Bilocal form factors and Regge couplings
Abstract
The infinitely many local observables defined by expanding the bilocal currents j^{μ}( x, y) on the light cone in powers of ( x y) ^{μ} are used to study scattering processes where one or two external lines are Reggeons. The algebra of bilocal form factors of Fritzsch and GellMann implies the existenc of an algebra of infinitely many form factors F^{J± }( bdk) of any spin J, definite signature±, and arbitrary momentum transfer k. These "signatured form factors" can be continued analytically in k as well as in J and superconvergence relations are obtained for the couplings of strongly interacting particles of arbitrarily high spin and for Regge couplings. Also the commutator of form factors with Regge residues vanishes, except at certain momentum transfers. In particular, the charges F^{Jη}(0) of spin J and signature η = () ^{J} act as "daughter lowering operators". The range of validity of these sum rules in momentum transfer is discussed by continuing the scattering amplitudes involving the spin J and spin J' currents analytically in J and J' When the sum rules break down one can truncate the intermediate sums at some value of the intermediate masses. In this way one obtains an algebraic form of finiteenergy sum rules. They consist in commutation rules among Reggeons with the righthand side being given by the Regge couplings that can be exchanged in the corresponding scattering process. The structure constants of this algebra are the corresponding tripleRegge couplings. As an example one may assume dominance of leading trajectories and finds that ϱ, A _{1}, π and f residues commute like O(5). Including also the commutators with vector and axial vector changes, one obtains the "supergroup" SU(2) × SU(2) × O(5). The Regge couplings we are dealing with here are all in the infinitemomentum frame. In order to give the connection with standard tchannel couplings the angular condition for bilocal form factors are derived and continued in angular momentum. As another technical side results we point out that under very weak assumptions the bilocal form factors F( k, z) are analytic in z. F( k, z) does not, however, possess Regge behaviour for  z → ∞ as often stated. Only signatured bilocal form factors do, as shown in this work.
 Publication:

Nuclear Physics B
 Pub Date:
 November 1973
 DOI:
 10.1016/05503213(73)902769
 Bibcode:
 1973NuPhB..65...77K