117287068
A New Approach to QCD Sum Rules and Inclusive $\tau$ Decay
We show that renormalization group improvement, making use of analyticity and the structure of the operator product expansion, combined with a non-perturbative expansion method allows one to describe quarkonium states via QCD sum rules without the need for explicit power corrections. This technique also allows an accurate determination of parameters related to the inclusive decay of the $\tau$ lepton.
16714961
Path-integral derivation of the anomaly for the hermitian equivalent of the complex PT-symmetric quartic Hamiltonian
It can be shown using operator techniques that the non-Hermitian PT-symmetric quantum mechanical Hamiltonian with a 'wrong-sign' quartic potential -gx{sup 4} is equivalent to a Hermitian Hamiltonian with a positive quartic potential together with a linear term. A naieve derivation of the same result in the path-integral approach misses this linear term. In a recent paper by Bender et al. it was pointed out that this term was in the nature of a parity anomaly and a more careful, discretized treatment of the path integral appeared to reproduce it successfully. However, on re-examination of this derivation we find that a yet more careful treatment is necessary, keeping terms that were ignored in that paper. An alternative, much simpler derivation is given using the additional potential that has been shown to appear whenever a change of variables to curvilinear coordinates is made in a functional integral.
36348760
delta expansion applied to strong-coupling Z(2), U(1), and SU(2) gauge theory on the lattice in four dimensions.
We generalize to four dimensions the linear {delta} expansion applied to gauge theory on the lattice, with {ital Z}(2), U(1), and SU(2) as the gauge groups and an unperturbed action appropriate to the strong-coupling regime. The calculation is carried to fourth order in {delta}, using the machinery of character expansions. The expansion is optimized in a bid to improve upon existing strong-coupling methods and our results are compared against results from these and from Monte Carlo calculations.
23488230
Optimization in the extended variational approach to SU(2) gauge theory on the lattice.
The linear [delta] expansion is applied to SU(2) gauge theory on the lattice, with a trial action based on single links. In contrast with previous calculations using this action, we use the principle of minimal sensitivity to determine the arbitrary parameter [ital J] which occurs in the interpolating action. We obtain a good fit to the Monte Carlo data on the weak-coupling side of the transition region: this can be combined with results using a different trial action to cover the entire range of [beta]. There is no sign that the procedure fails to converge.
42992493
Interpolating Lagrangians and SU(2) gauge theory on the lattice.
We apply the linear {delta} expansion to non-Abelian gauge theory on the lattice, with SU(2) as the gauge group. We establish an appropriate parametrization and evaluate the average plaquette energy {ital E}{sub {ital P}} to {ital O}({delta}). As a check on our results, we recover the large-{beta} expansion up to {ital O}(1/{beta}{sup 2}), which involves some {ital O}({delta}{sup 2}) contributions. Using these contributions we construct a variant of the 1/{beta} expansion which gives a good fit to the data down to the transition region.
19006666
Convergence of the optimized delta expansion for the connected vacuum amplitude: Anharmonic oscillator.
The convergence of the linear $\delta$ expansion for the connected generating functional of the quantum anharmonic oscillator is proved. Using an order-dependent scaling for the variational parameter $\lambda$, we show that the expansion converges to the exact result with an error proportional to $\exp(-cN^{1/3})$.
14308791
Constraining the difference in convective blueshift between the components of alpha Centauri with precise radial velocities
New radial velocities of Cen A & B obtained in the framework the Anglo-Australian Planet Search programme as well as in the CORALIE programme are added to those by Endl et al. (2001) to improve the pre- cision of the orbital parameters. The resulting masses are 1:105 0:0070 M and 0:934 0:0061 M for A and B respectively. The factors limiting how accurately these masses can be derived from a combined visual-spectroscopic solution are investigated. The total eect of the convective blueshift and the gravitational redshift is also inves- tigated and estimated to dier by 215 8m s 1 between the components. This suggests that the dierence in convective blueshift between the components is much smaller than predicted from current hydrodynamical model atmosphere calculations.
14171934
The Properties of the 500 K Dwarf UGPS J072227.51-054031.2, and a Study of the Far-Red Flux of Cold Brown Dwarfs
We present i and z photometry for 25 T dwarfs and 1 L dwarf. Combined with published photometry, the data show that the i – z, z – Y, and z – J colors of T dwarfs are very red, and continue to increase through to the late-type T dwarfs, with a hint of a saturation for the latest types with T eff 600 K. We present new 0.7-1.0 μm and 2.8-4.2 μm spectra for the very late type T dwarf UGPS J072227.51–054031.2, as well as improved astrometry for this dwarf. Examination of the spectral energy distribution using new and published data, with Saumon & Marley models, shows that the dwarf has T eff = 505 ± 10 K, a mass of 3-11 M Jupiter, and an age between 60 Myr and 1 Gyr. This young age is consistent with the thin disk kinematics of the dwarf. The mass range overlaps with that usually considered to be planetary, despite this being an unbound object discovered in the field near the Sun. This apparently young rapid rotator is also undergoing vigorous atmospheric mixing, as determined by the IRAC and WISE 4.5 μm photometry and the Saumon & Marley models. The optical spectrum for this 500 K object shows clearly detected lines of the neutral alkalis Cs and Rb, which are emitted from deep atmospheric layers with temperatures of 900-1200 K.
