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Register a new userContinuum limit of the axial anomaly and index for the staggered overlap Dirac operator: An overview
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Evaluation of the continuum limit of the axial anomaly and index is sketched for the staggered overlap Dirac operator. There are new complications compared to the usual overlap case due to the distribution of the spin and flavor components around lattice hypercubes in the staggered formalism. The index is found to correctly reproduce the continuum index, but for the axial anomaly this is only true after averaging over the sites of a lattice hypercube.
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We review the spectral flow techniques for computing the index of the overlap Dirac operator including results relevant for SUSY Yang-Mills theories. We describe properties of the overlap Dirac operator, and methods to implement it numerically. We use the results from the spectral flow to illuminate the difficulties in numerical calculations involving domain wall and overlap fermions.
We discuss the weak coupling expansion of lattice QCD with the overlap Dirac operator. The Feynman rules for lattice QCD with the overlap Dirac operator are derived and the quark self-energy and vacuum polarization are studied at the one-loop level. We confirm that their divergent parts agree with those in the continuum theory.
We present the first continuum extrapolation of the hyperon octet axial couplings ($g_{Sigma Sigma}$ and $g_{Xi Xi}$) from $N_f=2+1+1$ lattice QCD. These couplings are important parameters in the low-energy effective field theory description of the octet baryons and fundamental to the nonleptonic decays of hyperons and to hyperon-hyperon and hyperon-nucleon scattering with application to neutron stars. We use clover lattice fermion action for the valence quarks with sea quarks coming from configurations of $N_f=2+1+1$ highly improved staggered quarks (HISQ) generated by MILC Collaboration. Our work includes the first calculation of $g_{Sigma Sigma}$ and $g_{Xi Xi}$ directly at the physical pion mass on the lattice, and a full account of systematic uncertainty, including excited-state contamination, finite-volume effects and continuum extrapolation, all addressed for the first time. We find the continuum-limit hyperon coupling constants to be $g_{Sigma Sigma}=0.4455(55)_text{stat}(65)_text{sys}$ and $g_{Xi Xi} =-0.2703(47)_text{stat}(13)_text{sys}$, which correspond to low-energy constants of $D = 0.708(10)_text{stat}(6)_text{sys}$ and $F = 0.438(7)_text{stat}(6)_text{sys}$. The corresponding SU(3) symmetry breaking is 9% which is about a factor of 2 smaller than the earlier lattice estimate.
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.
We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic gauge configurations. We study both the unimproved and the HISQ Dirac operators. We compare the spectral flow index with the index obtained by identifying low-lying modes of large chirality.
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