On sets of irreducible polynomials closed by composition

Let $\mathcal S$ be a set of monic degree $2$ polynomials over a finite field and let $C$ be the compositional semigroup generated by $\mathcal S$. In this paper we establish a necessary and sufficient condition for $C$ to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set $\mathcal S$. Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree $2$ polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions

A Determination of the Hubble Constant from Cepheid Distances and a Model of the Local Peculiar Velocity Field

We present a measurement of the Hubble Constant based on Cepheid distances to 27 galaxies within 20 Mpc. We take the Cepheid data from published measurements by the Hubble Telescope Key Project on the Distance Scale (H0KP). We calibrate the Cepheid Period-Luminosity (PL) relation with data from over 700 Cepheids in the LMC obtained by the OGLE collaboration; we assume an LMC distance modulus of 18.50 mag (d=50.1 kpc). Using this PL calibration we obtain new distances to the H0KP galaxies. We correct the redshifts of these galaxies for peculiar velocities using two distinct velocity field models: the phenomenological model of Tonry et al. and a model based on the IRAS density field and linear gravitational instability theory. We combine the Cepheid distances with the corrected redshifts for the 27 galaxies to derive H_0, the Hubble constant. The results are H_0 = 85 +/- 5 km/s/Mpc (random error) at 95% confidence when the IRAS model is used, and 92 +/- 5 km/s/Mpc when the phenomenological model is used. The IRAS model is a better fit to the data and the Hubble constant it returns is more reliable. Systematic error stems mainly from LMC distance uncertainty which is not directly addressed by this paper. Our value of H_0 is significantly larger than that quoted by the H0KP, H_0 = 71 +/- 6 km/s/Mpc. Cepheid recalibration explains ~30% of this difference, velocity field analysis accounts for ~70%. We discuss in detail possible reasons for this discrepancy and future study needed to resolve it.Comment: 33 pages, 8 embedded figures. New table, 5 new references, text revision

The New Fat Higgs: Slimmer and More Attractive

In this paper we increase the MSSM tree level higgs mass bound to a value that is naturally larger than the LEP-II search constraint by adding to the superpotential a $\lambda S H_{u}H_{d}$ term, as in the NMSSM, and UV completing with new strong dynamics {\it before} $\lambda$ becomes non-perturbative. Unlike other models of this type the higgs fields remain elementary, alleviating the supersymmetric fine-tuning problem while maintaining unification in a natural way.Comment: 14 pages and 2 figures. Added references and updated argument about constraints from reheating temperatur

D-Terms, Unification, and the Higgs Mass

We study gauge extensions of the MSSM that contain non-decoupling D-terms, which contribute to the Higgs boson mass. These models naturally maintain gauge coupling unification and raise the Higgs mass without fine-tuning. Unification constrains the structure of the gauge extensions, limiting the Higgs mass in these models to roughly less than 150 GeV. The D-terms contribute to the Higgs mass only if the extended gauge symmetry is broken at energies of a few TeV, leading to new heavy gauge bosons in this mass range.Comment: 30+1 pages, 7 figure

Importance of Non-Perturbative QCD Parameters for Bottom Mesons

The importance of non-perturbative Quantum Chromodynamics [QCD] parameters is discussed in context to the predicting power for bottom meson masses and isospin splitting. In the framework of heavy quark effective theory, the work presented here focuses on the different allowed values of the two non perturbative QCD parameters used in heavy quark effective theory formula and using the best fitted parameter, masses of the excited bottom meson states in JP=(1/2)+ doublet in strange as well as non-strange sector are calculated here. The calculated masses are found to be matching well with experiments and other phenomenological models. The mass and hyperfine splitting has also been analyzed for both strange and non-strange heavy mesons with respect to spin and flavor symmetries.Comment: Volume 2014 (2014), Article ID 619783, 4 pages, Advances in High Energy Physics, 2014. arXiv admin note: text overlap with arXiv:1312.540