Integrability in heavy quark effective theory

TL;DR

This paper explores the integrability of renormalization group equations in heavy quark effective theory, linking them to spin chain models and QCD, providing a mathematical framework and insights into their relation.

Contribution

It offers a comprehensive mathematical analysis of integrable spin chains in HQET within the QISM framework and connects these models to large-spin limits in QCD.

Findings

Renormalization group equations in HQET are integrable and related to spin chain models.

Conserved charges and wave functions in HQET can be derived from light-quark models in a scaling limit.

The work bridges HQET integrable models with large-spin limits in QCD.

Abstract

It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry $C(u)$ of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the "ground state" wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.