Abstract
We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using a stochastic method. We use 2+1 flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings (a = 0:083; 0:055; 0:044 fm) to estimate the continuum limit. The discretization effect can be minimized by a generalization of the valence domain-wall fermion. The spectral density at relatively high eigenvalues can be matched with perturbation theory. We compare the lattice results with the perturbative expansion available to O(α4s).
Highlights
Eigenvalue spectrum of the Dirac operator carries rich information of QCD dynamics
The chiral condensate has been calculated on the lattice and precise determination is achieved [2]
We investigate the discretization effect for the domain-wall fermion formulation and find that the effect on the eigenvalue largely depends on the parameters in the formulation
Summary
A well-known example is the Banks-Casher relation [1], which relates the chiral condensate, a consequence of nonperturbative QCD dynamics, to the low-lying eigenvalue density Through this relation, the chiral condensate has been calculated on the lattice and precise determination is achieved [2]. With lattice volume V, bin size δ, and lattice spacing a Using this relation, we can calculate the Dirac spectral density by identifying A = 2a2D†D − 1, which is constructed by the Dirac operator D. By adjusting the value of the Pauli-Villars mass, the discretization error appearing in the Dirac eigenvalue is greatly reduced without sacrifysing the locality and chirality.
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