Total Widths And Slopes From Complex Regge Trajectories

Abstract

Maximally complex Regge trajectories are introduced for which both Re $\alpha (s)$ and Im $\alpha (s)$ grow as $s^{1-ϵ}$ ($ϵ$ small and positive). Our expression reduces to the standard real linear form as the imaginary part (proportional to $ϵ$) goes to zero. A scaling formula for the total widths emerges: ${\Gamma }_{TOT}/M\to$ constant for large M, in very good agreement with data for mesons and baryons. The unitarity corrections also enhance the space-like slopes from their time-like values, thereby resolving an old problem with the $\rho$ trajectory in $\pi N$ charge exchange. Finally, the unitarily enhanced intercept, ${\alpha }_{\rho }\approx 0.525$, \nolinebreak is in good accord with the Donnachie-Landshoff total cross section analysis.

Comments: 9 pages, 3 Figures