Neutrino Masses and Mixing, Quark-lepton Symmetry and Strong Right-handed Neutrino Hierarchy

Assuming the same form of all mass matrices as motivated by quark-lepton symmetry, we discuss conditions under which bi-large mixing in the lepton sector can be obtained with a minimal amount of fine tuning requirements for possible models. We assume hierarchical mass matrices, dominated by the 3-3 element, with off-diagonal elements much smaller than the larger neighboring diagonal element. Characteristic features of this scenario are strong hierarchy in masses of right-handed neutrinos, and comparable contributions of both lighter right-handed neutrinos to the resulting left-handed neutrino Majorana mass matrix. Due to obvious quark lepton symmetry, this approach can be embedded into grand unified theories. The mass of the lightest neutrino does not depend on details of a model in the leading order. The right-handed neutrino scale can be identified with the GUT scale in which case the mass of the lightest neutrino is given as (m_{top}^2/M_{GUT}) |U_{\tau 1}|^2.Comment: 7 page

Incidence of qq-statistics in rank distributions

We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or vanishes. The relevant statistical-mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints, and the resulting duality of entropy indexes is seen to portray physically relevant information. While the value of the index $\alpha$ fixes the distribution's power-law exponent, that for the dual index $2-\alpha$ ensures the extensivity of the deformed entropy.Comment: Santa Fe Institute working paper: http://www.santafe.edu/media/workingpapers/14-07-024.pdf. see: http://www.pnas.org/content/early/2014/09/03/1412093111.full.pdf+htm

Possible evidence of extended objects inside the proton

Recent experimental determinations of the Nachtmann moments of the inelastic structure function of the proton F2p(x, Q**2), obtained at Jefferson Lab, are analyzed for values of the squared four-momentum transfer Q**2 ranging from ~ 0.1 to ~ 2 (GeV/c)**2. It is shown that such inelastic proton data exhibit a new type of scaling behavior and that the resulting scaling function can be interpreted as a constituent form factor consistent with the elastic nucleon data. These findings suggest that at low momentum transfer the inclusive proton structure function originates mainly from the elastic coupling with extended objects inside the proton. We obtain a constituent size of ~ 0.2 - 0.3 fm.Comment: 1 reference adde

Quasiclassical Equations of Motion for Nonlinear Brownian Systems

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a ``bath'' of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely classical theory. The case of linear interactions is treated exactly, and nonlinear interactions are compared using classical and quantum perturbation theory.Comment: 24 pages, CALT-68-1848 (RevTeX 2.0 macros

Numerical indications of a q-generalised central limit theorem

We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called $q$-product with $q \le 1$. We show that, in the large $N$ limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are $q_e$-Gaussians, i.e., $p(x) \propto [1-(1-q_e) \beta(N) x^2]^{1/(1-q_e)}$, with $q_e=2-\frac{1}{q}$, and with coefficients $\beta(N)$ approaching finite values $\beta(\infty)$. The particular case $q=q_e=1$ recovers the celebrated de Moivre-Laplace theorem.Comment: Minor improvements and corrections have been introduced in the new version. 7 pages including 4 figure

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

Orbifold Family Unification

We study the possibility of complete family unification in higher-dimensional space-time. Three families of matters in SU(5) grand unified theory are derived from a single bulk multiplet of SU(N) gauge group (N >= 9) in the framework of S^1/Z_2 orbifold models. In the case of the direct orbifold breaking down to the standard model gauge group, there are models in which bulk fields from a single multiplet and a few brane fields compose three families of quarks and leptons.Comment: Comments added, version to appear in Physical Review D (v3); References added (v2); 19 pages (v1

The Invisible Axion and Neutrino Masses

We show that in any invisible axion model due to the effects of effective non-renormalizable interactions related to an energy scale near the Peccei-Quinn, grand unification or even the Planck scale, active neutrinos necessarily acquire masses in the sub-eV range. Moreover, if sterile neutrinos are also included and if appropriate cyclic $Z_N$ symmetries are imposed, it is possible that some of these neutrinos are heavy while others are light.Comment: An example included and new references added. To appear in PR

Alternative experimental evidence for chiral restoration in excited baryons

Given existing empirical spectral patterns of excited hadrons it has been suggested that chiral symmetry is approximately restored in excited hadrons at zero temperature/density (effective symmetry restoration). If correct, this implies that mass generation mechanisms and physics in excited hadrons is very different as compared to the lowest states. One needs an alternative and independent experimental information to confirm this conjecture. Using very general chiral symmetry arguments it is shown that strict chiral restoration in a given excited nucleon forbids its decay into the N \pi channel. Hence those excited nucleons which are assumed from the spectroscopic patterns to be in approximate chiral multiplets must only "weakly" decay into the N \pi channel, (f_{N^*N\pi}/f_{NN\pi})^2 << 1. However, those baryons which have no chiral partner must decay strongly with a decay constant comparable with f_{NN\pi}. Decay constants can be extracted from the existing decay widths and branching ratios. It turnes out that for all those well established excited nucleons which can be classified into chiral doublets N_+(1440) - N_-(1535), N_+(1710) - N_-(1650), N_+(1720) - N_-(1700), N_+(1680) - N_-(1675), N_+(2220) - N_-(2250), N_+(?) - N_-(2190), N_+(?) - N_-(2600), the ratio is (f_{N^*N\pi}/f_{NN\pi})^2 ~ 0.1 or much smaller for the high-spin states. In contrast, the only well established excited nucleon for which the chiral partner cannot be identified from the spectroscopic data, N(1520), has a decay constant into the N\pi channel that is comparable with f_{NN\pi}. This gives an independent experimental verification of the chiral symmetry restoration scenario.Comment: 4 pp. A new footnote with an alternative proof of impossibility of parity doublet decay into pi + N is added. To appear in Phys. Rev. Let

Orbifold Family Unification in SO(2N) Gauge Theory

We study the possibility of family unification on the basis of SO(2N) gauge theory on the five-dimensional space-time, $M^4\times S^1/Z_2$. Several SO(10), $SU(4) \times SU(2)_L \times SU(2)_R$ or SU(5) multiplets come from a single bulk multiplet of SO(2N) after the orbifold breaking. Other multiplets including brane fields are necessary to compose three families of quarks and leptons.Comment: 28 page