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

Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction

As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82 spherical chains and the Z=62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by ~100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported for the Skyrme family of nuclear energy density functionals. Comparing the calculated gaps with the experimental ones, we find that the theoretical errors have both signs implying that the D1S interaction has a reasonable overall strength. However, we find some systematic deficiencies comparing spherical and deformed chains and comparing the lighter chains with the heavier ones. The gaps for heavy spherical nuclei are too high, while those for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei show hardly any A-dependence, contrary to the data. Inclusion of the T-odd component of the interaction does not change these qualitative findings

Pion-Nucleon Phase Shifts in Heavy Baryon Chiral Perturbation Theory

We calculate the phase shifts in the pion-nucleon scattering using the heavy baryon formalism. We consider phase shifts for the pion energy range of 140 to $200$ MeV. We employ two different methods for calculating the phase shifts - the first using the full third order calculation of the pion-nucleon scattering amplitude and the second by including the resonances $\Delta$ and $N^*$ as explicit degrees of freedom in the Lagrangian. We compare the results of the two methods with phase shifts extracted from fits to the pion-nucleon scattering data. We find good to fair agreement between the calculations and the phase shifts from scattering data.Comment: 14 pages, Latex, 6figures. Revised version to appear in Phys.Rev.

Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable, assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to non-local effects in the fourth-root theory when the lattice spacing is non-zero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.Comment: Minor corrections. Revtex, 58 page

Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory

Durr and Hoelbling recently observed that the continuum and chiral limits do not commute in the two dimensional, one flavor, Schwinger model with staggered fermions. I point out that such lack of commutativity can also be seen in four-dimensional staggered chiral perturbation theory (SChPT) in quenched or partially quenched quantities constructed to be particularly sensitive to the chiral limit. Although the physics involved in the SChPT examples is quite different from that in the Schwinger model, neither singularity seems to be connected to the trick of taking the nth root of the fermion determinant to remove unwanted degrees of freedom ("tastes"). Further, I argue that the singularities in SChPT are absent in most commonly-computed quantities in the unquenched (full) QCD case and do not imply any unexpected systematic errors in recent MILC calculations with staggered fermions.Comment: 14 pages, 1 figure. v3: Spurious symbol, introduced by conflicting tex macros, removed. Clarification of discussion in several place

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.

Electric quadrupole and magnetic dipole moments of odd nuclei near the magic ones in a self-consistent approach

We present a model which describes the properties of odd-even nuclei with one nucleon more, or less, with respect to the magic number. In addition to the effects related to the unpaired nucleon, we consider those produced by the excitation of the closed shell core. By using a single particle basis generated with Hartree-Fock calculations, we describe the polarization of the doubly magic-core with Random Phase Approximation collective wave functions. In every step of the calculation, and for all the nuclei considered, we use the same finite-range nucleon-nucleon interaction. We apply our model to the evaluation of electric quadrupole and magnetic dipole moments of odd-even nuclei around oxygen, calcium, zirconium, tin and lead isotopes. Our Random Phase Approximation description of the polarization of the core improves the agreement with experimental data with respect to the predictions of the independent particle model. We compare our results with those obtained in first-order perturbation theory, with those produced by Hartree-Fock-Bogolioubov calculations and with those generated within the Landau-Migdal theory of finite Fermi systems. The results of our universal, self-consistent, and parameter free approach have the same quality of those obtained with phenomenological approaches where the various terms of the nucleon-nucleon interaction are adapted to reproduce some specific experimental data. A critical discussion on the validity of the model is presented.Comment: 18 pages, 7 figures, 7 table

Chiral logs with staggered fermions

We compute chiral logarithms in the presence of "taste" symmetry breaking of staggered fermions. The lagrangian of Lee and Sharpe is generalized and then used to calculate the logs in $\pi$ and $K$ masses. We correct an error in Ref. [1] [C. Bernard, hep-lat/0111051]; the issue turns out to have implications for the comparison with simulations, even at tree level. MILC data with three light dynamical flavors can be well fit by our formulas. However, two new chiral parameters, which describe order $a^2$ hairpin diagrams for taste-nonsinglet mesons, enter in the fits. To obtain precise results for the physical coefficients at order $p^4$, these new parameters will need to be bounded, at least roughly.Comment: talk presented by C. Bernard at Lattice2002(spectrum); 3 pages, 2 figure

A high-speed optical star network using TDMA and all-optical demultiplexing techniques

The authors demonstrate the use of time-division multiplexing (TDM) to realize a high capacity optical star network. The fundamental element of the demonstration network is a 10 ps, wavelength tunable, low jitter, pulse source. Electrical data is encoded onto three optical pulse trains, and the resultant low duty cycle optical data channels are multiplexed together using 25 ps fiber delay lines. This gives an overall network capacity of 40 Gb/s. A nonlinear optical loop mirror (NOLM) is used to carry out the demultiplexing at the station receiver. The channel to be switched out can be selected by adjusting the phase of the electrical signal used to generate the control pulses for the NOLM. By using external injection into a gain-switched distributed feedback (DFB) laser we are able to obtain very low jitter control pulses of 4-ps duration (RMS jitter <1 ps) after compression of the highly chirped gain switched pulses in a normal dispersive fiber. This enables us to achieve excellent eye openings for the three demultiplexed channels. The difficulty in obtaining complete switching of the signal pulses is presented. This is shown to be due to the deformation of the control pulse in the NOLM (caused by the soliton effect compression). The use of optical time-division multiplexing (OTDM) with all-optical switching devices is shown to be an excellent method to allow us to exploit as efficiently as possible the available fiber bandwidth, and to achieve very high bit-rate optical networks