Perfect Scalars on the Lattice

We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while thermodynamic quantities have tiny lattice artifacts. To make such actions applicable in simulations, we truncate the couplings to a unit hypercube and observe that spectrum and thermodynamics are still drastically improved compared to the standard lattice action. We show how preconditioning techniques can be applied successfully to this type of action. We also consider a number of variants of the perfect lattice action, such as the use of an anisotropic or triangular lattice, and modifications of the renormalization group transformations motivated by wavelets. Along the way we illuminate the consistent treatment of gauge fields, and we find a new fermionic fixed point action with attractive properties.Comment: 26 pages, 11 figure

Unravelling quantum carpets: a travelling wave approach

Quantum carpets are generic spacetime patterns formed in the probability distributions P(x,t) of one-dimensional quantum particles, first discovered in 1995. For the case of an infinite square well potential, these patterns are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of P(x,t). Each wave directly yields the time-averaged structure of P(x,t) along the (quantised)spacetime direction in which the wave propagates. The decomposition leads to new predictions of locations, widths depths and shapes of carpet structures, and results are also applicable to light diffracted by a periodic grating and to the quantum rotator. A simple connection between the waves and the Wigner function of the initial state of the particle is demonstrated, and some results for more general potentials are given.Comment: Latex, 26 pages + 6 figures, submitted to J. Phys. A (connections with prior literature clarified

Perturbation theory for the two-impurity Kondo problem-RKKY-induced vanishing of the Kondo temperature

The authors consider the two-impurity Kondo problem, in a basis in which the electron states are written in terms of their parity, with respect to the midpoint between impurities. They consider the scattering of electrons by the spin-one complexes formed by the impurities, making use of the fact that the RKKY interaction is diagonal in this basis and acts in much the same way that a crystal field acts in the degenerate Kondo problem. By expanding the equations of motion to leading logarithmic order the authors show that the resulting Kondo temperature is reduced by an increasing antiferromagnetic RKKY interaction, and for one of the electron parity channels crosses the antiferromagnetic RKKY singles. This happens when the RKKY interaction is of the order of the bare (no RKKY) Kondo temperature. The authors interpret this crossing as reflecting the divergence of Fermi liquid properties found in numerical studies along the lines of a phenomenological model introduced by two of the authors.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48869/2/cm932405.pd

Constraints on R-parity violating couplings from lepton universality

We analyze the one loop corrections to leptonic W and Z decays in an R-parity violating extension to the Minimal Supersymmetric Standard Model (MSSM). We find that lepton universality violation in the Z line-shape variables alone would strengthen the bounds on the magnitudes of the lambda' couplings, but a global fit on all data leaves the bounds virtually unchanged at |lambda'_{33k}| < 0.42 and |lambda'_{23k}| < 0.50 at the 2 sigma level. Bounds from W decays are less stringent: |lambda'_{33k}| < 2.4 at 2 sigma, as a consequence of the weaker Fermilab experimental bounds on lepton universality violation in W decays. We also point out the potential of constraining R-parity violating couplings from the measurement of the Upsilon invisible width.Comment: 26pages, 8 postscript figures, REVTeX. Updated references. Typos correcte

Constraints on R-parity violating couplings from LEP/SLD hadronic observables

We analyze the one loop corrections to hadronic Z decays in an R-parity violating extension to the Minimal Supersymmetric Standard Model (MSSM). Performing a global fit to all the hadronic observables at the Z-peak, we obtain stringent constraints on the R-violating couplings constants lambda' and lambda''. As a result of the strong constraints from the b asymmetry parameters A_b and A_FB(b), we find that the couplings lambda'{i31}, lambda'{i32}, and lambda''{321} are ruled out at the 1 sigma level, and that lambda'{i33} and lambda''{33i} are ruled out at the 2 sigma level. We also obtain Bayesian confidence limits for the R-violating couplings.Comment: 30 pages, 19 postscript figures, REVTeX, new section 8 on Bayesian confidence limits adde

Constraints on Two-Higgs Doublet Models at Large tan{beta} from W and Z decays

We study constraints on type-II two Higgs doublet models at large tan{beta} from LEP/SLD Z-pole data and from lepton universality violation in W decay. We perform a global fit and find that, in the context of Z decay, the LEP/SLD experimental values for lepton universality violation, R_b, and A_b all somewhat disfavor the model. Contributions from the neutral Higgs sector can be used to constrain the scalar-pseudoscalar Higgs mass splittings. Contributions from the charged Higgs sector allow us to constrain the charged Higgs mass. For tan{beta}=100 we obtain the 1 sigma classical (Bayesian) bounds of m_{H+} > 670 GeV (370 GeV) and 1 > m_{h0}/m_{A0} > 0.68 (0.64). The 2 sigma bounds are weak. Currently, the Tevatron experimental limits on lepton universality violation in W decay provide no significant constraint on the Higgs sector.Comment: 26 pages, 9 postscript figures, REVTe

Interpretations of the NuTeV sin⁡2θW\sin^2 \theta_W

We summarize theoretical explanations of the three $\sigma$ discrepancy between $\sin^2 \theta_W$ measured by NuTeV and predicted by the Standard Model global fit. Possible new physics explanations ({\it e.g.} an unmized $Z'$) are not compelling. The discrepancy would be reduced by a positive momentum asymmetry $s^-$ in the strange sea; present experimental estimates of $s^-$ are unreliable or incomplete. Upgrading the NuTeV analysis to NLO would alleviate concerns that the discrepancy is a QCD effect.Comment: (proceedings for the NuFact'02 Workshop); reference and footnote added, following the NuTeV proceeding

Coherent states of P{\"o}schl-Teller potential and their revival dynamics

A recently developed algebraic approach for constructing coherent states for solvable potentials is used to obtain the displacement operator coherent state of the P\"{o}schl-Teller potential. We establish the connection between this and the annihilation operator coherent state and compare their properties. We study the details of the revival structure arising from different time scales underlying the quadratic energy spectrum of this system.Comment: 13 pages, 6 figure

Recent Developments in Precision Electroweak Physics

Developments in precision electroweak physics in the two years since the symposium are briefly summarized.Comment: Update on recent developments, prepared for the publication of the Proceedings of Alberto Sirlin Symposium, New York University, October 2000. 10 pages, 1 figur

Top quark associated production of topcolor pions at hadron colliders

We investigate the associated production of a neutral physical pion with top quarks in the context of topcolor assisted technicolor. We find that single-top associated production does not yield viable rates at either the Tevatron or LHC. tt-associated production at the Tevatron is suppressed relative to Standard Model ttH, but at the LHC is strongly enhanced and would allow for easy observation of the main decay channels to bottom quarks, and possible observation of the decay to gluons.Comment: 13 pages, 4 figures, submitted to PR