Renormalization Group Study of the Minimal Majoronic Dark Radiation and Dark Matter Model

We study the 1-loop renormalization group equation running in the simplest singlet Majoron model constructed by us earlier to accommodate the dark radiation and dark matter content in the universe. A comprehensive numerical study was performed to explore the whole model parameter space. A smaller effective number of neutrinos $\triangle N_{eff}\sim 0.05$, or a Majoron decoupling temperature higher than the charm quark mass, is preferred. We found that a heavy scalar dark matter, $\rho$, of mass $1.5-4$ TeV is required by the stability of the scalar potential and an operational type-I see-saw mechanism for neutrino masses. A neutral scalar, $S$, of mass in the $10-100$ GeV range and its mixing with the standard model Higgs as large as $0.1$ is also predicted. The dominant decay modes are $S$ into $b\bar{b}$ and/or $\omega\omega$. A sensitive search will come from rare $Z$ decays via the chain $Z\rightarrow S+ f\bar{f}$, where $f$ is a Standard Model fermion, followed by $S$ into a pair of Majoron and/or b-quarks. The interesting consequences of dark matter bound state due to the sizable $S\rho \rho$-coupling are discussed as well. In particular, shower-like events with an apparent neutrino energy at $M_\rho$ could contribute to the observed effective neutrino flux in underground neutrino detectors such as IceCube.Comment: 33 pages,11 figures, published versio

Acyclic orientations on the Sierpinski gasket

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $SG_{2,b}(n)$ at stage $n$ with $b$ equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for $SG_{2,b}$ and $d$-dimensional Sierpinski gasket $SG_d$.Comment: 20 pages, 8 figures and 6 table

Relativistic Conic Beams and Spatial Distribution of Gamma-Ray Bursts

We study the statistics of gamma-ray bursts, assuming that gamma-ray bursts are cosmological and they are beamed in the form of a conical jet with a large bulk Lorentz factor $\sim 100$. In such a conic beam, the relativistic ejecta may have a spatial variation in the bulk Lorentz factor and the density distribution of gamma-ray emitting jet material. An apparent luminosity function arises because the axis of the cone is randomly oriented with respect to the observer's line of sight. The width and the shape of the luminosity function are determined by the ratio of the beam opening angle of the conical jet to the inverse of the bulk Lorentz factor, when the bulk Lorentz factor and the jet material density is uniform on the photon emitting jet surface. We calculate effects of spatial variation of the Lorentz factor and the spatial density fluctuations within the cone on the luminosity function and the statistics of gamma-ray bursts. In particular, we focus on the redshift distribution of the observed gamma-ray bursts. The maximum distance to and the average redshift of the gamma-ray bursts are strongly affected by the beaming-induced luminosity function. The bursts with the angle-dependent Lorentz factor which peaks at the center of the cone have substantially higher average gamma-ray burst redshifts. When both the jet material density and the Lorentz factor are inhomogeneous in the conical beam, the average redshift of the bursts could be 5 times higher than that of the case in which relativistic jet is completely homogeneous and structureless. Even the simplest models for the gamma-ray burst jets and their apparent luminosity distributions have a significant effect on the redshift distribution of the gamma-ray bursts.Comment: 15 pages, 4 figures, submitted to ApJ

The Conservation Reserve Program, Off-Farm Work, and Farm Household Technical Efficiencies

Using data from a national survey of farm households in the United States, this paper examines the effects of farm households’ decisions to participate in the Conservation Reserve Program (CRP) and to work off the farm on the technical efficiency of farm household production. After controlling for the self selection bias in estimating the multiple output-oriented distance functions, results show that operators’ decisions to work off the farm (both separately and combined with participation in CRP) lead to higher technical efficiencies for farm household production— implying improvements in the resource allocation between farm and other productive activities by farm households. The technical efficiencies of household production of those farm households participating only in the CRP are lower.Conservation Reserve Program, off-farm work, household technical efficiency, Agribusiness, Agricultural Finance, Farm Management,

Are Farmers' Decisions to Work off the Farm and Participate in the Conservation Reserve Program Independent, Joint or Sequential?

There is statistical evidence that decisions to participate in CRP and work off-farm are made simultaneously. Characteristics of households, farm operations other farm programs, and the local economies affect both decisions; some factors affect only one. Policy changes that affect one decision may affect another directly and/or indirectly.CRP, Off-farm labor, Choice Structure, Farm Management,