Constraints on the [Formula: see text] form factor from analyticity and unitarity.

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic [Formula: see text] 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 [Formula: see text] 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 [Formula: see text].

Mass and width of the lowest resonance in QCD.

We demonstrate that near the threshold, the pi pi scattering amplitude contains a pole with the quantum numbers of the vacuum--commonly referred to as the sigma--and determine its mass and width within small uncertainties. Our derivation does not involve models or parametrizations but relies on a straightforward calculation based on the Roy equation for the isoscalar S wave.