Preserving local gauge invariance with $t$-channel Regge exchange

Considering single-meson photo- and electroproduction off a baryon, it is shown how to restore local gauge invariance that was broken by replacing standard Feynman-type meson exchange in the $t$ channel by exchange of a Regge trajectory. This is achieved by constructing a contact current whose four-divergence cancels the gauge-invariance-violating contributions resulting from all states above the base state on the Regge trajectory. To illustrate the procedure, modifications necessary for the process $\gamma +p\to K^{+}+{\mathrm{\Sigma }}^{*0}$ are discussed in some detail. We also provide the general expression for the contact current for an arbitrary reaction.

Figure 1

Generic diagrams with external four-momenta of the photoproduction process of Eq. (1) satisfying $q+p^{\prime }=k+p$. Labels $s, u$, and $t$ at the hadronic $b\to m+b^{\prime }$ vertices refer to Mandelstam variables of the respective exchanged intermediate particles. Summations over all intermediate states compatible with initial and final states are implied. The right-most diagram depicts the contact-type interaction current. Time runs from right to left.

Figure 2

Generic vertex $F(p_{b^{\prime }},p_b)$ for $b\to m+b^{\prime }$ with associated momenta. The meson momentum $q_m=p_b-p_{b^{\prime }}$ is given by four-momentum conservation across the vertex.