Linear Regge Trajectories with a Left-Hand Cut

The properties of boson Regge trajectories alpha (s) with a left-hand cut for s<0 are studied, with the following assumptions: (a) Re alpha (s) is linear in the physical region of the s and t channels. (b) The imaginary part is asymptotically smaller than the real part. (c) At s =0, alpha (s) has a branch point due to the existence of a Regge cut alpha /sub c/(s) in the angular momentum plane with alpha /sub c/(0)= alpha (0). The branch point is attributed to the collision of the physical pole alpha (s) with a second-sheet pole alpha (s), at s=0. (d) The function alpha (s) is analytic in the s plane. Under these assumptions the imaginary part for each boson trajectory is obtained in terms of a parameter A and a parameter-free universal function is determined by solving an integral equation numerically. The parameter A is determined by requiring that the first meson of each trajectory have the observed width. The model gives imaginary parts increasing almost linearly with s for large mod s mod . (10 refs)