Applications of a Subordination Theorem

AbstractThe object of the present paper is to give applications of a subordination theorem due to Hallenbeck and Ruscheweyh [Proc. Amer. Math. Soc.52 (1975), Theorem 1]. Our results have some interesting corollaries and examples as special cases

Neutrinos and Nucleosynthesis in Supernova

The type II supernova is considered as a candidate site for the production of heavy elements. The nucleosynthesis occurs in an intense neutrino flux, we calculate the electron fraction in this environment.Comment: RevTex4 style, 3 pages including 1 figure. Presented at Mexican School of Astrophysics 2002, Guanajuato, Mexico, 31 Jul - 7 Aug 2002. Final version to appear in the Proceedings of IX Mexican Workshop on Particles and Fields Physics Beyond the Standard Model, Colima Col. Mexico, November 17-22, 200

Resolving Neutrino Mass Hierarchy and CP Degeneracy by Two Identical Detectors with Different Baselines

We explore the possibility of simultaneous determination of neutrino mass hierarchy and the CP violating phase by using two identical detectors placed at different baseline distances. We focus on a possible experimental setup using neutrino beam from J-PARC facility in Japan with beam power of 4MW and megaton (Mton)-class water Cherenkov detectors, one placed in Kamioka and the other at somewhere in Korea. We demonstrate, under reasonable assumptions of systematic uncertainties, that the two-detector complex with each fiducial volume of 0.27 Mton has potential of resolving neutrino mass hierarchy up to sin^2 2theta_{13} > 0.03 (0.055) at 2\sigma (3\sigma) CL for any values of delta and at the same time has the sensitivity to CP violation by 4 + 4 years running of nu_e and nu_e-bar appearance measurement. The significantly enhanced sensitivity is due to clean detection of modulation of neutrino energy spectrum, which is enabled by cancellation of systematic uncertainties between two identical detectors which receive the neutrino beam with the same energy spectrum in the absence of oscillations.Comment: 23 pages, 10 figures, version published in PR

On some first-order differential subordination

AbstractLet A denote the class of functions f that are analytic in the unit disc D and normalized by f(0)=f′(0)−1=0. In this paper, we investigate the class of functions such that Re{f′(z)+zf″(z)-β}>α in D. We determine conditions for α and β under which the function f is univalent, close-to-convex, and convex. To obtain this, we first estimate ∣Arg{f′(z)}∣ which improves the earlier results

What Fraction of Boron-8 Solar Neutrinos arrive at the Earth as a nu_2 mass eigenstate?

We calculate the fraction of B^8 solar neutrinos that arrive at the Earth as a nu_2 mass eigenstate as a function of the neutrino energy. Weighting this fraction with the B^8 neutrino energy spectrum and the energy dependence of the cross section for the charged current interaction on deuteron with a threshold on the kinetic energy of the recoil electrons of 5.5 MeV, we find that the integrated weighted fraction of nu_2's to be 91 \pm 2 % at the 95% CL. This energy weighting procedure corresponds to the charged current response of the Sudbury Neutrino Observatory (SNO). We have used SNO's current best fit values for the solar mass squared difference and the mixing angle, obtained by combining the data from all solar neutrino experiments and the reactor data from KamLAND. The uncertainty on the nu_2 fraction comes primarily from the uncertainty on the solar delta m^2 rather than from the uncertainty on the solar mixing angle or the Standard Solar Model. Similar results for the Super-Kamiokande experiment are also given. We extend this analysis to three neutrinos and discuss how to extract the modulus of the Maki-Nakagawa-Sakata mixing matrix element U_{e2} as well as place a lower bound on the electron number density in the solar B^8 neutrino production region.Comment: 23 pages, 8 postscript figures, latex. Dedicated to the memory of John Bahcall who championed solar neutrinos for many lonely year

A comprehensive study of neutrino spin-flavour conversion in supernovae and the neutrino mass hierarchy

