Bay State Circuit, Sage Park, July 1, 1931

Trott\u27s Official Score Card for the Wednesday, July 1, 1931 Bay State Circuit Races in Windsor, Connecticut published by F. G. Trott, printed by William J. Doyle. The score card contains Guy Kendall\u27s handwritten notes on race day results as well as photos mounted inside by Kendall

Bay State Circuit, Sage Park, July 2, 1931

Trott\u27s Official Score Card for the Thursday, July 2, 1931 Bay State Circuit Races in Windsor, Connecticut published by F. G. Trott, Boston, Mass., printed by William J. Doyle. Contains Guy Kendall\u27s handwritten notes on changes in the race line up and results as well as photos mounted by Kendall inside the score card

Bay State Circuit, Sage Park, July 4, 1931

Trott\u27s Official Score Card for the Saturday, July 4, 1931 Bay State Circuit Races in Windsor, Connecticut published by F. G. Trott, Boston, Massachusetts, printed by William J. Doyle. Contains race day photos taken by Guy Kendall as well as Kendall\u27s handwritten notes on race day results

Bay State Circuit, Sage Park, July 3, 1931

Trott\u27s Official Score Card for the Friday, July 3, 1931 Bay State Circuit Races in Windsor, Connecticut published by F.G. Trott, Boston, Mass., printed by William J. Doyle. Contains race day photos taken by Guy Kendall as well as Kendall\u27s handwritten notes on race day results

Grand Circuit Meeting, Aug. 1, 1932

Trott\u27s Official Score Card for the Monday, August 1, 1932 Grand Circuit Meeting, at Rockingham Park, Salem, N.H. published by F. G. Trott, Boston, Massachusetts. Contains race day photos taken by Guy Kendall as well as Kendall\u27s handwritten notes on race day results

Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator

The power series method has been adapted to compute the spectrum of the Schrodinger equation for central potential of the form $V(r)={d_{-2}\over r^2}+{d_{-1}\over r}+\sum_{i=0}^{\infty} d_{i}r^i$. The bound-state energies are given as zeros of a calculable function, if the potential is confined in a spherical box. For an unconfined potential the interval bounding the energy eigenvalues can be determined in a similar way with an arbitrarily chosen precision. The very accurate results for various spherically symmetric anharmonic potentials are presented.Comment: 16 pages, 5 figures, published in J. Phys

The Initial Mass Function in disc galaxies and in galaxy clusters: the chemo-photometric picture

The observed brightness of the Tully-Fisher relation suggests a low stellar M/L ratio and a "bottom-light" IMF in disc galaxies, but the corresponding efficiency of chemical enrichment tends to exceed the observational estimates. Either suitable tuning of the IMF slope and mass limits or metal outflows from disc galaxies must then be invoked. A standard Solar Neighbourhood IMF cannot explain the high metallicity of the hot intra-cluster medium: a different IMF must be at work in clusters of galaxies. Alternatively, if the IMF is universal and chemical enrichment is everywhere as efficient as observed in clusters, substantial loss of metals must occur from the Solar Neighbourhood and from disc galaxies in general; a "non-standard" scenario challenging our understanding of disc galaxy formation.Comment: 6 pages, 4 figures; in Proceedings of IMF@50: the Initial Mass Function 50 years later; Corbelli, Palla and Zinnecker (eds.

Off-Critical Logarithmic Minimal Models

We consider the integrable minimal models ${\cal M}(m,m';t)$, corresponding to the $\varphi_{1,3}$ perturbation off-criticality, in the {\it logarithmic limit\,} $m, m'\to\infty$, $m/m'\to p/p'$ where $p, p'$ are coprime and the limit is taken through coprime values of $m,m'$. We view these off-critical minimal models ${\cal M}(m,m';t)$ as the continuum scaling limit of the Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice. Applying Corner Transfer Matrices to the Forrester-Baxter RSOS models in Regime III, we argue that taking first the thermodynamic limit and second the {\it logarithmic limit\,} yields off-critical logarithmic minimal models ${\cal LM}(p,p';t)$ corresponding to the $\varphi_{1,3}$ perturbation of the critical logarithmic minimal models ${\cal LM}(p,p')$. Specifically, in accord with the Kyoto correspondence principle, we show that the logarithmic limit of the one-dimensional configurational sums yields finitized quasi-rational characters of the Kac representations of the critical logarithmic minimal models ${\cal LM}(p,p')$. We also calculate the logarithmic limit of certain off-critical observables ${\cal O}_{r,s}$ related to One Point Functions and show that the associated critical exponents $\beta_{r,s}=(2-\alpha)\,\Delta_{r,s}^{p,p'}$ produce all conformal dimensions $\Delta_{r,s}^{p,p'}<{(p'-p)(9p-p')\over 4pp'}$ in the infinitely extended Kac table. The corresponding Kac labels $(r,s)$ satisfy $(p s-p' r)^2< 8p(p'-p)$. The exponent $2-\alpha ={p'\over 2(p'-p)}$ is obtained from the logarithmic limit of the free energy giving the conformal dimension $\Delta_t={1-\alpha\over 2-\alpha}={2p-p'\over p'}=\Delta_{1,3}^{p,p'}$ for the perturbing field $t$. As befits a non-unitary theory, some observables ${\cal O}_{r,s}$ diverge at criticality.Comment: 18 pages, 5 figures; version 3 contains amplifications and minor typographical correction

EWPD Constraints on Flavor Symmetric Vector Fields

Electroweak precision data constraints on flavor symmetric vector fields are determined. The flavor multiplets of spin one that we examine are the complete set of fields that couple to quark bi-linears at tree level while not initially breaking the quark global flavor symmetry group. Flavor safe vector masses proximate to, and in some cases below, the electroweak symmetry breaking scale are found to be allowed. Many of these fields provide a flavor safe mechanism to explain the t tbar forward backward anomaly, and can simultaneously significantly raise the allowed values of the Standard Model Higgs mass consistent with electroweak precision data.Comment: Matches version published in JHE

Comment on Higgs Inflation and Naturalness

We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.Comment: 5 pages, 1 figure V3: Journal Versio