Chiral structure of the solutions of the Ginsparg-Wilson relation

Chiu, Ting‐Wai; Wang, Chih‐Wei; Zenkin, Sergei V.

doi:10.1016/s0370-2693(98)00982-4

Cited by 28 publications

(21 citation statements)

References 19 publications

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“…{γ 5 , D c } = 0; but, unlike D, it is non-local. This D c has been derived in the massless case [26,27,28] in association with the quark condensate and the solution of the Ginsparg-Wilson relation. For the massive case, it was pointed out [29,30] that the mass term ma should be added to the operator D c not D in the quark propagator and Eq.…”

Section: D)d(m)mentioning

confidence: 99%

Heavy and Light Quarks With Lattice Chiral Fermions

Liu

Dong

2005

Int. J. Mod. Phys. A

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The feasibility of using lattice chiral fermions which are free of O(a) errors for both the heavy and light quarks is examined. The fact that the effective quark propagators in these fermions have the same form as that in the continuum with the quark mass being only an additive parameter to a chirally symmetric antihermitian Dirac operator is highlighted. This implies that there is no distinction between the heavy and light quarks and no mass dependent tuning of the action or operators as long as the discretization error O(m 2 a 2 ) is negligible. Using the overlap fermion, we find that the O(m 2 a 2 ) (and O(ma 2 )) errors in the dispersion relations of the pseudoscalar and vector mesons and the renormalization of the axial-vector current and scalar density are small. This suggests that the applicable range of ma may be extended to ∼ 0.56 with only 5% error, which is a factor of ∼ 2.4 larger than that of the improved Wilson action. We show that the generalized Gell-Mann-Oakes-Renner relation with unequal masses can be utilized to determine the finite ma errors in the renormalization of the matrix elements for the heavy-light decay constants and semileptonic decay constants of the B/D meson.

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Section: D)d(m)mentioning

confidence: 99%

Heavy and Light Quarks With Lattice Chiral Fermions

Liu

Dong

2005

Int. J. Mod. Phys. A

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“…Here we just sketch the argument, which is valid for any reasonable action which satisfies the GWR. Starting from the Neuberger operator D N , one can define the associated operator [25] …”

Section: Four-fermion Operatorsmentioning

confidence: 99%

“…(1). Indeed, there exist lattice fermion actions which satisfy the GWR but which do not meet the above requirements [25]. A breakthrough in this field was achieved through the domain-wall formulation of lattice fermions [26] and by Neuberger through the overlap formulation [21].…”

Section: Introductionmentioning

confidence: 99%

Perturbative renormalization of weak Hamiltonian four-fermion operators with overlap fermions

Capitani

Giusti

2000

Phys. Rev. D

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The renormalization of the most general dimension-six four-fermion operators without power subtractions is studied at one loop in lattice perturbation theory using overlap fermions. As expected, operators with different chirality do not mix among themselves and parity-conserving and parity-violating multiplets renormalize in the same way. The renormalization constants of unimproved and improved operators are also the same. These mixing factors are necessary to determine physical matrix elements relevant to many phenomenological applications of weak interactions. The most important are the K 0 −K 0 and B 0 −B 0 mixings in the Standard Model and beyond, the ∆I = 1/2 rule and ǫ ′ /ǫ.

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“…(26). Indeed, there exist lattice fermion actions which satisfy the GWR but which do not meet the above requirements [16]. The Neuberger operator satisfies all the above requirements and is local in the weak coupling regime, as shown in Ref.…”

Section: The Schwinger Model Withmentioning

confidence: 99%

Schwinger model with the overlap-Dirac operator: Exact results versus a physics motivated approximation

2001

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We propose new techniques for the numerical implementation of the overlap-Dirac operator, which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the results are very promising. These techniques can be directly applied to QCD simulations. We also present a detailed computation of the spectrum and the chiral properties of the Schwinger model in the overlap lattice formulation.

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Chiral structure of the solutions of the Ginsparg-Wilson relation

Cited by 28 publications

References 19 publications

Heavy and Light Quarks With Lattice Chiral Fermions

Heavy and Light Quarks With Lattice Chiral Fermions

Perturbative renormalization of weak Hamiltonian four-fermion operators with overlap fermions

Schwinger model with the overlap-Dirac operator: Exact results versus a physics motivated approximation

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