DAUGHTER REGGE TRAJECTORY IN BETHE-SALPETER EQUATION

We solve the Bethe-Salpeter equation in the ladder approximation of the λΦ 3 theory by the Fredholm method. An implicit equation for the Regge trajectories is obtained by putting the Fredholm determinant equal to zero. In the weak-coupling limit we get the following results:a) Equal-mass case: The first daughter trajectory is horizontal to first order in the coupling constant and the residue of the pole vanishes to all orders of the coupling constant. b) Unequal-mass case: At s=0, the slope of the daughter is positive and smaller than that of the mother if the relative mass difference (m 2-μ 2)/μ 2=x is not too great. It becomes negative when x increases. The residue of the pole has the characteristic behaviour in (m 2-μ 2)2/s for s close to zero. We also find two other trajectories, the slope of one of them is negative for certain values of the masses. © 1969 Società Italiana di Fisica.