Boost-Invariant Running Couplings in Effective Hamiltonians

TL;DR

This paper develops a boost-invariant similarity renormalization group method for light-front Hamiltonians, deriving effective Hamiltonians with a running coupling that shows asymptotic freedom, consistent with traditional Feynman diagram results.

Contribution

It introduces a boost-invariant renormalization approach for light-front Hamiltonians, providing analytical integration and counterterms, and demonstrating the running coupling's behavior across frames.

Findings

Effective Hamiltonians exhibit a boost-invariant running coupling.

The evolution of the coupling matches Feynman diagram results.

The approach is valid in various moving frames, including the infinite momentum frame.

Abstract

We apply a boost-invariant similarity renormalization group procedure to a light-front Hamiltonian of a scalar field phi of bare mass mu and interaction term g phi^3 in 6 dimensions using 3rd order perturbative expansion in powers of the coupling constant g. The initial Hamiltonian is regulated using momentum dependent factors that approach 1 when a cutoff parameter Delta tends to infinity. The similarity flow of corresponding effective Hamiltonians is integrated analytically and two counterterms depending on Delta are obtained in the initial Hamiltonian: a change in mu and a change of g. In addition, the interaction vertex requires a Delta-independent counterterm that contains a boost invariant function of momenta of particles participating in the interaction. The resulting effective Hamiltonians contain a running coupling constant that exhibits asymptotic freedom. The evolution of the coupling with changing width of effective Hamiltonians agrees with results obtained using Feynman diagrams and dimensional regularization when one identifies the renormalization scale with the width. The effective light-front Schroedinger equation is equally valid in a whole class of moving frames of reference including the infinite momentum frame. Therefore, the calculation described here provides an interesting pattern one can attempt to follow in the case of Hamiltonians applicable in particle physics.