On Electron-Positron Annihilation into Nucleon-Antinucleon Pairs

We discuss the puzzling experimental results on baryon-antibaryon production in e+e− annihilation close to the threshold, in particular the fact that σ(e+e− → n̄n) >∼ σ(e+e− → p̄p). We discuss an interpretation in terms of a two-step process, via an intermediate coherent isovector state serving as an intermediary between e+e− and the baryon-antibaryon system. We provide evidence that the isovector channel dominates both e+e− → pions and from N̄N annihilation at rest, and show that the observed ratio of σ(e+e− → n̄n)/σ(e+e− → p̄p) can be understood quantitatively in this picture. CERN–TH/2001-234 TAUP–2678-01 August 2001 [email protected] [email protected] Experimental data from the FENICE collaboration [1] indicate that σ(ee → n̄n) is relatively large close to threshold. Their data may be compared with earlier data on ee → p̄p [2, 3] and also with data on the timereversed reaction p̄p → ee, for which more precise data are available [4]. As seen in Fig. 1, the combined data indicate that σ(ee → n̄n)/σ(ee → p̄p) > ∼ 1 when ECM ∼ 2 GeV. Averaging over the available data on both the direct and time-reversed reactions, which are very consistent, and ignoring any possible variation with energy, we find: σ(ee → p̄p) σ(e+e− → n̄n) = 0.66 +0.16 −0.11 (1) The fact that this ratio is less than unity requires confirmation, but even equal cross sections for ee → p̄p and ee → n̄n would be quite surprising. We recall that the ratio of the cross sections for the corresponding tchannel processes ep(n) → ep(n) should be infinite at zero momentum transfer, where the form factor simply measures the total proton and neutron charges, corresponding to a coherent sum over the electromagnetic charges of their constituent quarks. It is also believed that the ratio (1) should be large at high momentum transfers. In a naive perturbative description of ee annihilation into baryons, the virtual time-like photon first makes a ‘primary’ q̄q pair, which is then dressed by two additional quark-antiquark pairs that pop out of the vacuum. This dressing is thought to be a perturbative QCD process at high momentum transfers, which does not distinguish between the u and d quarks, since gluon couplings are flavor-blind. Thus, in this conventional perturbative picture, the only difference between the production rates of proton and neutron is through the different electric charges of the primary q̄q pairs. The total perturbative cross section is obtained by superposing the amplitudes with different primary q̄q pairs and squaring the result: σ(ee → N̄N) ∝ ∣