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Authors
Werner Kerler
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Instead of the Ginsparg-Wilson relation only generalized chiral symmetry is required. The resulting much larger class of Dirac operators for massless fermions is investigated and a general construction for them is given. It is also shown that the new class still leads properly to Weyl fermions and to chiral gauge theories.
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Instead of the Ginsparg-Wilson (GW) relation we only require generalized chiral symmetry and show that this results in a larger class of Dirac operators describing massless fermions, which in addition to GW fermions and to the ones proposed by Fujikawa includes many more general ones. The index turns out to depend solely on a basic unitary operator. We use spectral representations to analyze the new class and to obtain detailed properties. We also show that our weaker conditions still lead properly to Weyl fermions and to chiral gauge theories.
We study a recently proposed formulation of overlap fermions at finite density. In particular we compute the energy density as a function of the chemical potential and the temperature. It is shown that overlap fermions with chemical potential reproduce the correct continuum behavior.
A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces the four quark flavors described by the staggered fermion to two quark flavors; this pair can be taken as the up and down quarks in Lattice QCD. The exact flavored chiral symmetry of the staggered fermion gets converted into an unflavored Ginsparg-Wilson chiral symmetry of the new overlap fermion, which also has pairs of exact chiral zero-modes satisfying the Index Theorem. Stability under radiative corrections is checked. A domain wall formulation giving a truncation of this overlap construction is also outlined.
In this work we present the isovector flavor combination for the nucleon tensor charge extracted from lattice QCD simulations using overlap fermions on $N_f=2+1$ domain-wall configurations. The pion mass dependence is studied using six valence quark masses, each reproducing a value for the pion mass in the valence sector between 147 and 330 MeV. We investigate and eliminate systematic uncertainties due to contamination by excited states, by employing several values for the source-sink separation that span from 1 fm to 1.6 fm. We apply a chiral extrapolation in the valence sector using a quadratic and a logarithmic term to fit the pion mass dependence, which describes well the lattice data. The lattice matrix element is renormalized non-perturbatively, and the final result is $g_T=1.096(30)$ in the $overline{rm MS}$ scheme at a renormalization scale of 2 GeV.
We identify the chiral and angular momentum content of the leading quark-antiquark Fock component for the $rho(770)$ and $rho(1450)$ mesons using a two-flavor lattice simulation with dynamical Overlap Dirac fermions. We extract this information from the overlap factors of two interpolating fields with different chiral structure and from the unitary transformation between chiral and angular momentum basis. For the chiral content of the mesons we find that the $rho(770)$ slightly favors the $(1,0)oplus(0,1)$ chiral representation and the $rho(1450)$ slightly favors the $(1/2,1/2)_b$ chiral representation. In the angular momentum basis the $rho(770)$ is then a $^3S_1$ state, in accordance with the quark model. The $rho(1450)$ is a $^3D_1$ state, showing that the quark model wrongly assumes the $rho(1450)$ to be a radial excitation of the $rho(770)$.
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