Lattice QCD with domain wall quarks and applications to weak matrix elements

Using domain wall fermions, we estimate $B_K(\mu\approx 2 GeV)=0.628(47)$ in quenched QCD which is consistent with previous calculations. At \gbeta=6.0 and 5.85 we find the ratio $f_K/m_\rho$ in agreement with the experimental value, within errors. These results support expectations that $O(a)$ errors are exponentially suppressed in low energy ($E\ll a^{-1}$) observables, and indicate that domain wall fermions have good scaling behavior at relatively strong couplings. We also demonstrate that the axial current numerically satisfies the lattice analog of the usual continuum axial Ward identity.Comment: Contribution to Lattice '97. 3 pages, 2 epsf figure

OT 060420: A Seemingly Optical Transient Recorded by All-Sky Cameras

We report on a ~5th magnitude flash detected for approximately 10 minutes by two CONCAM all-sky cameras located in Cerro Pachon - Chile and La Palma - Spain. A third all-sky camera, located in Cerro Paranal - Chile did not detect the flash, and therefore the authors of this paper suggest that the flash was a series of cosmic-ray hits, meteors, or satellite glints. Another proposed hypothesis is that the flash was an astronomical transient with variable luminosity. In this paper we discuss bright optical transient detection using fish-eye all-sky monitors, analyze the apparently false-positive optical transient, and propose possible causes to false optical transient detection in all-sky cameras.Comment: 7 figures, 3 tables, accepted PAS

Domain wall fermions in vector gauge theories

I review domain wall fermions in vector gauge theories. Following a brief introduction, the status of lattice calculations using domain wall fermions is presented. I focus on results from QCD, including the light quark masses and spectrum, weak matrix elements, the $n_f=2$ finite temperature phase transition, and topology and zero modes and conclude with topics for future study.Comment: LATTICE98. Plenary review talk. LaTeX(espcrc2.sty), 13 pages, 17 eps figure

Massless Composite Fermions in Two Dimensions and the Overlap

There exist chiral gauge models in two dimensions that have massless composite fermions. Two examples are presented and it is suggested that they be accepted as benchmark test-cases for generic proposals of non-perturbatively regulating chiral gauge theories in any dimension. We apply the overlap to the simpler of the two benchmarks and present the results of a numerical simulation of modest size.Comment: 12 pages, Plain TeX with epsf, 2 PS figure

SU(4) lattice gauge theory with decuplet fermions: Schr\"odinger functional analysis

We complete a program of study of SU(N) gauge theories coupled to two flavors of fermions in the two-index symmetric representation by performing numerical simulations in SU(4). The beta function, defined and calculated via the Schr\"odinger functional, runs more slowly than the two-loop perturbative result. The mass anomalous dimension levels off in strong coupling at a value of about 0.45, rendering this theory unsuitable for walking technicolor. A large-N comparison of this data with results from SU(2) and SU(3) reveals striking regularities.Comment: 15 pages, 15 figure

One loop renormalization for the axial Ward-Takahashi identity in Domain-wall QCD

We calculate one-loop correction to the axial Ward-Takahashi identity given by Furman and Shamir in domain-wall QCD. It is shown perturbatively that the renormalized axial Ward-Takahashi identity is satisfied without fine tuning and the ``conserved'' axial current receives no renormalization, giving $Z_A=1$. This fact will simplify the calculation of the pion decay constant in numerical simulations since the decay constant defined by this current needs no lattice renormalization factor.Comment: 16 pages, 3 axodraw.sty figure

Learning with the Weighted Trace-norm under Arbitrary Sampling Distributions

We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions. We show that the standard weighted trace-norm might fail when the sampling distribution is not a product distribution (i.e. when row and column indexes are not selected independently), present a corrected variant for which we establish strong learning guarantees, and demonstrate that it works better in practice. We provide guarantees when weighting by either the true or empirical sampling distribution, and suggest that even if the true distribution is known (or is uniform), weighting by the empirical distribution may be beneficial