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

New Uncertainties in QCD-QED Rescaling Factors using Quadrature Method

In this paper we briefly outline the quadrature method for estimating uncertainties in a function of several variables and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of fermion mass renormalization. Our present calculations are found to be new and also reliable compared to the earlier values employed by various authors.Comment: 14 page

Assessment of inter-population genetic diversity and preliminary evaluation of suitable clones of teak (Tectona grandis Linn. F.)

Productivity, uniformity and sustainability are the three important characters of the clonally propagated plants. With the increased use of clonal technology, the scarcity of wood products evidently decreased which has also led to reduced pressure on natural forests and ecosystem. However, the success of clonal technology rests on wise selection and deployment of suitable clones by studying the inter-population genetic diversity. The present study was conducted in a clonal seed orchard (CSO) of teak (Tectona grandis Linn. F.) comprising of 13 different clones to estimate the inter-clonal variation in terms of growth performance and genetic variability at 32 and 33 years of age. Clone ORANP2 exhibited maximum DBH (26.61cm), height (23.69 m), and stem volume (235.40 m3ha-1) with MAI of 7.133 m3ha-1year-1. The highest CAI of DBH (1.08 cm) and volume (18.558m3/ha) was reported in ORANP5 and ORANR3, respectively. The study found that clone ORANP2 is a superior genotype and thus can be recommended for vegetative multiplication and ex-situ mass planting in reforestation programmes. Both heritability and genetic advance values were low for all the plant traits studied (DBH, height and stem volume) indicating that these traits are of less use for a tree breeder for furthering the selection and breeding process on teak or other tropical hardwood species across globe

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

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