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A Regge approach to the reaction processes $\gamma p\to\pi^-\Delta^{++}$ and$\gamma p\to\pi^+\Delta^0$ is presented for the description of existing data upto $E_\gamma= 16$ GeV. The model consists of the $t$-channel$\pi(139)+\rho(775)+a_2(1320)$ exchanges which are reggeized from the relevantBorn amplitude. Discussion is given on the minimal gauge prescription for the$\pi$ exchange to render convergent the divergence of the $u$-channel$\Delta$-pole in the former process. A new Lagrangian is constructed for the$a_2N\Delta$ coupling in this work and applied to the process for the firsttime with the coupling constant deduced from the duality plus vector dominance.It is shown that, while the $\pi$ exchange dominates over the process, the roleof the $a_2$ exchange is crucial rather than the $\rho$ in reproducing thecross sections for total, differential, and photon polarization asymmetry toagree with data at high energy.

Investigating convergence of the reaction $\gamma p\to\pi^\pm\Delta$ and tensor meson $a_2$ exchange at high energy