Monopole and instanton effects in QCD

Abstract

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.

Chiral symmetry breaking and catalytic effect induced by monopole and instanton creations in QCD

“…This Examining the effects of the finite lattice volume (left) and the discretization (right) on the fitting results of the slope AN I . The outcomes of β = 6.0000, V = 14 4 and β = 6.0522, V = 18 3 × 32 are reported in our previous research [39,41] shows that the numerical results are consistent with the prediction (5) and that the effects of the finite lattice volume are negligible.…”

“…In the previous research [39,41], we found that the added monopole with a magnetic charge of +1 and antimonopole with a magnetic charge of -1 make one instanton or anti-instanton. The value of the chiral condensate, which is an order parameter of symmetry breaking, is defined as a negative number and decreases in direct proportion to the square root of the number density of the instantons and anti-instantons.…”

“…We use the numerical technique [48] and calculate approximately 100 pairs of low-lying eigenvalues and eigenvectors for each configuration by using the subroutines (ARPACK). The numbers of configurations N conf used for the calculations of the eigenvalues and eigenvectors are in Table 28 in B and Table 30 in C. The definition and parameters of the massless overlap Dirac operator are the same as those in our previous studies [39,41].…”

“…(iv) V = 18 3 × 32 of β = 6.0522. (The numerical results were given in [41].) (v) V = 20 3 × 40 of β = 6.1356.…”

Instanton effects on chiral symmetry breaking and hadron spectroscopy

“…We compared the numerical results with the predictions and discovered the effects of the added monopole and anti-monopoles and the created instantons and anti-instantons on the observables as follows [16]:…”