On the Predictiveness of Single-Field Inflationary Models

We re-examine the predictiveness of single-field inflationary models and discuss how an unknown UV completion can complicate determining inflationary model parameters from observations, even from precision measurements. Besides the usual naturalness issues associated with having a shallow inflationary potential, we describe another issue for inflation, namely, unknown UV physics modifies the running of Standard Model (SM) parameters and thereby introduces uncertainty into the potential inflationary predictions. We illustrate this point using the minimal Higgs Inflationary scenario, which is arguably the most predictive single-field model on the market, because its predictions for $A_s$, $r$ and $n_s$ are made using only one new free parameter beyond those measured in particle physics experiments, and run up to the inflationary regime. We find that this issue can already have observable effects. At the same time, this UV-parameter dependence in the Renormalization Group allows Higgs Inflation to occur (in principle) for a slightly larger range of Higgs masses. We comment on the origin of the various UV scales that arise at large field values for the SM Higgs, clarifying cut off scale arguments by further developing the formalism of a non-linear realization of $\rm SU_L(2) \times U(1)$ in curved space. We discuss the interesting fact that, outside of Higgs Inflation, the effect of a non-minimal coupling to gravity, even in the SM, results in a non-linear EFT for the Higgs sector. Finally, we briefly comment on post BICEP2 attempts to modify the Higgs Inflation scenario.Comment: 31 pp, 4 figures v4: Minor correction to section 3.1. Main arguments and conclusions unchange

Source Finding in the Era of the SKA (Precursors): Aegean 2.0

In the era of the SKA precursors, telescopes are producing deeper, larger images of the sky on increasingly small time-scales. The greater size and volume of images place an increased demand on the software that we use to create catalogues, and so our source finding algorithms need to evolve accordingly. In this paper, we discuss some of the logistical and technical challenges that result from the increased size and volume of images that are to be analysed, and demonstrate how the Aegean source finding package has evolved to address these challenges. In particular, we address the issues of source finding on spatially correlated data, and on images in which the background, noise, and point spread function vary across the sky. We also introduce the concept of forced or prioritised fitting

A randomized, comparative trial: does pillow type alter cervico-thoracic spinal posture when side lying?

This is an Open Access article which permits unrestricted noncommercial use, provided the original work is properly cited.Background: Many patients ask for advice about choosing a pillow. This research was undertaken to determine if pillow type alters cervico-thoracic spine position when resting in the side-lying position. Aim: To investigate the effect of different pillow shape and content on the slope of cervico-thoracic spine segments when side lying. Materials and methods: The study was a randomized blinded comparative trial set in a laboratory that replicated a bedroom. The subjects were side sleepers aged over 18 years. Exclusion criteria were history of surgery to the cervico-thoracic spine, an injury or accident to the cervico-thoracic spine in the preceding year, or currently receiving treatment for neck symptoms. Each participant rested in a standardized side-lying position for 10 minutes on each of the trial pillows: regular shaped polyester, foam, feather, and latex pillows, and a contour shaped foam pillow. Reflective markers were placed on external occipital protuberance (EOP), C2, C4, C7, and T3, and digital images were recorded of subjects at 0 and 10 minutes on each pillow. Images were digitized using each reflective marker and the slope of each spinal segment calculated. Univariate analysis of variance models were used to investigate slope differences between pillows at 0 and 10 minutes. Significance was established at P < 0.01 to take account of chance effects from repeated measures and multiple comparisons. Results: At 0 and 10 minutes, the EOP-C2, C2-C4, and C4-C7 segmental slopes were significantly different across all pillows. Significant differences were identified when comparing the feather pillow with the latex, regular and contour foam pillows, and when comparing the polyester and foam contour pillows. The regular and contour foam pillows produced similar slopes at all spinal segments. Conclusion: Cervico-thoracic spinal segment slope alters significantly when people change from a foam, latex, or polyester pillow to a feather pillow and vice versa. The shape of a foam pillow (contour versus regular shape) does not significantly alter cervico-thoracic spinal segment slope

Closed form solution for a double quantum well using Gr\"obner basis

Analytical expressions for spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and effective masses are different. This was achieved by Gr\"obner basis algorithm which allows to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.Comment: 4 figures, Mathematica full calculation noteboo

Towards the Anomalous Dimension to Order Lambda_QCD/m_b for Phase Space Restricted B --> X(u) ell anti-nu and B --> X(s) gamma

We examine the anomalous dimension matrix appropriate for the phase space restricted B --> X(u) ell anti-nu and B --> X(s) gamma decay spectra to subleading nonperturbative order. The effects of the time ordered products of the HQET Lagrangian with the leading order shape function operator are calculated, as are the anomalous dimensions of subleading operators. We establish the renormalizability and closure of a subset of the non-local operator basis, a requirement for the establishment of factorization theorems at this order. Operator mixing is found between the operators which occur to subleading order, requiring the subleading operator basis be extended. We comment on the requirement for new shape functions to be introduced to characterize the matrix elements of these new operators, and the phenomenological consequences for extractions of $|V_{ub}|$.Comment: 23 pages, 3 figures V2- Minor Typos Fixe

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