content_image/400449.jpg content_image/400461.jpg
curve) at W = √$_{s}$ = 2 . 2 GeV in comparison with the on- shell parameterization of the proton’s Dirac form factor F p $_{1}$( Q $^{2}$) Eq. (42) (solid curve). It is clearly seen that F$_{s}$ is considerably harder than F p $_{1}$. This difference reflects the influence of the higher lying resonances. 

There is an additional effect which we would like to take into account. In Refs. [25, 27] it has been observed that in exclusive reaction ( e, e ′ π $^{+}$) the slope of partonic contributions which is driven by the intrinsic transverse momentum distribution of partons slightly decreases with increasing value of Q $^{2}$. Since in our present description the contribution of resonances is dual to direct partonic interaction we accommodate this anti-shrinkage effect in the transition form factors F s ( u $_{)}$, see Eq. (13), using the slope parameter 

with a ≃ 2 . 4. This behavior has been found from the fit to the ( Q $^{2}$, W ) dependence of the transverse partonic DIS slope of [25, 27]. Eq. (45) is effective in electroproduc- tion and in the resonance transition form factors F s ( u $_{)}$, Eq. (13), only. For real photons the phase of F s ( u ) is that of F γππ and a proper Regge limit of [29] is guaranteed. Then using the r/p -transition form factor, Eq. (43), 

the transverse cross section dσ$_{T}$/dt gets large (solid curve) in agreement with JLAB data, see Figure 4. The effect of resonances is much smaller in the longitudinal response dσ$_{L}$/dt but it improves the description of data at higher values of − t . As we shall see, the same effect will strongly influence the interference cross sections and allow to explain both the sign and magnitude of dσ$_{TT}$/dt and dσ$_{LT}$/dt . The solid curves include the effect of the DIS slope, Eq. (45). The dash-dash-dotted curves corre- spond to the results without Eq. (45); the effect is rather small at forward angles and could be partially absorbed in a redefinition of ξ . To be in line with [25, 27] we keep 

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this phenomenological behavior. 

The model parameters are summarized in Table I. The Regge phase pattern discussed above and used in the calculations is also shown for different reggeon ex- change contributions. The cut-off Λ$_{γππ}$ in the pion form factor, Eq. (14), is a fit parameter. From the fit to the longitudinal data we observe essentially three re- gions. At small values of Q 2 < 0 . 4 GeV 2 the model results are remarkably consistent with a VMD value of Λ 2 γππ = m 2 ρ (770) ≃ 0 . 59 GeV $^{2}$. The intermediate region 0 . 6 < Q 2 < 1 . 5 GeV 2 in F π -1 experiment [2] demands somewhat smaller value of Λ 2 γππ ≃ 0 . 4 GeV $^{2}$. In the deep ( Q $^{2}$, W ) region the JLAB, Cornell and DESY data can be well described using Λ 2 γππ ≃ 0 . 46 GeV $^{2}$. In our calculations we shall follow these prescriptions for Λ$_{γππ}$. 

## VII. JLAB F π -1, F π -2 AND π -CT DATA 

In this section we study the r/p -effects in partial π + electroproduction cross sections measured at JLAB. We compare the model results with the differential cross sec- tions in the p ( γ ∗ , π $^{+}$) n reaction from the F π -1 [2], F π - 2 [1] and π -CT [3] experiments. At JLAB the reaction n ( γ ∗ , π − ) p has been also measured off the deuteron tar- get and π − data will be soon reported [50]. 

In Figure 6 we show our results for the p ( γ ∗ , π $^{+}$) n reac- tion together with the high- Q 2 data from [1, 3]. The data points in each ( Q $^{2}$, W ) bin correspond to slightly differ- ent values of Q 2 and W for the various − t bins. The numbers displayed in the plots are the average ( Q $^{2}$, W ) values. For simplicity we perform the calculations for values of ( Q $^{2}$, W ) corresponding to the first − t bin. A proper binning of the curves does not change much the results [25]. 

At first, we consider again the reggeized π -exchange only. The value of the cut-off in the pion from factor is 

