Cut Diagrams Research Articles

S-channel discontinuities and the two-Reggeon cut

We make a detailed calculation of the $s$-channel discontinuities of the two-Reggeon cut in order to see how the singularities of the Reggeon-particle vertices affect the weight with which an intermediate state contributes to the cutlike part of the amplitude. We confirm the counting of Halliday and Sachrajda for the Mandelstam graph and show the extent to which this result can be applied to more general cut diagrams so that the results of Abramovskii, Gribov, and Kancheli hold. We also consider amplitudes with vertices constructed from the precepts of multi-Regge theory (for instance, from a dual model) in which the counting of terms is different: In particular, the simultaneous discontinuity through both Reggeons does not contribute to the cut. The weight of a given $n$-particle intermediate state in forming the cut depends crucially on the analytic properties of the vertex one chooses.

Large Angle Behavior, Multiple Scattering and Regge Cut with Urbaryon Line Diagram

The usefulness of Regge cut models has recently been examined but its definition has much ambiguity. We examine a Regge cut derived from the assumption of a multiple scattering mechanism in terms of urbaryon line diagrams for hadron reactions for the com­ posite particle reaction. We compare the urbaryon-line-diagram scheme with the Feynman­ diagram one in the case of Regge cuts and look at the difference between them in large-angle scattering. Assuming the unitarity relation for the urbaryon-line diagram, we examine how urbaryons behave in the multiple scattering mechanism, when the selection rule of the third double spectral function for the Regge cut is applied to urbaryon cut diagrams.

Mixing of Regge Poles and Cuts in a Field-Theory Model

The Regge poles generated by ladder diagrams in a λ φ3 theory are mixed with the moving cuts generated by a class of nonplanar graphs containing an internal ladder. Since the contribution from the cut-generating diagram is of order t−2ln mt, where t is the asymptotic variable, the t−2 behavior of the pure ladder graphs is examined and the trajectory of the Regge pole near ℓ = −2 is calculated. The Mellin transform method is used throughout. The transformed amplitude corresponding to a single cut insertion is given by a product of the form pole-cut-pole, where it is only the second Regge trajectory that mixes with the cut. The cut itself depends on the leading trajectory. This result substantiates the predictions as to form of other work based on unitarity, but differs in that the cut and pole depend on different trajectory functions. Finally, multiple insertions of the cut diagrams are shown to generate an amplitude with two moving poles on each sheet of the cut.