Abstract
AbstractWe present the results of our computation of the dimensionless chiral condensater0Σ1/3withNf= 2 andNf= 2 + 1 + 1 flavours of maximally twisted mass fermions. The condensate is determined from the Dirac operator spectrum, applying the spectral projector method proposed by Giusti and Lüscher. We use 3 lattice spacings and several quark masses at each lattice spacing to perform the chiral and continuum extrapolations. We study the effect of the dynamical strange and charm quarks by comparing our results forNf= 2 andNf= 2 + 1 + 1 dynamical flavours.
Highlights
Recently a method has been proposed [31] to effectively make use of the Banks-Casher relation and explore the chiral properties of QCD on the lattice, in particular to compute the chiral condensate
We present the results of our computation of the dimensionless chiral condensate r0Σ1/3 with Nf = 2 and Nf = 2 + 1 + 1 flavours of maximally twisted mass fermions
The method consists in stochastically evaluating the mode number, i.e. the number of eigenmodes of the Dirac operator below some spectral threshold value and using the dependence of this number of eigenmodes on the threshold value to calculate the observable of interest
Summary
Many interesting properties of the chiral regime of QCD can be understood from the behaviour of quantities related to the low-lying spectrum of the Dirac operator One of such spectral quantities, essential in the determination of the chiral condensate, is the mode number, i.e. the number of eigenvectors of the massive Hermitian Dirac operator D†D with eigenvalue magnitude smaller than some threshold value M 2. È If M is the orthogonal projector to the subspace of fermion fields spanned by the lowest lying eigenmodes of the massive Hermitian Dirac operator D†D with eigenvalues below some threshold value M 2, the mode number ν(M, μ) can be represented stochastically by:. Which is defined to match the chiral condensate to leading order of chiral perturbation theory
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