14800854
Application of Bayesian model inadequacy criterion for multiple data sets to radial velocity models of exoplanet systems
We present a simple mathematical criterion for determining whether a given statistical model does not describe several independent sets of measurements, or data modes, adequately. We derive this criterion for two data sets and generalise it to several sets by using the Bayesian updating of the posterior probability density. To demonstrate the usage of the criterion, we apply it to observations of exoplanet host stars by re-analysing the radial velocities of HD 217107, Gliese 581, and υ Andromedae and show that the currently used models are not necessarily adequate in describing the properties of these measurements. We show that while the two data sets of Gliese 581 can be modelled reasonably well, the noise model of HD 217107 needs to be revised. We also reveal some biases in the radial velocities of υ Andromedae and report updated orbital parameters for the recently proposed 4-planet model. Because of the generality of our criterion, no assumptions are needed on the nature of the measurements, models, or model parameters. The method we propose can be applied to any astronomical problems, as well as outside the field of astronomy, because it is a simple consequence of the Bayes’ rule of conditional probabilities.
15452372
High-eccentricity planets from the Anglo-Australian Planet Search
We report Doppler measurements of the stars HD 187085 and HD 20782 which indicate two high eccentricity low-mass companions to the stars. We find HD 187085 has a Jupiter-mass companion with a �1000 d orbit. Our formal ‘best fit’ solution suggests an eccentricity of 0.47, however, it does not sample the periastron passage of the companion and we find that orbital solutions with eccentricities between 0.1 and 0.8 give only slightly poorer fits (based on RMS and � 2) and are thus plausible. Observations made during periastron passage in 2007 June should allow for the reliable determination of the orbital eccentricity for the companion to HD 187085. Our dataset for HD 20782 does sample periastron and so the orbit for its companion can be more reliably determined. We find the companion to HD 20782 has M sin i = 1.77±0.22 MJup, an orbital period of 595.86±0.03 d and an orbit with an eccentricity of 0.92±0.03. The detection of such high-eccentricity (and relatively low velocity amplitude) exoplanets appears to be facilitated by the long-term precision of the Anglo-Australian Planet Search. Looking at exoplanet detections as a whole, we find that those with higher eccentricity seem to have relatively higher velocity amplitudes indicating higher mass planets and/or an observational bias against the detection of high eccentricity systems.
18735984
Benchmark cool companions: ages and abundances for the PZ Telescopii system
We present new ages and abundance measurements for the pre-main-sequence star PZ Telescopii (more commonly known as PZ Tel). PZ Tel was recently found to host a young and low-mass companion. Such companions, whether they are brown dwarfs or planetary systems, can attain benchmark status by detailed study of the properties of the primary, and then evolutionary and bulk characteristics can be inferred for the companion. Using Fibre-fed Extended Range Optical Spectrograph spectra, we have measured atomic abundances (e.g. Fe and Li) and chromospheric activity for PZ Tel and used these to obtain the metallicity and age estimates for the companion. We have also determined the age independently using the latest evolutionary models. We find PZ Tel A to be a rapidly rotating (v sin i = 73 ± 5 km s −1 ), approximately solar metallicity star [log N(Fe) =− 4.37 ± 0.06 dex or [Fe/H] = 0.05 ± 0.20 dex]. We measure a non-local thermodynamic equilibrium lithium abundance of log N(Li) = 3.1 ± 0.1 dex, which from depletion models gives rise to an age of 7 +4 −2 Myr for the system. Our measured chromospheric activity (log R � HK of −4.12) returns an age of 26 ± 2 Myr, as does fitting pre-main-sequence evolutionary tracks (τ evol = 22 ± 3 Myr), both of these are in disagreement with the lithium age. We speculate on reasons for this difference and introduce new models for lithium depletion that incorporate both rotation and magnetic field effects. We also synthesize solar, metal-poor and metal-rich substellar evolutionary models to better determine the bulk properties of PZ Tel B, showing that PZ Tel B is probably more massive than previous estimates, meaning the companion is not a giant exoplanet, even though a planetary-like formation origin can go some way to describing the distribution of benchmark binaries currently known. We show how PZ Tel B compares to other currently known age and metallicity benchmark systems and try to empirically test the effects of dust opacity as a function of metallicity on the near-infrared colours of brown dwarfs. Current models suggest that in the near-infrared observations are more sensitive to low-mass companions orbiting more metal rich stars. We also look for trends between infrared photometry and metallicity amongst a growing population of substellar benchmark objects, and identify the need for more data in mass–age–metallicity parameter space.