Experimental data for mesons and baryons imply a scaling formula for the total widths ${\Gamma }_{\mathrm{tot}}/\overrightarrow{M}\mathrm{const},$ for large M. This leads to both real and imaginary parts of Regge trajectories to grow asymptotically in the same way. For this purpose, maximally complex Regge trajectories are introduced for which both $\mathrm{Re}\alpha \mathrm{}\left(s\right)\mathrm{}$ and $\mathrm{Im}\alpha \mathrm{}\left(s\right)\mathrm{}$ grow as $s^{1-\epsilon }\hspace{0.5em}(\epsilon$ small and positive). Our expression reduces to the standard real linear form as the imaginary part (proportional to $\epsilon )$ goes to zero. The unitarity corrections also enhance the spacelike slopes from their timelike values, thereby resolving an old problem with the $\rho$ trajectory in $\pi N$ charge exchange. Finally, the unitarily enhanced intercept, ${\alpha }_{\rho }\approx 0.525,$ is in good accord with the Donnachie-Landshoff total cross section analysis.

• Received 4 August 1998

DOI:https://doi.org/10.1103/PhysRevD.59.076003