Monopole and instanton effects in QCD
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Springer
Received: July 9, 2020 Accepted: August 6, 2020 Published: September 17, 2020
Monopole and instanton effects in QCD
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow 141980, Russia
E-mail: [email protected] 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 antimonopole 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. Keywords: Lattice QCD, Lattice Quantum Field Theory, Solitons Monopoles and Instantons, Spontaneous Symmetry Breaking ArXiv ePrint: 1807.04808
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)113
JHEP09(2020)113
Masayasu Hasegawa
Contents 1 Introduction
2
2 Monopoles 2.1 The monopole creation operator 2.2 The simulation parameters 2.3 The monopole density and the length of the monopole loops
5 5 5 6 9 9 9 12
4 Predictions of the chiral condensate and the decay constants 4.1 The predictions of the chiral condensate 4.2 The predictions of the decay constants
17 18 20
5 The 5.1 5.2 5.3 5.4 5.5
20 21 23 25 26 29
PCAC relation, decay constants, and chiral condensate The correlation functions The PCAC relation The renormalization constants ZˆS and ZA The decay constant of the pseudoscalar FPS The chiral condensate
6 Instanton effects 6.1 The normalization factors 6.2 The instanton effects on the decay constant F0 6.3 The instanton effects on the chiral condensate 6.4 The decay constants and masses of the pion and kaon 6.5 The light quark masses 6.6 The instant
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