On the Proton Form Factors in the Time-like Region

The process p̄p → ee is considered in the general case of polarized initial particles. A relation between the difference of the phases of the electromagnetic form factors GM and GE in the time-like region and measurable asymmetries is derived. It is shown that the moduli of the form factors can be determined from measurements of the total unpolarized cross section and of the integral asymmetry for longitudinally polarized (or transversely polarized) p̄ and p. The behaviour of the proton form factors at high q in the time-like region is also discussed. From the Phragmén-Lindelöf’s theorem it follows that the asymptotical behaviour of the form factors in the space-like and time-like regions must be the same. An analysis of experimental data in both regions based on perturbative QCD is presented. The charge and magnetic form factors of the nucleon, GE(q ) and GM(q ), are classical objects of investigation. For a long time these fundamental quantities have been investigated in the region of space-like q. Starting from the seventies some informations on the electromagnetic form factors of the proton in the time-like region have been obtained. Recently rather accurate measurements of the proton form factors in the time-like region, from q = 4M up to q = 4.2GeV, have been done at LEAR [1]. Some informations on the electromagnetic form factor of the proton at high time-like q were also obtained at Fermilab [2]. There exist several QCD calculations of the electromagnetic form factors in the spacelike region [3]. According to our knowledge there are no QCD-based calculations of the form factors in the time-like region. The phenomenological models which try to describe the behaviour of the form factors in both space-like and time-like regions are based on the vector meson dominance models [4]. However, even taking into account all known meson resonances it is not possible to obtain a statistically acceptable description of all the existing experimental data. The understanding of the behaviour of nucleon electromagnetic form factors still remains a challenge for the theory. It is clear that any additional information about the form factors which could be obtained from experiment is very important. † Talk presented at the Workshop on Exclusive Reactions at High Momentum Transfer, 24-26 June 1993, Marciana Marina, Elba, Italy.