Mass dependence of the hairpin vertex in quenched QCD

The pseudoscalar ``hairpin'' vertex (i.e. quark-disconnected vertex) plays a key role in quenched chiral perturbation theory. Direct calculations using lattice simulations find that it has a significant dependence on quark mass. I show that this mass dependence can be used to determine the quenched Gasser-Leutwyler constant L5. This complements the calculation of L5 using the mass dependence of the axial decay constant of the pion. In an appendix, I discuss power counting for quenched chiral perturbation theory and describe the particular scheme used in this paper.Comment: 12 pages, 4 figures. Version to appear in Phys. Rev. D. Central result unchanged, but explanation of calculation improved and minor errors corrected. New appendix discusses power counting schemes in quenched chiral perturbation theor

Enhanced chiral logarithms in partially quenched QCD

I discuss the properties of pions in ``partially quenched'' theories, i.e. those in which the valence and sea quark masses, $m_V$ and $m_S$, are different. I point out that for lattice fermions which retain some chiral symmetry on the lattice, e.g. staggered fermions, the leading order prediction of the chiral expansion is that the mass of the pion depends only on $m_V$, and is independent of $m_S$. This surprising result is shown to receive corrections from loop effects which are of relative size $m_S \ln m_V$, and which thus diverge when the valence quark mass vanishes. Using partially quenched chiral perturbation theory, I calculate the full one-loop correction to the mass and decay constant of pions composed of two non-degenerate quarks, and suggest various combinations for which the prediction is independent of the unknown coefficients of the analytic terms in the chiral Lagrangian. These results can also be tested with Wilson fermions if one uses a non-perturbative definition of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected (alpha_4 is replaced by alpha_4/2

Physical Results from Unphysical Simulations

We calculate various properties of pseudoscalar mesons in partially quenched QCD using chiral perturbation theory through next-to-leading order. Our results can be used to extrapolate to QCD from partially quenched simulations, as long as the latter use three light dynamical quarks. In other words, one can use unphysical simulations to extract physical quantities - in this case the quark masses, meson decay constants, and the Gasser-Leutwyler parameters L_4-L_8. Our proposal for determining L_7 makes explicit use of an unphysical (yet measurable) effect of partially quenched theories, namely the double-pole that appears in certain two-point correlation functions. Most of our calculations are done for sea quarks having up to three different masses, except for our result for L_7, which is derived for degenerate sea quarks.Comment: 26 pages, 12 figures (discussion on discretization errors at end of sec. IV clarified; minor improvements in presentation; results unchanged

Partially quenched chiral perturbation theory without Φ0\Phi_0

This paper completes the argument that lattice simulations of partially quenched QCD can provide quantitative information about QCD itself, with the aid of partially quenched chiral perturbation theory. A barrier to doing this has been the inclusion of $\Phi_0$, the partially quenched generalization of the $\eta'$, in previous calculations in the partially quenched effective theory. This invalidates the low energy perturbative expansion, gives rise to many new unknown parameters, and makes it impossible to reliably calculate the relation between the partially quenched theory and low energy QCD. We show that it is straightforward and natural to formulate partially quenched chiral perturbation theory without $\Phi_0$, and that the resulting theory contains the effective theory for QCD without the $\eta'$. We also show that previous results, obtained including $\Phi_0$, can be reinterpreted as applying to the theory without $\Phi_0$. We contrast the situation with that in the quenched effective theory, where we explain why it is necessary to include $\Phi_0$. We also compare the derivation of chiral perturbation theory in partially quenched QCD with the standard derivation in unquenched QCD. We find that the former cannot be justified as rigorously as the latter, because of the absence of a physical Hilbert space. Finally, we present an encouraging result: unphysical double poles in certain correlation functions in partially quenched chiral perturbation theory can be shown to be a property of the underlying theory, given only the symmetries and some plausible assumptions.Comment: 45 pages, no figure

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.

Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe

Heavy meson chiral perturbation theory in finite volume

We present the first step towards the estimation of finite volume effects in heavy-light meson systems using heavy meson chiral perturbation theory. We demonstrate that these effects can be amplified in both light-quark and heavy-quark mass extrapolations (interpolations) in lattice calculations. As an explicit example, we perform a one-loop calculation for the neutral B meson mixing system and show that finite volume effects, which can be comparable with currently quoted errors, are not negligible in both quenched and partially quenched QCD.Comment: Talk presented at Lattice2004(heavy), Fermilab, June 21st-26th, 2004. Three pages, two figure

Chiral corrections to the axial charges of the octet baryons from quenched QCD

We calculate one-loop correction to the axial charges of the octet baryons using quenched chiral perturbation theory, in order to understand chiral behavior of the axial charges in quenched approximation to quantum chromodynamics (QCD). In contrast to regular behavior of the full QCD chiral perturbation theory result, $c_0+c_{l2}m_\pi^2\,\ln{m_\pi^2}+\cdots$, we find that the quenched chiral perturbation theory result, $c_0^Q+(c_{l0}^Q+c_{l2}^Qm_\pi^2)\ln{m_\pi^2}+c_2^Q m_\pi^2+\cdots$, is singular in the chiral limit.Comment: standard LaTeX, 16 pages, 4 epsf figure

Radiative, actively cooled panel tests results

The radiative, actively cooled panel designed to withstand a uniform incident heat flux of 136 kW/sq m to a 444 K surface temperature was evaluated. The test program consisted of preliminary static thermal mechanical loading and aerothermal flow tests. Test results are briefly discussed

Impact of the finite volume effects on the chiral behavior of fK and BK

We discuss the finite volume corrections to fK and BK by using the one-loop chiral perturbation theory in full, quenched, and partially quenched QCD. We show that the finite volume corrections to these quantities dominate the physical (infinite volume) chiral logarithms.Comment: 16 pages, 3 figures [published version