated by the $rho(770)^0$, we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the $f_2(1270)$ and $rho(1450)^0$. The major achievement is a good reproduction of the experimental $m_{pipi}^2$ distribution, and of the partial as well as the total $Dppp$ branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a byproduct, we predict a value for the poorly known $Dto sigma$ transition form factor at $q^2=m_pi^2$.
We study the Dalitz plot of the decay D^+ --> K^- pi^+ pi^+ with a sample of 15090 events from Fermilab experiment E791. Modeling the decay amplitude as the coherent sum of known K pi resonances and a uniform nonresonant term, we do not obtain an acceptable fit. If we allow the mass and width of the K^*_0(1430) to float, we obtain values consistent with those from PDG but the chi^2 per degree of freedom of the fit is still unsatisfactory. A good fit is found when we allow for the presence of an additional scalar resonance, with mass 797 +/- 19 +/- 43 MeV/c^2 and width 410 +/- 43 +/- 87 MeV/c^2. The mass and width of the K^*_0(1430) become 1459 +/- 7 +/- 5 MeV/c^2 and 175 +/- 12 +/- 12 MeV/c^2, respectively. Our results provide new information on the scalar sector in hadron spectroscopy.
Using $2.93 rm fb^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the first observation of the doubly Cabibbo-suppressed decay $D^+to K^+pi^+pi^-pi^0$ is reported. After removing decays that contain narrow intermediate resonances, including $D^+to K^+eta$, $D^+to K^+omega$, and $D^+to K^+phi$, the branching fraction of the decay $D^+to K^+pi^+pi^-pi^0$ is measured to be $(1.13 pm 0.08_{rm stat} pm 0.03_{rm syst})times 10^{-3}$. The ratio of branching fractions of $D^+to K^+pi^+pi^-pi^0$ over $D^+to K^-pi^+pi^+pi^0$ is found to be $(1.81pm0.15)$%, which corresponds to $(6.28pm0.52)tan^4theta_C$, where $theta_C$ is the Cabibbo mixing angle. This ratio is significantly larger than the corresponding ratios for other doubly Cabibbo-suppressed decays. The asymmetry of the branching fractions of charge-conjugated decays $D^pmto K^pmpi^pmpi^mppi^0$ is also determined, and no evidence of $CP$ violation is found. In addition, the first evidence of the $D^+to K^+omega$ decay, with a statistical significance of 3.3$sigma$, is presented and its decay branching fraction is determined to be $({5.7^{+2.5}_{-2.1}}_{rm stat}pm0.2_{rm syst})times10^{-5}$.
We briefly review the recent results obtained by Fermilab experiment E791 on the Dalitz plot analysis of the decay D+ -> K- pi+ pi+, where indication for a light Kpi scalar resonance, the kappa, was found. We also present preliminary studies providing further information on the phase behavior of the scalar components at low mass, supporting the previous indication for the kappa.
The N*(1440) -> N pi pi decay is studied by making use of the chiral reduction formula. This formula suggests a scalar-isoscalar pion-baryon contact interaction which is absent in the recent study of Hern{a}ndez et al. The contact interaction is introduced into their model, and is found to be necessary for the simultaneous description of g_{RN pi pi} and the pi-pi and pi-N invariant mass distributions.
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