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Register a new userTesting the consistency of the $omegapi$ transition form factor with unitarity and analyticity
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Authors
I. Caprini
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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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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.
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.
We investigate the scalar K pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t=0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher order ChPT corrections at the second Callan-Treiman point.
The eta-photon transition form factor is evaluated in a formalism based on a phenomenological description at low values of the photon virtuality, and a QCD-based description at high photon virtualities, matching at a scale $Q_{0}^{2}$. The high photon virtuality description makes use of a Distribution Amplitude calculated in the Nambu-Jona-Lasinio model with Pauli-Villars regularization at the matching scale $Q_{0}^{2}$, and QCD evolution from $Q_{0}^{2}$ to higher values of $Q^{2}$. A good description of the available data is obtained. The analysis indicates that the recent data from the BaBar collaboration on pion and eta transition form factor can be well reproduced, if a small contribution of twist three at the matching scale $Q_{0}^{2}$ is included.
Recently the BaBar Collaboration published new data on the cross section for the annihilation e+e- -> phi pi0, obtained using the initial state radiation technique at a center of mass energy of 10.6 GeV. Such a process represents an interesting test bed for the quark model. Indeed, since the phi-pi0 production via e+e- annihilation proceeds through a mechanism which violates the Okubo-Zweig-Iizuka rule, the corresponding cross section could be characterized by contributions from non-qqbar bound states, like hybrids or tetraquarks. The phi-pi0 cross section is analyzed in connection with other data coming from different processes, that involve the same mesons, using a method which implements the analyticity in the phi-pi0 transition form factor by means of a dispersion relation procedure.
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