Multi-Reggeon Behavior of Production Amplitudes

Abstract

Gribov's approach is used to investigate the asymptotic properties of production amplitudes. When it is applied to an analysis of double Reggeon exchange, the results of previous authors are confirmed. In particular, it is verified that the amplitude $f_{{\alpha }_1{\alpha }_2}$ for the coupling of two Reggeons, ${\alpha }_1$ and ${\alpha }_2$, to a particle (of mass $M$) depends not only on the masses ${q_1}^{\prime 2}$ and ${q_2}^{\prime 2}$ of the Reggeons, but also on ${q_3}^{\prime 2}={({q_1}^{\prime }-{q_2}^{\prime })}^2$. (Primed vectors are spacelike and perpendicular to the incident beam.) On the basis of a diagrammatic model, the dependence of $f_{{\alpha }_1{\alpha }_2}$ on ${q_3}^{\prime 2}$ is elucidated. When $M=m_{\pi }$, a strong variation of $f_{{\alpha }_1{\alpha }_2}$ throughout the physical region is expected. The same approach is applied to an analysis of a Reggeon triangle graph. Gribov's rules are found to apply provided that certain extra factors are included in the integrand. Because of these factors, the Reggeon "Ward identity" suggested by Anselm and Dyatlov no longer holds. The analytic structure of the corresponding double partial-wave amplitude is investigated. It has ordinary two-Reggeon singularities in each angular momentum separately, together with a leading curve depending on both variables. For the triangle graph, it turns out that the leading curve determines the asymptotic behavior, which is of the form $\frac{s^J}{\ln s}$, where the exponent $J$ depends on ${q_3}^{\prime 2}$ as well as on ${q_1}^{\prime 2}$ and ${q_2}^{\prime 2}$. This type of behavior has no analog in two-body scattering, and it would be of interest to identify such behavior experimentally. Finally, it is pointed out that underlying the definition of the approximate double partial wave used in this paper is the asymptotic simplicity of analytic structure in energy variables of the production amplitude.