Masayasu Hasegawa

This study investigates the effects on the connected and disconnected correlations for the scalar density that are induced by created monopoles and instantons in the QCD vacuum. To reveal the effects, we add a monopole and anti-monopole pair in the gauge field configurations in SU(3) by applying the monopole creation operator to the vacuum. We vary the magnetic charges of the monopole and anti-monopole and increase the number of monopoles and anti-monopoles in the configurations. The Dirac operator of overlap fermions preserves the exact chiral symmetry in lattice gauge theory and exact zero-modes exist in its spectrum. The eigenvalues and eigenvectors of the overlap Dirac operator have been calculated using these configurations, and the numbers of instantons and anti-instantons which are created by these additional monopoles and anti-monopoles have been estimated from the numbers of topological charges in our previous studies. In this study, we demonstrate the preliminary results that instantons and monopoles influence the masses that are evaluated from the connected and disconnected correlation functions for the scalar density using low-lying eigenvalues and eigenvectors of the overlap Dirac operator.

This study investigates the effects on the connected and disconnected correlations for the scalar density that are induced by created monopoles and instantons in the QCD vacuum. To reveal the effects, we add a monopole and anti-monopole pair in the gauge field configurations in \textit{SU}(3) by applying the monopole creation operator to the vacuum. We vary the magnetic charges of the monopole and anti-monopole and increase the number of monopoles and anti-monopoles in the configurations. The Dirac operator of overlap fermions preserves the exact chiral symmetry in lattice gauge theory and exact zero-modes exist in its spectrum. The eigenvalues and eigenvectors of the overlap Dirac operator have been calculated using these configurations, and the numbers of instantons and anti-instantons which are created by these additional monopoles and anti-monopoles have been estimated from the numbers of topological charges in our previous studies. In this study, we demonstrate the preliminary results that instantons and monopoles influence the masses that are evaluated from the connected and disconnected correlation functions for the scalar density using low-lying eigenvalues and eigenvectors of the overlap Dirac operator.

Our research reveals the relations among monopoles, color confinement, instantons, and chiral symmetry breaking which experiments can detect, by numerical calculations of lattice gauge theory. We first add a monopole and an anti-monopole varying their magnetic charges to the gauge field configurations in the quenched approximation of quantum chromodynamics (QCD), by applying the monopole creation operator and investigate the effects of the added monopoles and anti-monopoles on color confinement. Second, we reveal the quantitative relations among instantons, anti-instantons, and observables using the eigenvalues and eigenvectors of the overlap Dirac operator, which are calculated using the normal configurations and the configurations with the additional monopoles and anti-monopoles. Finally, we ascertain the outcomes by comparing them with the predictions. We have already discovered the catalytic effect: the decay width of the charged pion becomes wider and its lifetime becomes shorter than the experimental outcomes by increasing the number density of instantons and anti-instantons. However, the outcomes in the previous study were obtained using one lattice volume and lattice spacing. In this research, we improve the previous study using a variety of configurations of different lattice volumes and values of the lattice spacing from low to finite temperatures. The main purposes of this study are to inspect the influences of the finite lattice volume and discretization on the observables and quantitative relations that we have obtained in our previous research and to acquire the interpolated results at the continuum limit.

We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) The monopole creation operator makes the monopoles and anti-monopoles in the QCD vacuum. (ii) A monopole and anti-monopole pair creates an instanton or anti-instanton without changing the structure of the QCD vacuum. (iii) The monopole and anti-monopole pairs change only the scale of the spectrum distribution without affecting the spectra of the Dirac operator by comparing the spectra with random matrix theory. Next, we find the instanton effects by increasing the number density of the instantons and anti-instantons as follows: (iv) The decay constants of the pseudoscalar increase. (v) The values of the chiral condensate, which are defined as negative numbers, decrease. (vi) The light quarks and the pseudoscalar mesons become heavy. The catalytic effect on the charged pion is estimated using the numerical results of the pion decay constant and the pion mass. (vii) The decay width of the charged pion becomes wider than the experimental result, and the lifetime of the charged pion becomes shorter than the experimental result. These are the effects of the monopoles and instantons in QCD.