Neutrino Mass Matrix and Hierarchy

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for $\Delta_{sol}$ and $\Delta_{atm}$, and for the mixing angles determined from neutrino oscillation experiments, including that from KamLAND. Since the hierarchy assumption is a statement about mass ratios, it lets us obtain all three neutrino masses. We obtain a mass matrix, $M_\nu$ and a mixing matrix, $U$, where both $M_\nu$ and $U$ are given in terms of powers of $\Lambda$, the analog of the Cabibbo angle $\lambda$ in the Wolfenstein representation, and two parameters, $\rho$ and $\kappa$, each of order one. The expansion parameter, $\Lambda$, is defined by $\Lambda^2 = m_2/m_3 = \surd (\Delta_{sol}/\Delta_{atm}) \approx$ 0.16, and $\rho$ expresses our ignorance of the lightest neutrino mass $m_1, (m_1 = \rho \Lambda^4 m_3$), while $\kappa$ scales $s_{13}$ to the experimental upper limit, $s_{13} = \kappa \Lambda^2 \approx 0.16 \kappa$. These matrices are similar in structure to those for the quark and lepton families, but with $\Lambda$ about 1.6 times larger than the $\lambda$ for the quarks and charged leptons. The upper limit for the effective neutrino mass in double $\beta$-decay experiments is $4 \times 10^{-3} eV$ if $s_{13} = 0$ and $6 \times 10^{-3} eV$ if $s_{13}$ is maximal. The model, which is fairly unique, given the hierarchy assumption and the data, is compared to supersymmetric extension and texture zero models of mass generation.Comment: 8 pages, LaTex, This paper updates an earlier version by incorporating KamLAND dat

From symmetries to quarks and beyond

Attempts to understand the plethora of meson baryon and meson resonances by the introduction of symmetries, which led to the invention of quarks and the quark model, and finally to the formulation of QCD, are described

From symmetries to quarks and beyond

Attempts to understand the plethora of meson baryon and meson resonances by the introduction of symmetries, which led to the invention of quarks and the quark model, and finally to the formulation of QCD, are described

The Symmetries of Nature

The study of the symmetries of nature has fascinated scientists for eons. The application of the formal mathematical description of symmetries during the last century has produced many breakthroughs in our understanding of the substructure of matter. In this talk, a number of these advances are discussed, and the important role that George Sudarshan played in their development is emphasize

Comment On ``Grand Unification and Supersymmetric Threshold"

Barbieri and Hall have argued that threshold effects at the scale of grand-unification wipe out predictions on the SUSY scale, M_S. Using triviality arguments we give upper bounds on ultraheavy particles, while proton stability gives lower bounds on the mass of the higgs color-triplet. We find no useful lower bound on the $\Sigma$ supermultiplet, but if the strong coupling constant is as large as recent experiments suggest, unification in the minimal SUSY SU(5) model requires that the $Sigma$ masses be $\sim 10^{-7}M_V$ and that the color octet and weak triplet be split in mass by a factor of $\sim$100.Comment: 6 pages (revised

The US Program in Ground-Based Gravitational Wave Science: Contribution from the LIGO Laboratory

Recent gravitational-wave observations from the LIGO and Virgo observatories have brought a sense of great excitement to scientists and citizens the world over. Since September 2015,10 binary black hole coalescences and one binary neutron star coalescence have been observed. They have provided remarkable, revolutionary insight into the "gravitational Universe" and have greatly extended the field of multi-messenger astronomy. At present, Advanced LIGO can see binary black hole coalescences out to redshift 0.6 and binary neutron star coalescences to redshift 0.05. This probes only a very small fraction of the volume of the observable Universe. However, current technologies can be extended to construct "3rd Generation" (3G) gravitational-wave observatories that would extend our reach to the very edge of the observable Universe. The event rates over such a large volume would be in the hundreds of thousands per year (i.e. tens per hour). Such 3G detectors would have a 10-fold improvement in strain sensitivity over the current generation of instruments, yielding signal-to-noise ratios of 1000 for events like those already seen. Several concepts are being studied for which engineering studies and reliable cost estimates will be developed in the next 5 years