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Search Results: 1 - 10 of 1006 matches for " Maarten Golterman "
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QCD with rooted staggered fermions
Golterman, Maarten
High Energy Physics - Phenomenology , 2008,
Abstract: In this talk, I will give an overview of the theoretical status of staggered Lattice QCD with the "fourth-root trick." In this regularization of QCD, a separate staggered quark field is used for each physical flavor, and the inherent four-fold multiplicity that comes with the use of staggered fermions is removed by taking the fourth root of the staggered determinant for each flavor. At nonzero lattice spacing, the resulting theory is nonlocal and not unitary, but there are now strong arguments that this disease is cured in the continuum limit. In addition, the approach to the continuum limit can be understood in detail in the framework of effective field theories such as staggered chiral perturbation theory.
Applications of chiral perturbation theory to lattice QCD
Maarten Golterman
Physics , 2009,
Abstract: These notes contain the written version of lectures given at the 2009 Les Houches Summer School "Modern perspectives in lattice QCD: Quantum field theory and high performance computing." The goal is to provide a pedagogical introduction to the subject, and not a comprehensive review. Topics covered include a general introduction, the inclusion of scaling violations in chiral perturbation theory, partial quenching and mixed actions, chiral perturbation theory with heavy kaons, and the effects of finite volume, both in the p- and epsilon-regimes.
QCD with rooted staggered fermions
Maarten Golterman
Physics , 2008,
Abstract: In this talk, I will give an overview of the theoretical status of staggered Lattice QCD with the "fourth-root trick." In this regularization of QCD, a separate staggered quark field is used for each physical flavor, and the inherent four-fold multiplicity that comes with the use of staggered fermions is removed by taking the fourth root of the staggered determinant for each flavor. At nonzero lattice spacing, the resulting theory is nonlocal and not unitary, but there are now strong arguments that this disease is cured in the continuum limit. In addition, the approach to the continuum limit can be understood in detail in the framework of effective field theories such as staggered chiral perturbation theory.
Connections Between Lattice Gauge Theory and Chiral Perturbation Theory
Maarten Golterman
Physics , 1997, DOI: 10.1007/BFb0104897
Abstract: In this talk, I address the comparison between results from lattice QCD computations and Chiral Perturbation Theory (ChPT). I briefly discuss how ChPT can be adapted to the much-used quenched approximation and what it tells us about the special role of the $\eta'$ in the quenched theory. I then review lattice results for some quantities (the pion mass, pion scattering lengths and the $K^+\to\pi^+\pi^0$ matrix element) and what quenched ChPT has to say about them.
Lattice Chiral Gauge Theories
Maarten Golterman
Physics , 2000, DOI: 10.1016/S0920-5632(01)00953-7
Abstract: I review the substantial progress which has been made recently with the non-perturbative construction of chiral gauge theories on the lattice. In particular, I discuss three different approaches: a gauge invariant method using fermions which satisfy the Ginsparg-Wilson relation, and two gauge non-invariant methods, one using different cutoffs for the fermions and the gauge fields, and one using gauge fixing. Open problems within all three approaches are addressed.
Chiral Perturbation Theory, Non-leptonic Kaon Decays, and the Lattice
Maarten Golterman
Physics , 2000,
Abstract: In this talk, I first motivate the use of Chiral Perturbation Theory in the context of Lattice QCD. In particular, I explain how partially quenched QCD, which has, in general, unequal valence- and sea-quark masses, can be used to obtain real-world (i.e. unquenched) results for low-energy constants. In the second part, I review how Chiral Perturbation Theory may be used to overcome theoretical difficulties which afflict the computation of non-leptonic kaon decay rates from Lattice QCD. I argue that it should be possible to determine at least the O(p^2) weak low-energy constants reliably from numerical computations of the K to pi and K to vacuum matrix elements of the corresponding weak operators.
On the phase diagram of quenched QCD with Wilson fermions
Maarten Golterman
Physics , 2003, DOI: 10.1016/S0920-5632(03)02460-5
Abstract: In this talk, I reported on recent work on the Aoki phase diagram for quenched QCD with two flavors of Wilson fermions. Part of this work was done in collaboration with Yigal Shamir, and a shorter account of this part appeared recently. In this write-up, I will therefore limit myself to reporting on work done with Steve Sharpe and Robert Singleton, Jr, which has not been published yet. We discuss the symmetries of quenched QCD, paying careful attention to non-perturbative issues. This allows us to derive an effective lagrangian which agrees with standard quenched chiral perturbation theory, but which can also be used to address questions of a non-perturbative nature.
On tadpole improvement for staggered fermions
Maarten Golterman
Physics , 1998, DOI: 10.1016/S0920-5632(99)85240-2
Abstract: An explanation is proposed for the fact that Lepage--Mackenzie tadpole improvement does not work well for staggered fermions. The idea appears to work for all renormalization constants which appear in the staggered fermion self-energy. Wilson fermions are also discussed.
On the foundations of partially quenched chiral perturbation theory
Bernard, Claude;Golterman, Maarten
High Energy Physics - Phenomenology , 2013,
Abstract: It has been widely assumed that partially quenched chiral perturbation theory is the correct low-energy effective theory for partially quenched QCD. Here we present arguments supporting this assumption. First, we show that, for partially quenched QCD with staggered quarks, a transfer matrix can be constructed. This transfer matrix is not Hermitian, but it is bounded, and it can be used to construct correlation functions in the usual way. Combining these observations with an extension of the Vafa--Witten theorem to the partially quenched theory allows us to argue that the partially quenched theory satisfies the cluster property. By extending Leutwyler's analysis of the unquenched case to the partially quenched theory, we then conclude that the existence and properties of the transfer matrix as well as clustering are sufficient for partially quenched chiral perturbation theory to be the correct low-energy theory for partially quenched QCD.
Chiral Perturbation Theory for the Quenched Approximation of QCD
Claude Bernard,Maarten Golterman
Physics , 1992, DOI: 10.1103/PhysRevD.46.853
Abstract: [This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_\pi$, $m_\pi$, $m_K$, and the ratio of $\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.
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