Spacelike zero crossings and timelike phases in the electromagnetic form factors of vector mesons

Some form factors of ground-state hadrons with spin might show a zero crossing at spacelike momenta of electron-hadron scattering. In the timelike region of hadron-antihadron production by electron-positron collisions the form factors become complex. When the hadrons decay, the relative phases between form factors can be measured by the angular distributions of their decay products. Using analyticity and the QCD high-energy limits for constraint-free form factors and for helicity amplitudes, we show how a single zero crossing in the spacelike region is related to the high-energy limit of the phase in the timelike region. Theoretical predictions for such zero crossings can therefore be tested by experimental measurements, e.g. by Belle II, in the high-energy timelike region. In the present work, this line of reasoning is applied to vector mesons.