Color confinement, chiral symmetry breaking, and catalytic effect induced by monopole and instanton creations (2203.11357v2)

Abstract: 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.