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$omega to 3pi$ and $omegapi^{0}$ transition form factor revisited

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 Added by Miguel Albaladejo
 Publication date 2020
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and research's language is English




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In light of recent experimental results, we revisit the dispersive analysis of the $omega to 3pi$ decay amplitude and of the $omegapi^0$ transition form factor. Within the framework of the Khuri-Treiman equations, we show that the $omega to 3pi$ Dalitz-plot parameters obtained with a once-subtracted amplitude are in agreement with the latest experimental determination by BESIII. Furthermore, we show that at low energies the $omegapi^0$ transition form factor obtained from our determination of the $omega to 3pi$ amplitude is consistent with the data from MAMI and NA60 experiments.



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Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic $omegapi$ form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds.We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the $omegapi$ form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around 0.6 GeV.
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We perform a dispersive analysis of the $omegapi$ electromagnetic transition form factor, using as input the discontinuity provided by unitarity below the $omegapi$ threshold and including for the first time experimental data on the modulus measured from $e^+e^-toomegapi^0$ at higher energies. The input leads to stringent parameterization-free constraints on the modulus of the form factor below the $omegapi$ threshold, which are in disagreement with some experimental values measured from $omegato pi^0gamma^*$ decay. We discuss the dependence on the input parameters in the unitarity relation, using for illustration an $N/D$ formalism for the P partial wave of the scattering process $omegapi to pipi$, improved by a simple prescription which simulates the rescattering in the crossed channels. Our results confirm the existence of a conflict between experimental data and theoretical calculations of the $omegapi$ form factor in the region around 0.6 GeV and bring further arguments in support of renewed experimental efforts to measure more precisely the $omegatopi^0gamma^*$ decay.
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70 - C. Hanhart , S. Holz , B. Kubis 2016
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