Scale invariant correlations and the distribution of prime numbers

Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.Comment: 13 pages, 8 figures, version to appear in J. Phys.

Electron Beam Dynamics of SAMEER Linac

In the design of a linac such as the 4 MeV linac fabricated at SAMEER, simulation of electron beam dynamics plays an important role. We study electron beam dynamics to help in design of buncher cavity dimensions, linac length and effect of beam loading on electron energy and spectrum. We have written a program to calculate the electron trajectories for a given power input, with cavity dimensions, rf couplings and electron beam input voltage and current as parameters. By calculating the trajectories of electrons arriving at different rf phases, we get the average electron energy, percent of beam transmitted and electron energy spectrum. By running the program with different input parameters, we can choose the best combination for a required application such as radiography or cancer therapy

21:27 WSPC/INSTRUCTION FILE LFunctions Correlations in Prime Number Distribution and L-function Zeros

A simple analysis of the gaps in primes shows an interesting correlation between neighbouring primes. Neighbouring primes are more likely to have differing remainders on being divided by 6 (the remainders can be 1 or 5). We give a heuristic argument for the observed correaltion. We apply the tool of rescaled range analysis to study the statistical properties

Can HERA See an eu−−>ece u --> e c Signal of a Virtual Leptoquark?

Virtual leptoquarks could be detected at HERA through some nonstandard effects. Here we explore the possibility that virtual leptoquarks could be discovered via $e u --> e c$ scattering, assuming integrated luminosity of 200 pb$^{-1}$ and charm identification efficiency of 1%. We study the implications of low energy data for the leptoquarks couplings and find that the most relevant bound for the HERA cross sections comes from inclusive $c --> e^+e^-~+~any$. This bound implies that the $e u --> e c$ cross sections for virtual leptoquarks are just too small for observation of the signal. With an improvement by a factor of ~2 on the luminosity or on charm identification it could be possible to see virtual leptoquarks with {\it maximum couplings} up to ~1.5 - 2 TeV. However, the prospects for discovering the virtual particles if their couplings are somewhat below present bounds are very dim. We point out that this cross section could be very large for leptoquarks lighter than HERA's kinematical limit, and if such a leptoquark is discovered we recommend searching for a possible $e u --> e c$ signal. Our results may also serve as an update on the maximum cross sections for leptoquark mediated $e u --> \mu c$ scattering.Comment: 15 Pages (LaTeX), including 4 postscript figures at the end of the file. Feynman diagrams available by reques

Bounds on second generation scalar leptoquarks from the anomalous magnetic moment of the muon

We calculate the contribution of second generation scalar leptoquarks to the anomalous magnetic moment of the muon (AMMM). In the near future, E-821 at Brookhaven will reduce the experimental error on this parameter to $\Delta a_\mu^{\rm exp}<4\times 10^{-10}$, an improvement of 20 over its current value. With this new experimental limit we obtain a lower mass limit of $m_{\Phi_L}>186$\ GeV for the second generation scalar leptoquark, when its Yukawa-like coupling $\lambda_{\Phi_L}$\ to quarks and leptons is taken to be of the order of the electroweak coupling $g_2$.Comment: 5 pages, plain tex, 1 figure (not included available under request

The Neutrino Magnetic Moment Induced by Leptoquarks

Allowing leptoquarks to interact with both right-handed and left-handed neutrinos (i.e., ``non-chiral'' leptoquarks), we show that a non-zero neutrino magnetic moment can arise naturally. Although the mass of the non-chiral vector leptoquark that couples to the first generation fermions is constrained severely by universality of the $\pi^+$ leptonic decays and is found to be greater than 50 TeV, the masses of the second and third generation non-chiral vector leptoquarks may evade such constraint and may in general be in the range of $1\sim 100$ TeV. With reasonable input mass and coupling values, we find that the neutrino magnetic moment due to the second generation leptoquarks is of the order of $10^{-12}\sim 10^{-16} \mu_{\rm B}$ while that caused by the third generation leptoquarks, being enhanced significantly by the large top quark mass, is in the range of $10^{-10}\sim 10^{-14} \mu_{\rm B}$.Comment: 11 pages, 3 eps figures, uses revte

Trapping dust particles in the outer regions of protoplanetary disks

In order to explain grain growth to mm sized particles and their retention in outer regions of protoplanetary disks, as it is observed at sub-mm and mm wavelengths, we investigate if strong inhomogeneities in the gas density profiles can slow down excessive radial drift and can help dust particles to grow. We use coagulation/fragmentation and disk-structure models, to simulate the evolution of dust in a bumpy surface density profile which we mimic with a sinusoidal disturbance. For different values of the amplitude and length scale of the bumps, we investigate the ability of this model to produce and retain large particles on million years time scales. In addition, we introduced a comparison between the pressure inhomogeneities considered in this work and the pressure profiles that come from magnetorotational instability. Using the Common Astronomy Software Applications ALMA simulator, we study if there are observational signatures of these pressure inhomogeneities that can be seen with ALMA. We present the favorable conditions to trap dust particles and the corresponding calculations predicting the spectral slope in the mm-wavelength range, to compare with current observations. Finally we present simulated images using different antenna configurations of ALMA at different frequencies, to show that the ring structures will be detectable at the distances of the Taurus Auriga or Ophiucus star forming regions.Comment: Pages 15, Figures 14. Accepted for publication in Astronomy and Astrophysic

The Three Families from SU(4)A⊗SU(3)C⊗SU(2)L⊗U(1)XSU(4)_A\otimes SU(3)_C\otimes SU(2)_L\otimes U(1)_X SM-like Chiral Models

We give a detailed description of the model construction procedures about our new approach to the family structure of the standard model. SM-like chiral fermion spectra, largely "derivable" from the gauge anomaly constraints, are formulated in a $SU(N)\otimes SU(3)\otimes SU(2)\otimes U(1)$ symmetry framework as an extension of the SM symmetry. The $N=4$ case gives naturally three families as a result, with $U(1)_Y$ nontrivially embedded into the $SU(4)_A\otimes U(1)_X$. Such a spectrum has extra vector-like quarks and leptons. We illustrate how an acceptable symmetry breaking pattern can be obtained through a relatively simple scalar sector which gives naturally hierarchical quark mass matrices. Compatibility with various FCNC constraints and some interesting aspects of the possible phenomenological features are discussed, from a non-model specific perspective. The question of incorporating supersymmetry without putting in the Higgses as extra supermultiplet is also addressed.Comment: 43 pages RevTex, including 9 tables and 3 figure

Naturally Light Leptoquarks

Light first generation leptoquarks are being hunted for in HERA and at FNAL and there are various proposals for further searches in future machines. Such leptoquarks are however problematic from a theoretical point of view: Low energy precision measurements imply strong constraints on the couplings of the leptoquarks, and up till now the fulfilment of these constraints seemed extremely unnatural. Here we show that horizontal symmetries, which are very conventional and widely used in the literature for completely different purposes, can suppress the unwanted couplings. Therefore light first generation leptoquarks can be natural.Comment: 12 pages LaTeX. WIS-94/27/Jul-P