Lattice regularization for chiral perturbation theory

Lewis, Randy; Ouimet, Pierre-Philippe A.

doi:10.1103/physrevd.64.034005

Cited by 28 publications

(44 citation statements)

References 19 publications

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“…For example, we have shown that the same physics results from use of lattice size as a regulator [16]. The purpose of the cutoff function is to remove the model-dependent short distance portions of the loop integrals which are not suppressed in dim reg.…”

Section: Introductionmentioning

confidence: 89%

Long distance regularization in chiral perturbation theory with decuplet fields

et al. 2002

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We investigate the use of long distance regularization in SU (3) baryon chiral perturbation theory with decuplet fields. The one-loop decuplet contributions to the octet baryon masses, axial couplings, S-wave nonleptonic hyperon decays and magnetic moments are evaluated in a chirally consistent fashion by employing a cutoff to implement long distance regularization. The convergence of the chiral expansions of these quantities is improved compared to the dimensionally regularized version which indicates that the propagation of Goldstone bosons over distances smaller than a typical hadronic size, which is beyond the regime of chiral perturbation theory but included by dimensional regularization, is removed by use of a cutoff.

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Section: Introductionmentioning

confidence: 89%

Long distance regularization in chiral perturbation theory with decuplet fields

et al. 2002

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“…In Ref. [115] a lattice regularized version of ChPT is used to determine the typical size of discretization errors. For physical values of m q , baryon masses turn out to be essentially independent of lattice spacing when π/a Λ χ .…”

Section: Brief Survey Of Lattice Qcd Resultsmentioning

confidence: 99%

Quark mass dependence of nucleon observables and lattice QCD

Procura¹,

Musch²,

Hemmert³

et al. 2006

AIP Conference Proceedings

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SummaryUnderstanding hadron structure from first principles is one of the great unsolved problems in physics. Lattice QCD on one side and chiral effective field theory on the other are progressively developing as important tools to deal with the non-perturbative nature of low-energy QCD and the structure of the nucleon. At present, however, there is a gap between the relatively large quark masses accessible in fully-dynamical lattice simulations and the small quark masses relevant for comparison with physical quantities. We combine Chiral Perturbation Theory, which predicts the quark mass dependence of nucleon observables, with lattice computations where the quark mass is a tunable parameter. We explore the feasibility of a systematic approach, based on the chiral effective Lagrangian, for the chiral extrapolation of lattice QCD data. In the framework of baryon chiral effective field theories with and without explicit ∆ (1232) degrees of freedom, we work out the quark mass dependence of the nucleon mass M N and the axialvector coupling constant g A at one-loop order and perform a numerical analysis of the relevant formulae using as input the most recent lattice QCD results. ZusammenfassungEs ist eines der großen ungelösten Probleme in der Physik, die hadronische Struktur von Anfang an zu verstehen. Gitter-QCD auf der einen Seite und chirale effektive Feldtheorie auf der anderen entwickeln sich schrittweise zu wichtigen Werkzeugen, mit der nicht-perturbativen Natur der Niederenergie-QCD und der Nukleonstruktur umzugehen. Momentan besteht jedoch eine Lücke zwischen den relativ großen Quarkmassen, die in voll-dynamischen Gittersimulationen verwendet werden müssen, und den kleinen Quarkmassen, die für den Vergleich mit physikalischen Größen relevant sind. Wir kombinieren Chirale Störungstheorie, die die Quarkmassenabhängigkeit von Nukleon-Observablen vorhersagt, mit Gitterrechnungen, in denen die Quarkmasse ein veränderbarer Parameter ist. Wir untersuchen, ob ein systematischer Zugang zur chiralen Extrapolation von Gitter-QCD-Daten, basierend auf der chiralen effektiven Lagrangedichte, möglich ist. Im Rahmen von baryonischen chiralen effektiven Feldtheorien mit und ohne explizitem ∆ (1232)-Freiheitsgrad berechnen wir die Quarkmassenabhängigkeit der Nukleonmasse M N und der Axialvektor-Kopplungskonstante g A in führender Ein-Schleifen-Ordnung und führen eine numerische Analyse der relevanten Formeln mit den neuesten Gitter-QCD-Ergebnissen als Input durch. 5 6

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“…We end this section with a number of remarks: 14 Our normalization is such that in the real world f π = 130.4 MeV. Another common convention uses a value smaller by a factor √ 2.…”

Section: Conserved Currentsmentioning

confidence: 99%

“…It therefore describes all pion physics to leading order in pion momenta. For example, writing φ as φ = φ a T a , with T a the generators of SU(3) obeying 14) one finds the leading-order prediction for the pion scattering amplitude from a tree-level calculation using Eq. (2.13):…”

mentioning

confidence: 99%

Applications of chiral perturbation theory to lattice QCD

Golterman¹

2011

Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance ComputingLecture Notes of the Les Houches Summer

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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 ǫ-regimes.

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Lattice regularization for chiral perturbation theory

Cited by 28 publications

References 19 publications

Long distance regularization in chiral perturbation theory with decuplet fields

Long distance regularization in chiral perturbation theory with decuplet fields

Quark mass dependence of nucleon observables and lattice QCD

Applications of chiral perturbation theory to lattice QCD

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