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Related papers: Improving the Dirac Operator in Lattice QCD

200 papers

Using N=1 Supersymmetric QCD (SQCD) as a prototype model, this work presents a formulation of overlap quarks and gluinos on the lattice, with particular emphasis on the construction of chirally symmetric Yukawa terms. By incorporating the…

High Energy Physics - Lattice · Physics 2025-07-23 Marios Costa , Eleni Ioannou , Haralambos Panagopoulos

We construct a hierarchy of lattice fermions, where the coarser lattice Dirac operator is the Schur complement of the block UL decomposition of the finer lattice operator. We show that the construction is an exact gauged renormalisation…

High Energy Physics - Lattice · Physics 2007-05-23 Artan Borici

We propose the formulation of lattice QCD wherein all elements of the theory (gauge action, fermionic action, theta-term, and all operators) are constructed from a single object, namely the lattice Dirac operator D with exact chiral…

High Energy Physics - Lattice · Physics 2007-05-23 Ivan Horvath

A new class of lattice Dirac operators $D$ have been recently proposed on the basis of the generalized Ginsparg-Wilson relation, $\gamma_5(\gamma_5 D) + (\gamma_5 D)\gamma_5 =2a^{2k+1}(\gamma_5 D)^{2k+2}$, where $k$ is a non-negative…

High Energy Physics - Lattice · Physics 2007-05-23 Kazuo Fujikawa , Masato Ishibashi

A distinctive feature of the presence of spontaneous chiral symmetry breaking in QCD is the condensation of low modes of the Dirac operator near the origin. The rate of condensation must be equal to the slope of (Mpi^2 Fpi^2)/2 with respect…

High Energy Physics - Phenomenology · Physics 2015-03-25 Georg P. Engel , Leonardo Giusti , Stefano Lottini , Rainer Sommer

We compute the ratio between the scale $\Lambda_L$ associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\Lambda_{MS-bar}$. To this end, the one-loop relation between the lattice coupling $g_0$ and the coupling…

High Energy Physics - Lattice · Physics 2015-06-25 C. Alexandrou , E. Follana , H. Panagopoulos , E. Vicari

We show that the Wilson Dirac operator in lattice gauge theory can be identified as a mathematical object in $K$-theory and that its associated spectral flow is equal to the index. In comparison to the standard lattice Dirac operator index,…

High Energy Physics - Theory · Physics 2025-07-08 Shoto Aoki , Hidenori Fukaya , Mikio Furuta , Shinichiroh Matsuo , Tetsuya Onogi , Satoshi Yamaguchi

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the…

High Energy Physics - Lattice · Physics 2014-11-17 Ting-Wai Chiu

We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following…

High Energy Physics - Lattice · Physics 2015-08-26 Mario Kieburg , Jacobus J. M. Verbaarschot , Savvas Zafeiropoulos

A remarkable feature of a lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson lattice Dirac operator does not possess topological zero modes for any…

High Energy Physics - Lattice · Physics 2011-02-16 Ting-Wai Chiu

We consider two-flavor QCD in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken at order a and hence the isovector axial currents require improvement as well as a finite…

High Energy Physics - Lattice · Physics 2007-05-23 Roland Hoffmann

We construct a lattice Dirac operator of overlap type that describes the propagation of a Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it is believed…

High Energy Physics - Lattice · Physics 2009-11-11 Masashi Hayakawa , Hiroto So , Hiroshi Suzuki

The $SU(3)\otimes SU(2) \otimes U(1)$ standard model maps smoothly onto a conventional lattice gauge formulation, including the parity violation of the weak interactions. The formulation makes use of the pseudo-reality of the weak group and…

High Energy Physics - Lattice · Physics 2024-01-08 Michael Creutz

We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…

High Energy Physics - Lattice · Physics 2009-04-14 Martina Joergler , C. B. Lang

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields.…

High Energy Physics - Lattice · Physics 2008-11-26 W. Bietenholz

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…

High Energy Physics - Lattice · Physics 2009-11-07 Werner Kerler

In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories…

High Energy Physics - Lattice · Physics 2009-10-31 J. J. M. Verbaarschot

We simulate Quantum Chromodynamics in four Euclidean dimensions with two (degenerate mass) flavors of dynamical quarks. The Dirac operator is the so-called chirally improved operator that has been studied so far in quenched calculations. We…

High Energy Physics - Lattice · Physics 2007-05-23 C. B. Lang , Pushan Majumdar , Wolfgang Ortner

I review recent progress achieved on the lattice in the quantitative comprehension of chiral symmetry breaking in QCD. Emphasis is given to the recent precise computations of the spectral density of the Dirac operator in the continuum…

High Energy Physics - Lattice · Physics 2015-11-30 Leonardo Giusti

I review the lattice formulations of vector-like gauge theories (e.g. QCD) with domain-wall/overlap fermions, and discuss how to optimize the chiral symmetry for any finite $ N_s $ (sites in the fifth dimension). In this formulation, quark…

High Energy Physics - Lattice · Physics 2011-02-16 Ting-Wai Chiu