Constraints on the omega-pi form factor from analyticity and unitarity

Abstract

Abstract. 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. From this information, we derive upper and lower bounds on the modulus of the ωπ 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.

Pion Interactions and the Standard Model at High Precision

“…If the small rescattering effects were to be turned off, then the problem would amount to one where the imaginary part of the form factor would be known along the elastic part of the unitarity cut, Refs. [53,54].It may be mentioned that the work above has led to an enrichment of the theory of unitarity bounds, with applications in analytic interpolation theory of functional analysis.…”