The Vector Meson Mass in Chiral Effective Field Theory

TL;DR

This paper explores the use of Effective Field Theory to calculate the rho meson mass in lattice QCD, examining regularization schemes, finite-volume effects, and the challenges of unquenching due to meson instability.

Contribution

It formulates an EFT for the rho meson, compares regularization schemes, and assesses the feasibility of unquenching in lattice QCD, highlighting the instability of rho mesons.

Findings

No stable unquenching procedure for rho mesons was found.

Finite-volume effects were quantified and incorporated into mass calculations.

Rho mesons are inherently unstable, complicating unquenching efforts.

Abstract

A brief overview of Quantum Chromodynamics (QCD) as a non-Abelian gauge field theory, including symmetries and formalism of interest, will precede a focused discussion on the use of an Effective Field Theory (EFT) as a low energy perturbative expansion technique. Regularization schemes involved in Chiral Perturbation Theory (\c{hi}PT) will be reviewed and compared with EFT. Lattices will be discussed as a useful procedure for studying large mass particles. An Effective Field Theory will be formulated, and the self energy of the \r{ho} meson for a Finite-Range Regulated (FRR) theory will be calculated. This will be performed in both full QCD and the simpler quenched approximation (QQCD). Finite-volume artefacts, due to the finite box size on the lattice, will be quantified. Currently known lattice results will be used to calculate the \r{ho} meson mass, and the possibility of unquenching will be explored. The aim of the research was to determine whether a stable unquenching procedure for the \r{ho} meson could be discovered. The results from the original research indicate that there is no such procedure because the \r{ho} mesons are unstable. Unless additional data involving lighter quark masses is available, an element of modelling is needed for successful unquenching.