On Infrared Universality in Massive Theories. Another Example

TL;DR

This paper explores the infrared properties of ${}^3$-theory, revealing classical integrability and solutions via hypergeometric functions, with implications for soft scattering in massive theories.

Contribution

It demonstrates classical integrability of the effective ${}^3$-theory and provides explicit solutions, connecting infrared behavior with integrability concepts.

Findings

Effective ${}^3$-theory is classically integrable.

Explicit solutions are expressed in hypergeometric functions.

Potential applications to multiparticle soft scattering are discussed.

Abstract

The infrared behaviour of the ${\phi}^3$-theory is discussed stressing analogies with the Witten-Seiberg story about $N=2$ $QCD$. Though the microscopic theory is apparently not integrable, the effective theory is shown to be integrable at classical level, and a general solution of it in terms of hypergeometric functions is obtained. An effective theory for the multiparticle soft scattering is sketched.