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We investigate the role driven by the scalar meson $\sigma$ exchange in thephotoproduction of the vector meson $\phi$(1020) off a proton by using aReggeized model. Based on the $\pi^0(135)+\sigma(500)+f_2(1270)$+Pomeronexchanges, we demonstrate that the $\sigma$ exchange plays the role toreproduce the bump structure at the forward angle in the differential crosssection as well as the peaking behavior in the total cross section observed inthe CLAS Collaboration. We also discuss the possible observation of the scaledcross section $s^7d\sigma /dt$ at the production angle $\theta=90^{\circ}$ fromthe CLAS data. It is found that the axial vector meson $f_1(1285)$ exchangewith the trajectory $\alpha_{f_1}(t)=0.028\,t+0.9\pm0.2$ arising from the axialanomaly of the QCD vacuum plays the role to clarify the scaling up to 5 GeV.

Role of $\sigma$ exchange in the $\gamma p\to \phi p$ process and scaling with the $f_1$ axial vector meson from a Reggeized model