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Register a new userConstraints on the $omegapi$ form factor from analyticity and unitarity
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Balasubramanian Ananthanarayan
Publication date
2014
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English
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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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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.
A careful reanalysis of both Argonne National Laboratory and Brookhaven National Laboratory data for weak single pion production is done. We consider deuteron nuclear effects and normalization (flux) uncertainties in both experiments. We demonstrate that these two sets of data are in good agreement. For the dipole parametrization of $C_5^A(Q^2)$, we obtain $C_5^A(0)=1.19pm 0.08$, $M_A=0.94pm 0.03$ GeV. As an application we present the discussion of the uncertainty of the neutral current 1$pi^0$ production cross section, important for the T2K neutrino oscillation experiment.
The $eta^prime$ transition form factor is reanalyzed in view of the recent BESIII first observation of the Dalitz decay $eta^primetogamma e^+e^-$ in both space- and time-like regions at low and intermediate energies using the Pade approximants method. The present analysis provides a suitable parameterization for reproducing the measured form factor in the whole energy region and allows to extract the corresponding low-energy parameters together with a prediction of its values at the origin, related to $Gamma_{eta^primetogammagamma}$, and the asymptotic limit. The $eta$-$eta^prime$ mixing is reassessed within a mixing scheme compatible with the large-$N_c$ chiral perturbation theory at next-to-leading order, with particular attention to the OZI-rule--violating parameters. The $J/psi$, $Ztoeta^{(prime)}gamma$ decays are also considered and predictions reported.
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