0 1 2 3 -t+t$_{min}$ [GeV$^{2}$] 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 d U  /dt [nb/GeV 2 ] HERMES 0 1 2 3 -t+t$_{min}$ [GeV$^{2}$] HERMES 0 1 2 3 -t+t$_{min}$ [GeV$^{2}$] HERMES 0 1 2 3 -t+t$_{min}$ [GeV$^{2}$] HERMES 1 < Q$^{2}$< 2 GeV 2 2 < Q$^{2}$< 3 GeV 2 3 < Q$^{2}$< 4 GeV 2 4 < Q$^{2}$< 11 GeV 2 0.02 < x$_{B}$ < 0.15 0.06 < x$_{B}$ < 0.23 0.11 < x$_{B}$ < 0.31 0.15 < x$_{B}$ < 0.55 20 FIG. 14: (Color online) − t + t$_{min}$ dependence of the differential cross section dσ$_{U}$/dt = dσ$_{T}$/dt + ϵdσ$_{L}$/dt in exclusive reaction p ( γ $^{∗}$, π $^{+}$) n at HERMES. The experimental data are from Ref. [7]. The calculations are performed for the average values of ( Q $^{2}$, x$_{B}$ ) in a given Q 2 and Bjorken x$_{B}$ bin. The solid curves are the full model results. The dash-dotted curves correspond to the longitudinal ϵdσ$_{L}$/dt and the dashed curves to the transverse dσ$_{T}$/dt components of the cross section. The dash-dash-dotted curves describe the results without the resonance/partonic effects. denotes the minimum value of − t for a given Q 2 and x$_{B}$ . The different panels in Figure 14 correspond to the differ- ent Q 2 and x bins. In the calculations we use the cut-off Λ 2 γππ = 0 . 46 GeV 2 in the pion form factor, Eq. (14). This is an optimal va lue needed for the description of high Q 2 data at JLAB. I n Figure 14 the model results which in- clude both the meson-exchange and r/p -contributions are shown by th e solid curves. The dash-dotted and the dashed curves co rrespond to the longitudinal ϵdσ$_{L}$/dt and to the transverse dσ$_{T}$/dt components of the cross section, respectively. T he dash-dash-dotted curves describe the results without the r/p -contributions. We perform the calculations for the average ( Q $^{2}$, x ) val- ues in a given Q 2 and x$_{B}$ bin [57]. In Figure 14 instead of t , the quantity − t + t$_{min}$ is again used, where − t$_{min}$ Interestingly, the physics of p ( γ ∗ , π $^{+}$) n in the DIS re- gion at HERM ES is essentially the same as at JLAB where the value of W is smaller (2 GeV vs. 4 GeV). Just contrary to the situation in the JLAB experiment the longitudinal cro ss section at HERMES determines the total differential cross section at small − t . As at JLAB the transverse cr oss section at HERMES is dominated by the r/p -mecha nism. At JLAB the transverse cross sec- tion is somewhat larger and at forward angles comparable with the longitu dinal cross section. In deeply virtual pro- duction of π + at HERMES the transverse cross section gets smaller at forward angles and the cross section is dominated by th e exchange of Regge trajectories, with π being the domin ant trajectory. The π -reggeon exchange contributes ma inly to the longitudinal response σ$_{L}$ and at low momentum transfer − t the variation of the forward cross section with Q 2 falls down as the electromagnetic form factor of the pion σ$_{L}$ ∝ ( F$_{γππ}$ ( Q $^{2}$))$^{2}$. In the off- forward region, − t > 1 GeV $^{2}$, because of the exponential FIG. 15: (Color online) dσ$_{U}$/dt in exclusive reaction p ( γ $^{∗}$, π $^{+}$) n for the average values of Q 2 = 1 . 4 GeV 2 and x$_{B}$ = 0 . 08. The HERMES data, the solid and the dash-dotted curves are the same as in the left panel of Figure 14. The dashed and dash-dash-dotted curves describe the contribu- tions of the π -exchange and resonance/partonic mechanisms to ϵdσ$_{L}$/dt , respectively. The dot-dot-dashed curve describe the π + photoproduction for E$_{γ}$ = 8 GeV ( W ≃ 4 GeV). The photoproduction data are from [54]. 0 1 2 3 4 -t+t$_{min}$ [GeV$^{2}$] 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 d σ$^{U}$ /dt [nb/GeV 2 ] photoproduction /  W=4 GeV HERMES /  W=4 GeV 1 < Q$^{2}$< 2 GeV 2 p( )n