arXiv subjects

Maarten Golterman

Publications and source records attributed to Maarten Golterman.

174 records · Page 10Linked to original sources

arXiv1997

Chiral perturbation theory for K+ to pi+ pi0 decay in the continuum and on the lattice

In this paper we use one-loop chiral perturbation theory in order to compare lattice computations of the K+ to pi+ pi0 decay amplitude with the experimental value. This makes it possible to investigate three systematic effects that plague lattice computations: quenching, finite-volume effects, and the fact that lattice computations have been done at unphysical values of the quark masses and pion external momenta (only this latter effect shows up at tree level). We apply our results to the most recent lattice computation, and find that all three effects are substantial. We conclude that one-loop corrections in chiral perturbation theory help in explaining the discrepancy between lattice results and the real-world value. We also revisit B_K, which is closely related to the K+ to pi+ pi0 decay amplitude by chiral symmetry.

hep-lat↗

arXiv1996

A Gauge-Fixing Action for Lattice Gauge Theories

We present a lattice gauge-fixing action $S_{gf}$ with the following properties: (a) $S_{gf}$ is proportional to the trace of $(\sum_μ\partial_μA_μ)^2$, plus irrelevant terms of dimension six and higher; (b) $S_{gf}$ has a unique absolute minimum at $U_{x,μ}=I$. Noting that the gauge-fixed action is not BRST invariant on the lattice, we discuss some important aspects of the phase diagram.

hep-lat↗

arXiv1995

The relation between the waveguide and overlap implementations of Kaplan's domain wall fermions

Recently, Narayanan and Neuberger proposed that the fermion determinant for a lattice chiral gauge theory be defined by an overlap formula. The motivation for that formula comes from Kaplan's five dimensional lattice domain wall fermions. In the case that the target continuum theory contains $4n$ chiral families, we show that the effective action defined by overlap formula is identical to the effective action of a modified waveguide model that has extra bosonic ghost fields. This raises serious questions about the viability of the overlap formula for defining chiral gauge theories on the lattice.

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arXiv1995

Why the overlap formula does not lead to chiral fermions

We describe a conceptually simple, but important test for the overlap approach to the construction of lattice chiral gauge theories. We explain the equivalence of the overlap formula with a certain waveguide model for a simple set of gauge configurations (the trivial orbit). This equivalence is helpful in carrying out the test, and casts serious doubts on the viability of the overlap approach. A recent note by Narayanan and Neuberger which points out a mistake in our previous work is irrelevant in this context.

hep-lat↗

arXiv1995

Scattering in the quenched approximation

We study, in the quenched approximation, Luescher's relation between pion scattering lengths and the finite-volume energy of two pions at rest. The quenched relation is drastically different from the full theory one; in particular, ``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$ occur at one loop ($L$ is the linear size of the box), due to the special properties of the $η'$ in the quenched approximation. Numerical examples show that the size of these effects can be substantial.

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arXiv1995

Finite-volume two-pion energies and scattering in the quenched approximation

We investigate how Lüscher's relation between the finite-volume energy of two pions at rest and pion scattering lengths has to be modified in quenched QCD. We find that this relation changes drastically, and in particular, that ``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$ occur at one loop ($L$ is the linear size of the box), due to the special properties of the $η'$ in the quenched approximation. We define quenched pion scattering lengths, and show that they are linearly divergent in the chiral limit. We estimate the size of these various effects in some numerical examples, and find that they can be substantial.

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arXiv1994

Domain wall fermions in a waveguide: the phase diagram at large Yukawa coupling

In this paper we return to a model with domain wall fermions in a waveguide. This model contains a Yukawa coupling $y$ which is needed for gauge invariance. A previous paper left the analysis for large values of this coupling incomplete. We fill the gap by developing a systematic expansion suitable for large $y$, and using this, we gain an analytic understanding of the phase diagram and fermion spectrum. We find that in a sense all the species doublers come back for large $y$. The conclusion that no lattice chiral gauge theory can be obtained from this approach therefore remains valid.

hep-lat↗

arXiv1993

Partially Quenched Gauge Theories and a Application to Staggered Fermions

We extend our lagrangian technique for chiral perturbation theory for quenched QCD to include theories in which only some of the quarks are quenched. We discuss the relationship between the partially quenched theory and a theory in which only the unquenched quarks are present. We also investigate the peculiar infrared divergences associated with the $η'$ in the quenched approximation, and find the conditions under which such divergences can appear in a partially quenched theory. We then apply our results to staggered fermion QCD in which the square root of the fermion determinant is taken, using the observation that this should correspond to a theory with four quarks, two of which are quenched. [Uses harvmac macro package. No postscipt for the figures is available (sorry), but the figures are simple and we include do-it-yourself instructions for drawing them.]

hep-lat↗

arXiv1992

The Quenched Approximation in Health and in Sickness

We present results for physical quantities computed in quenched chiral perturbation theory and compare them with the corresponding unquenched expressions. We also point out an apparent theoretical problem of the quenched approximation. latex, file espcrc2.sty needed (appended at the end: search for espcrc2.sty).

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arXiv1992

Chern-Simons Currents and Chiral Fermions on the Lattice

We compute the Chern-Simons current induced by Wilson fermions on a $d=2n+1$ dimensional lattice, making use of a topological interpretation of the momentum space fermion propagator as a map from the torus to the sphere, $T^{d}\to S^{d}$. These mappings are shown to fall in different homotopy classes depending on the value of $m/r$, where $m$ is the fermion mass and $r$ is the Wilson coupling. As a result, the induced Chern-Simons term changes discontinuously at $d+1$ different values for $m$, unlike in the continuum. This behavior is exactly what is required by the peculiar spectrum found for a recently proposed model of chiral lattice fermions as zeromodes bound to a domain wall.

hep-lat↗

arXiv1992

Absence of Chiral Fermions in the Eichten--Preskill Model

The model proposed by Eichten and Preskill for obtaining theories with chiral fermions from the lattice is shown to undergo spontaneous symmetry breaking. In addition, the fermions appear to be Dirac-like everywhere in the phase diagram with no room for undoubled Weyl fermions. The phase diagram of a closely related Higgs-Yukawa model is similar to that of the Smit--Swift model, which also does not give rise to chiral fermions. These results cast serious doubts on the original scenario for the emergence of chiral fermions.

hep-lat↗

arXiv1992

Chiral Perturbation Theory for the Quenched Approximation of QCD

[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 $f_K/f_π$, $m_π$, $m_K$, 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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