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

TL;DR

This study uses lattice QCD simulations to explore how external magnetic fields influence monopoles, the Dirac spectrum, instantons, and the eta-prime meson mass, revealing magnetic field effects on QCD topological and chiral properties.

Contribution

It provides new insights into the impact of magnetic fields on monopoles, spectral properties, and meson masses in lattice QCD with physical quark masses.

Findings

Magnetic fields affect monopole density and loop lengths.

Spectral densities and eigenvalue fluctuations are influenced by magnetic fields.

The eta-prime meson mass and chiral condensate show magnetic field dependence.

Abstract

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 fields are 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 ratio $\frac{m_{s}}{m_{u, d}}$. Standard configurations and configurations with applied external magnetic fields are generated in the color confinement and deconfinement phases. The intensity of external magnetic fields varies from $e|B|$ = 0.57 to 1.14 [GeV$^{2}$]. To examine the influence of external magnetic fields 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.