Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields

The effects of external magnetic fields on monopoles, spectra of the overlap Dirac operator, instantons, and the mass of the eta-prime meson are examined by conducting lattice QCD simulations. The uniform external magnetic field is applied to gauge field configurations with \(N_f=2+1\) flavor quarks. The bare quark masses are tuned in order to obtain the physical values of the pion mass and of the \(m_s/m_{u,d}\) ratio. Standard configurations and configurations with an applied external magnetic field are generated in the color confinement and deconfinement phases. The intensity of the external magnetic field varies from \(e|B|=0.57\,\mathrm{GeV}^2\) to \(e|B|=1.14\,\mathrm{GeV}^2\). To examine the influence of the external magnetic field on monopoles, we first calculate the monopole density, measure the lengths of the monopole loops, and compare them with the absolute value of the Polyakov loops. Next, using the generated configurations, we compute the eigenvalues and eigenvectors of the overlap Dirac operator, which preserves exact chiral symmetry. To investigate how external magnetic fields affect the spectra of the overlap Dirac operator, we compute spectral densities, compare fluctuations of the eigenvalues of the overlap Dirac operator with the predictions of random matrix theory, and estimate the number of instantons and anti-instantons from the topological charges. In addition, we analyze smearing effects on these observables and chiral symmetry breaking. Finally, we calculate the decay constant of the pseudoscalar meson, the chiral condensate, and the square mass of the eta-prime meson using the eigenvalues and eigenvectors. We then extrapolate the numerical results in the chiral limit and demonstrate the effects of external magnetic fields on the extrapolation results. This article presents preliminary results.