On the Spectrum of Lattice Massive SU(2) Yang-Mills

TL;DR

This study uses lattice simulations to analyze the spectrum of Massive SU(2) Yang-Mills theory, revealing energy gap behaviors near a critical mass that suggest long-range correlations and possible bound state formations.

Contribution

It provides new lattice simulation results on the energy spectrum and correlations in Massive SU(2) Yang-Mills theory, highlighting phenomena near the critical mass value.

Findings

Energy gaps in I=1,J=1 channel follow the bare mass away from criticality.

Near the critical mass, a bifurcation in the energy gap indicates different correlation regimes.

I=0 gaps show a dramatic drop near the critical mass, suggesting bound state formation.

Abstract

On the basis of extended simulations we provide some results concerning the spectrum of Massive SU(2) Yang-Mills on the lattice. We study the "time" correlator of local gauge invariant operators integrated over the remaining three dimensions. The energy gaps are measured in the isospin I=0,1 and internal spin J=0,1 channels. No correlation is found in the I=1,J=0 channel. In the I=1, J=1 channel and far from the critical mass value $m_c$ the energy gap roughly follows the bare value $m$ (vector mesons). In approaching the critical value $m_c$ at $\beta$ fixed, there is a bifurcation of the energy gap: one branch follows the value $m$, while the new is much larger and it shows a more and more dominant weight. This phenomenon might be the sign of two important features: the long range correlation near the fixed point at $\beta \to \infty$ implied by the low energy gap and the screening (or confining) mechanisms across the $m=m_c$ associated to the larger gap. The I=0, J=0,1 gaps are of the same order of magnitude, typically larger than the I=1, J=1 gap (for $m>>m_c$). For $m\sim m_c$ both I=0 gaps have a dramatic drop with minima near the value $m$. This behavior might correspond to the formation of I=0 bound states both in the J=0 and J=1 channels.