Abstract
Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic omega pi 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 omega pi 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, text {GeV}.
Highlights
Recent dispersive treatments [5,6] of the ωπ electromagnetic form factor fωπ (t) are in disagreement with experimental data in the region around 0.6 GeV [7,8,9], which show strong deviations from even approximate vector-mesondominance behavior [10]
Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic ωπ 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
Summary
Recent dispersive treatments [5,6] of the ωπ electromagnetic form factor fωπ (t) are in disagreement with experimental data in the region around 0.6 GeV [7,8,9], which show strong deviations from even approximate vector-mesondominance behavior [10]. The main ingredient in the dispersion relation is unitarity, which allows one to express the discontinuity of the form factor in terms of the P partial wave of the process π π → ωπ [6,11] and the pion electromagnetic form factor, quantities determined with precision Speaking, this relation is valid only in the elastic region, 4m2π ≤ t < 2 π. Due to the lack of information on the discontinuity in the inelastic region, elastic unitarity is assumed to be valid at higher energies in the evaluation of the dispersion integral This assumption may affect the precision of the theoretical treatment. Having in view the disagreement with some experimental data on | fωπ (t)| below t+, it is of interest to investigate the form factor in a more model-independent framework, which avoids this assumption
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