Eur. Phys. J. C (2014) 74: 3209
https://doi.org/10.1140/epjc/s10052-014-3209-4

Regular Article - Theoretical Physics

Constraints on the $$\mathbf {\omega \pi }$$ form factor from analyticity and unitarity

¹ Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560 012, India
² Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125, Magurele, Romania
³ Helmholtz-Institut für Strahlen-und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany

^* e-mail: anant@cts.iisc.ernet.in

Received: 24 October 2014
Accepted: 27 November 2014
Published online: 17 December 2014

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 $$0.6\, \text {GeV}$$.