Instanton effects on chiral symmetry breaking and hadron spectroscopy

TL;DR

This study investigates how monopoles and instantons influence chiral symmetry breaking and hadron masses in QCD, showing that instanton density affects meson properties and estimating the eta-prime meson mass.

Contribution

It introduces a method to incorporate monopoles and instantons into quenched SU(3) QCD and analyzes their effects on chiral symmetry and meson masses.

Findings

Monopoles relate to quark confinement without altering vacuum structure.

Instanton density correlates with chiral condensate decrease.

Eta-prime meson mass increases with instanton density.

Abstract

This project aims to give indications to find monopole and instanton effects in QCD on the observables by experiments. First, we add the monopole and anti-monopole to the QCD vacuum of the quenched SU(3) and calculate the physical observables using the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry. We have found that the additional monopole and anti-monopole make the long monopole loops are closely related to the quark confinement without changing the vacuum structure. Furthermore, we have confirmed that the additional monopole and anti-monopole create instantons and anti-instantons are closely associated with the chiral symmetry breaking. We have shown that the chiral condensate (minus value) decreases in direct proportion to the square root of the number density of the instantons and anti-instantons. The decay constants and masses of pion and kaon increase in direct proportion to the one-fourth root of the number density of the instantons and anti-instantons. This report estimates the eta meson mass using these outcomes as the input values, and the eta-prime meson mass is calculated in two ways: (i) Substituting the numerical results of the topological charge and pion decay constant to the Witten and Veneziano mass formula. (ii) Calculating the correlations of the disconnected (hairpin) graphs. The preliminary results of the eta-prime meson mass estimated in the quenched SU(3) are as follows. (i) m$_{\eta'}$ = 1.055(15)$\times10^{3}$ [MeV] (at the continuum limit). (ii) m$_{\eta'}$ = 1.04(2)$\times10^{3}$ [MeV] (at the chiral and continuum limits). Finally, we demonstrate that the eta-prime meson mass becomes heavy with increasing the number density of the instantons and anti-instantons.