On Lattice Computations of K+ --> pi+ pi0 Decay at m_K =2m_pi

We use one-loop chiral perturbation theory to compare potential lattice computations of the K+ --> pi+ pi0 decay amplitude at m_K=2m_pi with the experimental value. We find that the combined one-loop effect due to this unphysical pion to kaon mass ratio and typical finite volume effects is still of order minus 20-30%, and appears to dominate the effects from quenching.Comment: 4 pages, revte

Applications of Partially Quenched Chiral Perturbation Theory

Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B_K and the K+ decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta are also considered. We find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in Phys. Rev.

Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation Theory

We study the gauge-fixing approach to the construction of lattice chiral gauge theories in one-loop weak-coupling perturbation theory. We show how infrared properties of the gauge degrees of freedom determine the nature of the continuous phase transition at which we take the continuum limit. The fermion self-energy and the vacuum polarization are calculated, and confirm that, in the abelian case, this approach can be used to put chiral gauge theories on the lattice in four dimensions. We comment on the generalization to the nonabelian case.Comment: 31 pages, 5 figures, two refs. adde

How good is the quenched approximation of QCD?

The quenched approximation for QCD is, at present and in the foreseeable future, unavoidable in lattice calculations with realistic choices of the lattice spacing, volume and quark masses. In this talk, I review an analytic study of the effects of quenching based on chiral perturbation theory. Quenched chiral perturbation theory leads to quantitative insight on the difference between quenched and unquenched QCD, and reveals clearly some of the diseases which are expected to plague quenched QCD. Uses jnl.tex and epsf.tex for figure 3. Figures 1 and 2 not included, sorry. Available as hardcopy on request.Comment: 22 pages, Wash. U. HEP/94-62 (Forgotten set of macros now included, sorry.

The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory

We consider a lattice discretization of a covariantly gauge-fixed abelian gauge theory. The gauge fixing is part of the action defining the theory, and we study the phase diagram in detail. As there is no BRST symmetry on the lattice, counterterms are needed, and we construct those explicitly. We show that the proper adjustment of these counterterms drives the theory to a new type of phase transition, at which we recover a continuum theory of (free) photons. We present both numerical and (one-loop) perturbative results, and show that they are in good agreement near this phase transition. Since perturbation theory plays an important role, it is important to choose a discretization of the gauge-fixing action such that lattice perturbation theory is valid. Indeed, we find numerical evidence that lattice actions not satisfying this requirement do not lead to the desired continuum limit. While we do not consider fermions here, we argue that our results, in combination with previous work, provide very strong evidence that this new phase transition can be used to define abelian lattice chiral gauge theories.Comment: 42 pages, 30 figure

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

We investigate how L\"uscher'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 $\eta'$ 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.Comment: 22 pages, uuencoded, compressed postscript fil

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 $f_K/f_\pi$, $m_\pi$, $m_K$, 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.Comment: 14 page