Resonant spin-flavour (RSF) conversions of supernova neutrinos, which is induced by the interaction between the nonzero neutrino magnetic moment and supernova magnetic fields, are studied for both normal and inverted mass hierarchy. As the case for the pure matter-induced neutrino oscillation (Mikheyev--Smirnov--Wolfenstein (MSW) effect), we find that the RSF transitions are strongly dependent on the neutrino mass hierarchy as well as the value of $\theta_{13}$. Flavour conversions are solved numerically for various neutrino parameter sets, with presupernova profile calculated by Woosley and Weaver. In particular, it is very interesting that the RSF-induced \nu_\rme\to\bar\nu_\rme transition occurs, if the following conditions are all satisfied: the value of $\mu_\nu B$ ($\mu_\nu$ is the neutrino magnetic moment, and $B$ is the magnetic field strength) is sufficiently strong, the neutrino mass hierarchy is inverted, and the value of $\theta_{13}$ is large enough to induce adiabatic MSW resonance. In this case, the strong peak due to original \nu_\rme emitted from neutronization burst would exist in time profile of the neutrino events detected at the Super-Kamiokande detector. If this peak were observed in reality, it would provide fruitful information on the neutrino properties. On the other hand, characters of the neutrino spectra are also different between the neutrino models, but we find that there remains degeneracy among several models. Dependence on presupernova models is also discussed.Comment: 23 pages, 11 figures, corrected minor typos, added references. Final version to appear in Journal of Cosmology and Astroparticle Physic

KamLAND, terrestrial heat sources and neutrino oscillations

We comment on the first indication of geo-neutrino events from KamLAND and on the prospects for understanding Earth energetics. Practically all models of terrestrial heat production are consistent with data within the presently limited statistics, the fully radiogenic model being closer to the observed value ($\approx 9$ geo-events). In a few years KamLAND should collect sufficient data for a clear evidence of geo-neutrinos, however discrimination among models requires a detector with the class and size of KamLAND far away from nuclear reactors. We also remark that the event ratio from Thorium and Uranium decay chains is well fixed $N(Th)/N(U) \simeq 0.25$, a constraint that can be useful for determining neutrino oscillation parameters. We show that a full spectral analysis, including this constraint, further reduces the oscillation parameter space compared to an analysis with an energy threshold $E_{vis}>2.6 MeV$.Comment: 12 pages, RevTeX file, 3 ps figures included in the correct order, corrected some typos and added references. Accepted for publication on Phys. Lett.

Determining Neutrino Mass Hierarchy by Precision Measurements in Electron and Muon Neutrino Disappearance Experiments

Recently a new method for determining the neutrino mass hierarchy by comparing the effective values of the atmospheric \Delta m^2 measured in the electron neutrino disappearance channel, \Delta m^2(ee), with the one measured in the muon neutrino disappearance channel, \Delta m^2(\mu \mu), was proposed. If \Delta m^2(ee) is larger (smaller) than \Delta m^2(\mu \mu) the hierarchy is of the normal (inverted) type. We re-examine this proposition in the light of two very high precision measurements: \Delta m^2(\mu \mu) that may be accomplished by the phase II of the Tokai-to-Kamioka (T2K) experiment, for example, and \Delta m^2(ee) that can be envisaged using the novel Mossbauer enhanced resonant \bar\nu_e absorption technique. Under optimistic assumptions for the systematic uncertainties of both measurements, we estimate the parameter region of (\theta_13, \delta) in which the mass hierarchy can be determined. If \theta_13 is relatively large, sin^2 2\theta_13 \gsim 0.05, and both of \Delta m^2(ee) and \Delta m^2(\mu \mu) can be measured with the precision of \sim 0.5 % it is possible to determine the neutrino mass hierarchy at > 95% CL for 0.3 \pi \lsim \delta \lsim 1.7 \pi for the current best fit values of all the other oscillation parameters.Comment: 12 pages, 6 postscript figure