Four-pomeron vertex

TL;DR

This paper investigates the four-pomeron vertex in perturbative QCD, constructing leading order terms, analyzing its properties, and estimating its impact on collisions, revealing a relatively small influence of quadruple pomeron interactions.

Contribution

It introduces a detailed construction of the four-pomeron vertex in perturbative QCD, including its dominant terms and equations of motion, and provides numerical estimates of its effects.

Findings

The four-pomeron vertex consists of two main terms with different physical interpretations.

Iterative solutions are limited to small rapidities and large coupling constants, with instability issues.

Numerical estimates suggest the quadruple pomeron interaction has a small effect in practical collisions.

Abstract

The four-pomeron vertex is studied in the perturbative QCD. Its dominating terms of the leading (zeroth and first) orders in the coupling constant and subdominant in the number of colors are constructed. The vertex consists of two terms, one with a derivative in rapidity $\pd_y$ and the other with the BFKL interaction between pomerons. The corresponding part of the action and equations of motion are found. The iterative solution of the latter is possible only for rapidities smaller than 2 and quite large coupling constant $\alpha_s$, of the order or greater than unity, when the quadruple pomeron interaction is relatively small. Also iteration of the part with $\pd_y$ is unstable in the infrared region and compels to introduce an infrared cut. The variational approach with simple trying functions allows to find the minimum of the action at $\alpha_s$ of the order 0.2 and rapidities up to 25. Numerical estimates for O-O collisions show that actually the influence of the quadruple pomeron interaction turns out to be rather small.