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

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 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.Comment: 50 pages, TeX, two eps figures included, minor changes, no changes in results or conclusions, version to appear in Phys.Rev.

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

Sensitivity of Efficiency Frontiers Developed For Farm Enterprise Choice Decisions

The sensitivity of efficiency frontiers in farm enterprise choice under risk is examined. With expected return levels held constant, substantial variation was found in farm organizations off the efficiency frontier. However, there was relatively little additional risk associated with suboptimal organizations. Expected return level substantially influenced the sensitivity of frontiers

Purification and Characterization of p68/70, Regeneration-Associated Proteins from Goldfish Brain

Two acidic proteins (p68/70) previously shown to be associated with regeneration of the goldfish optic nerve were purified 887-fold from brain homogenates of Carassius auratus. Purification to homogeneity was achieved by sequential chromatography of a 100,000 g brain supernatant fraction on DEAE-Sephacel, Cu 2+ -charged iminodiacetic acid agarose, and gel filtration. The Stokes radius of the doublet was determined to be 5.8 nm, and the sedimentation coefficient calculated to be 5 2. From these values a molecular mass of 128 kDa and a frictional coefficient ratio of 1.6 were calculated. Chromatofocusing on a high-resolution DEAE column resolved the protein doublet into three dimeric species of p68, p68/70, and p70. These results indicate that the proteins are highly elongated and associate as homodimers or as a hetero-dimer. Subcellular localization and membrane extraction experiments indicated p68/70 to be a component of the plasma membrane associated primarily through hydro-phobic interactions. p68/70 demonstrated biphasic behavior in phase partition experiments using Triton 114. Analysis of hydrolytic products indicated p68/70 to be a glyco-protein, containing 11% carbohydrate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65206/1/j.1471-4159.1994.62031182.x.pd