Total Widths And Slopes From Complex Regge Trajectories

Abstract

Maximally complex Regge trajectories are introduced for which both Re $α(s)$ and Im $α(s)$ 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: $Γ_{TOT}/M\to$ 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 $ρ$ trajectory in $πN$ charge exchange. Finally, the unitarily enhanced intercept, $α_ρ\approx 0.525$, \nolinebreak is in good accord with the Donnachie-Landshoff total cross section analysis.