scholarly journals Determination of chiral condensate from low-lying eigenmodes of Mobius domain-wall Dirac operator

2017 ◽  
Author(s):  
Shoji Hashimoto ◽  
Guido Cossu ◽  
Hidenori Fukaya ◽  
Takashi Kaneko ◽  
Jun-Ichi Noaki
Keyword(s):  
Domain Wall ◽  
Dirac Operator ◽  
Chiral Condensate

scholarly journals Minimally doubled fermions and spontaneous chiral symmetry breaking

2018 ◽  
Vol 175 ◽  
pp. 04002 ◽  
Author(s):  
Rudina Osmanaj (Zeqirllari) ◽  
Dafina Hyka (Xhako)
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Low Energy ◽  
Reliable Determination ◽  
Spontaneous Chiral Symmetry Breaking ◽  
Energy Physics

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

scholarly journals Stochastic calculation of the Dirac spectrum on the lattice and a determination of chiral condensate in 2 + 1-flavor QCD

2016 ◽  
Vol 2016 (9) ◽  
pp. 093B06 ◽  
Author(s):  
Guido Cossu ◽  
Hidenori Fukaya ◽  
Shoji Hashimoto ◽  
Takashi Kaneko ◽  
Jun-Ichi Noaki
Keyword(s):  
Chiral Condensate ◽  
Dirac Spectrum

Determination of Intrinsic Magnetic Parameters of SmCo5 Phase in Sintered Samples

2005 ◽  
Vol 498-499 ◽  
pp. 129-133 ◽  
Author(s):  
Marcos Flavio de Campos ◽  
Fernando José Gomes Landgraf
Keyword(s):  
Powder Metallurgy ◽  
Domain Wall ◽  
Kerr Effect ◽  
Critical Diameter ◽  
Optical Microscope ◽  
Domain Theory ◽  
Magnetic Domains ◽  
Magnetic Parameters ◽  
Intrinsic Parameters

SmCo5 magnets are usually produced by powder metallurgy route, including milling, compaction and orientation under magnetic field, sintering and heat treatment. The samples produced by powder metallurgy, with grain size around 10 μm, are ideal for determination of intrinsic parameters. The first step for determination of intrinsic magnetic parameters is obtaining images of domain structure in demagnetized samples. In the present study, the domain images were produced by means of Kerr effect, in a optical microscope. After the test of several etchings, Nital appears as the most appropriate for observation of magnetic domains by Kerr effect. Applying Stereology and Domain Theory, several intrinsic parameters of SmCo5 phase were determined: domain wall energy 120 erg/cm2, critical diameter for single domain particle size 2 μm and domain wall thickness 60 Å. In the case of SmCo5, and also other phases with high magnetocrystalline anisotropy, Domain Theory presents several advantages when compared with Micromagnetics.

scholarly journals Stochastic calculation of the QCD Dirac operator spectrum with Mobius domain-wall fermion

2016 ◽  
Author(s):  
Shoji Hashimoto ◽  
Guido Cossu ◽  
Hidenori Fukaya ◽  
Takashi Kaneko ◽  
Jun Noaki
Keyword(s):  
Domain Wall ◽  
Dirac Operator ◽  
Operator Spectrum ◽  
Domain Wall Fermion

scholarly journals Monopole and instanton effects in QCD

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Masayasu Hasegawa
Keyword(s):  
Dirac Operator ◽  
Matrix Theory ◽  
Charged Pion ◽  
Lattice Gauge Theory ◽  
Pion Mass ◽  
Magnetic Monopoles ◽  
Chiral Condensate ◽  
Creation Operator ◽  
Experimental Result ◽  
Qcd Vacuum

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.

scholarly journals Chiral condensate and Dirac spectrum of one-and two-flavor QCD at nonzero θ-angle

2018 ◽  
Vol 175 ◽  
pp. 04004 ◽  
Author(s):  
Mario Kieburg ◽  
Jacobus Verbaarschot ◽  
Tilo Wettig
Keyword(s):  
Dirac Operator ◽  
Quark Mass ◽  
Imaginary Axis ◽  
Chiral Condensate ◽  
Dirac Spectrum ◽  
Quark Masses ◽  
Zero Modes

In previous work we showed that the chiral condensate of one-flavor QCD exhibits a Silver Blaze phenomenon when the quark mass crosses m = 0: the chiral condensate remains constant while the quark mass crosses the spectrum of the Dirac operator, which is dense on the imaginary axis. This behavior can be explained in terms of exponentially large cancellations between contributions from the zero modes and from the nonzero modes when the quark mass is negative. In these proceedings we show that a similar Silver Blaze phenomenon takes places for QCD with one flavor and arbitrary θ- angle, and for QCD with two flavors with different quark masses m1 and m2. In the latter case the chiral condensate remains constant when m1 crosses zero at fixed m2 > 0 until the Dashen point m1 = –m2 is reached, where the chiral condensate has a discontinuity. In terms of contributions from the Dirac spectrum the shift of the discontinuity from m1 = 0 to m1 = -m2 also arises from exponentially large cancellations between the zero and nonzero modes when m1m2 < 0. All calculations are performed in the microscopic or ε-domain of QCD. Results for arbitrary θ-angle are discussed as well.

Sign in / Sign up

Export Citation Format

Share Document