arXiv subjects

Masayasu Hasegawa

Publications and source records attributed to Masayasu Hasegawa.

10 recordsLinked to original sources

arXiv2024

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 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.

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arXiv2023

Monopole and instanton effects on connected and disconnected correlations for scalar density

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.

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arXiv2022

Color confinement, chiral symmetry breaking, and catalytic effect induced by monopole and instanton creations

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.

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arXiv2022

Instanton effects on chiral symmetry breaking and hadron spectroscopy

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$_{η'}$ = 1.055(15)$\times10^{3}$ [MeV] (at the continuum limit). (ii) m$_{η'}$ = 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.

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arXiv2020

Monopole and instanton effects in QCD

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.

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arXiv2016

Chiral symmetry breaking and monopoles

To understand the relation between the chiral symmetry breaking and monopoles, the chiral condensate which is the order parameter of the chiral symmetry breaking is calculated in the $\overline{\mbox{MS}}$ scheme at 2 [GeV]. First, we add one pair of monopoles, varying the monopole charges $m_{c}$ from zero to four, to SU(3) quenched configurations by a monopole creation operator. The low-lying eigenvalues of the Overlap Dirac operator are computed from the gauge links of the normal configurations and the configurations with additional monopoles. Next, we compare the distributions of the nearest-neighbor spacing of the low-lying eigenvalues with the prediction of the random matrix theory. The low-lying eigenvalues not depending on the scale parameter $Σ$ are compared to the prediction of the random matrix theory. The results show the consistency with the random matrix theory. Thus, the additional monopoles do not affect the low-lying eigenvalues. Moreover, we discover that the additional monopoles increase the scale parameter $Σ$. We then evaluate the chiral condensate in the $\overline{\mbox{MS}}$ scheme at 2 [GeV] from the scale parameter $Σ$ and the renormalization constant $Z_{S}$. The final results clearly show that the chiral condensate linearly decreases by increasing the monopole charges.

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arXiv2015

Chiral symmetry breaking, instantons, and monopoles

The purpose of this study is to show that monopoles induce the chiral symmetry breaking. In order to indicate the evidence, we add one pair of monopoles with magnetic charges to the quenched SU(3) configurations by a monopole creation operator, and investigate the propaties of the chiral symmetry breaking using the Overlap fermion. We show that instantons are created by the monopoles. The pseudoscalar meson mass and decay constant are computed from the correlation functions, and the renormalization constant $Z_{S}$ is determined by the non perturbative method. The renormalization group invariant chiral condensate in $\overline{\mbox{MS}}$-scheme at 2 [GeV] is evaluated by the Gell-Mann-Oakes-Renner formula, and the random matrix theory. Finally, we estimate the renormalization group invariant quark masses $\bar{m} = (m_{u} + m_{d})/2$, and $m_{s}$ in $\overline{\mbox{MS}}$-scheme at 2 [GeV]. The preliminary results indicate that the chiral condensate decreases and the quark masses become slightly heavy by increasing the number of monopole charges.

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arXiv2015

Zero modes of Overlap fermions, instantons, and monopoles

The purpose of this study is to investigate the relations between instantons, monopoles, and Chiral symmetry breaking. The monopoles are important topological configurations existing in QCD which are believed to produce colour confinement. The groups of University of Kanazawa and Pisa have produced by Lattice simulations many results supporting the idea that QCD vacuum is a dual superconductor. Instantons are related to Chiral symmetry breaking, as explained e.g. in the instanton liquid model of E. V. SHURYAK. Clarifying quantitatively the relation between monopoles and instantons is not easy, also because monopoles are three dimensional objects, while instantons are four dimensional. We generate configurations, adding monopole-antimonopole pairs of opposite charges by a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops in the configurations. Then, we count the number of fermion zero modes in the configurations using Overlap fermions as a tool. Finally, we find that one monopole-antimonopole pair makes one zero mode of plus or minus chirality, that is to say, one instanton of plus or minus charge.

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arXiv2015

Instantons and Monopoles

This study is part of a research program aimed to investigate the relations between instantons, monopoles, and chiral symmetry breaking. Monopoles are important 3-dimensional topological configurations existing in QCD, which are believed to produce colour confinement. Instantons are 4-dimensional topological configurations and are known to be related to chiral symmetry breaking. To study the relation between monopoles and instantons we generate configurations adding to the vacuum state static monopole-antimonopole pairs of opposite charges by use of a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops to the configurations. We then count the number of fermion zero modes using Overlap fermions as a tool. As a result we find that each monopole-antimonopole pair of magnetic charge one adds one zero mode of chirality $\pm1$, i.e. one instanton of topological charge $\pm1$.

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arXiv2014

Zero modes, Instantons, and Monopoles

The purpose of this study is to show the relations between monopoles instantons and Chiral symmetry breaking. First, in order to show the relation between instantons and monopoles, we generate configurations, adding monopoles by a monopole creation operator. Then, we count the number of fermion zero modes in the configurations using Overlap fermions as a tool. As a result we find that one monopole with plus one charge and one anti-monopole with minus one charge make one instanton of charge plus or minus one. We have already reported these results elsewhere. In addition, in this report, the relation between the additional monopoles and Chiral symmetry breaking is discussed. We compute the Chiral condensate, the pseudo-scalar mass, and the pion decay constant. Preliminary results show that the additional monopoles do affect Chiral symmetry breaking.

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