Vanishing corrections on the intermediate scale and implications for unification of forces

In two-step breaking of a class of grand unified theories including SO(10),we prove a theorem showing that the scale $M_I$ where the Pati-Salam gauge symmetry with parity breaks down to the standard gauge group,has vanishing corrections due to all sources emerging from higher scales $\mu >M_I$ such as the one-loop and all higher loop effects,the GUT-threshold,gravitational smearing,and string threshold effects. Implications of such a scale for the unification of gauge couplings with small Majorana neutrino masses are discussed.In string inspired SO(10) we show that $M_I \simeq 5\times 10^{12}$,needed for neutrino masses,with the GUT scale $M_U \simeq M_{str}$ can be realized provided certain particle states in the predicted spectum are light.Comment: 21 pages, Late

Normal, Abby Normal, Prefix Normal

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number $pnw(n)$ of prefix normal words of length $n$, showing that $pnw(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)$ for some $c$ and $pnw(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)$. We introduce efficient algorithms for testing the prefix normal property and a "mechanical algorithm" for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes to stay normal but Bob wants to drive her "abnormal" -- we discuss which parameter settings allow Alice to succeed.Comment: Accepted at FUN '1

Solutions of the Renormalisation Group Equation in Minimal Supersymmetric Standard Model

Renormalisation Group Equation(RGE) for color and top couplings sector of MSSM has been solved. The mass of the top comes out to be 180.363$\pm$ 10.876 GeV and $\beta_{top}$=$\frac{\pi}{2}$. It is conjectured that the masses of the other 11 fermions and the CKM phase angle $\phi$ can be theoretically estimated. The results confirm the fact that the quarks and leptons have been created having equal mass $\sim$ 115 GeV at the MSSM GUT scale $\sim ~2.2\times 10^{16}$ GeV

Type II Seesaw Dominance in Non-supersymmetric and Split Susy SO(10) and Proton Life Time

Recently type II seesaw dominance in a supersymmetric SO(10) framework has been found useful in explaining large solar and atmospheric mixing angles as well as larger values of $theta_{13}$ while unifying quark and lepton masses. An important question in these models is whether there exists consistency between coupling unification and type II seesaw dominance. Scenarios where this consistency can be demonstrated have been given in a SUSY framework. In this paper we give examples where type II dominance occurs in SO(10) models without supersymmetry but with additional TeV scale particles and also in models with split-supersummetry. Grand unification is realized in a two-step process via breaking of SO(10) to SU(5) and then to a TeV scale standard model supplemented by extra fields and an SU(5) Higgs multiplet ${15}_H$ at a scale about $10^{12}$ GeV to give type-II seesaw. The predictions for proton lifetime in these models are in the range $\tau_p^0 = 2\times 10^{35}$ yrs. to $\tau_p^0 = 6\times 10^{35}$ yrs.. A number of recent numerical fits to GUT-scale fermion masses can be accommodated within this model.Comment: 7 pages LaTeX, 3 figures, related areas: hep-ex, hep-th, astro-ph; Reference added, typo corrected, version to appear in Physical Review

Quark lepton complementarity and renormalization group effects

We consider a scenario for the Quark-Lepton Complementarity relations between mixing angles in which the bi-maximal mixing follows from the neutrino mass matrix. According to this scenario in the lowest order the angle \theta_{12} is \sim 1\sigma (1.5 - 2^\circ) above the best fit point coinciding practically with the tri-bimaximal mixing prediction. Realization of this scenario in the context of the seesaw type-I mechanism with leptonic Dirac mass matrices approximately equal to the quark mass matrices is studied. We calculate the renormalization group corrections to \theta_{12} as well as to \theta_{13} in the standard model (SM) and minimal supersymmetric standard model (MSSM). We find that in large part of the parameter space corrections \Delta \theta_{12} are small or negligible. In the MSSM version of the scenario the correction \Delta \theta_{12} is in general positive. Small negative corrections appear in the case of an inverted mass hierarchy and opposite CP parities of \nu_1 and \nu_2 when leading contributions to \theta_{12} running are strongly suppressed. The corrections are negative in the SM version in a large part of the parameter space for values of the relative CP phase of \nu_1 and \nu_2: \phi > \pi/2.Comment: version as published in PRD, 14 pages, 12 figure

Neutrino Mixings and Leptonic CP Violation from CKM Matrix and Majorana Phases

The high scale mixing unification hypothesis recently proposed by three of us (R. N. M., M. K. P. and G. R.) states that if at the seesaw scale, the quark and lepton mixing matrices are equal then for quasi-degenerate neutrinos, radiative corrections can lead to large solar and atmospheric mixings and small reactor angle at the weak scale in agreement with data. Evidence for quasi-degenerate neutrinos could, within this framework, be interpreted as a sign of quark-lepton unification at high scale. In the current work, we extend this model to show that the hypothesis works quite successfully in the presence of CP violating phases (which were set to zero in the first paper). In the case where the PMNS matrix is identical to the CKM matrix at the seesaw scale, with a Dirac phase but no Majorana phase, the low energy Dirac phase is predicted to be ($\simeq 0.3^{\circ}$) and leptonic CP-violation parameter $J_{CP} \simeq (4 - 8)\times 10^{-5}$ and $\theta_{13} = 3.5^{\circ}$. If on the other hand, the PMNS matrix is assumed to also have Majorana phases initially, the resulting theory damps radiative magnification phenomenon for a large range of parameters but nevertheless has enough parameter space to give the two necessary large neutrino mixing angles. In this case, one has $\theta_{13} = 3.5^{\circ} - 10^{\circ}$ and $|J_{CP}|$ as large as $0.02-0.04$ which are accessible to long baseline neutrino oscillation experiments.Comment: 15 pages and 10 figures, typo correcte

Predictions for Proton Lifetime in Minimal Non-Supersymmetric SO(10) Models: An Update

We present our best estimates of the uncertainties due to heavy particle threshold corrections on the unification scale $M_U$, intermediate scale $M_I$ and coupling constant Alpha_U in the minimal non-supersymmetric SO(10) models. Using these , we update the predictions for proton life-time in these models.Comment: UMD-PP-94-117 ( 20 pages;latex; no figures

Low-energy formulas for neutrino masses with tan⁡β\tan \beta-dependent hierarchy

Using radiative correction and seesaw mechanism,we derive analytic formulas for neutrino masses in SUSY unified theories exhibiting, for the first time, a new hierarchial relation among them.The new hierarchy is found to be quite significant especially for smaller values of $\tan\beta$.Comment: 10 pages,REVTEX, no figures,typographical errors rectifie

Generation of large flavor mixing from radiative corrections

We provide a model independent criterion which would guarantee a large flavor mixing of two quasi-degenerate Majorana neutrinos at the low scale, irrespective of the mixing at the high scale. We also show that such a situation is realizable for a phenomenologically interesting range of parameters of the weak scale theory. We further show that for a similar condition to be implementable for the three generation case, the CP parity of one of the neutrinos needs to be opposite to that of the others.Comment: 14 pages RevTeX, 2 eps figures. Minor changes made, a few references adde