An Effective pTp_T Cutoff for the Isolalated Lepton Background from Bottom Decay --

There is a strong correlation between the $p_T$ and isolation of the lepton coming from $B$ decay. Consequently the isolated lepton background from $B$ decay goes down rapidly with increasing lepton $p_T$; and there is a $p_T$ cutoff beyond which it effectively vanishes. For the isolation cut of $E^{AC}_T < 10$ GeV, appropriate for LHC, the lepton $p_T$ cutoff is 80 GeV. This can be exploited to effectively eliminate the $B$ background from the like sign dilepton channel apropriate for Majorana particle searches, as well as the unlike sign dilepton and the single lepton channels appropriate for the top quark search. We illustrate this with a detailed analysis of the $B$ background in these channels along with the signals at LHC energy using both parton level MC and ISAJET programs.Comment: TIFR/TH/93-23 (LATEX, 20 pages, 7 figures available on request

A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

Perturbative schemes utilizing a spectral moment expansion are well known and extensively used for investigating the physics of model Hamiltonians and real material systems. The advantages they offer, in terms of being computationally inexpensive, with real frequency output at zero and finite temperatures, compensate for their deficiencies and offer a quick, qualitative analysis of the system behavior. In this work, we have developed a method, that can be classified as a multi-orbital iterative perturbation theory (MO-IPT) to study N-fold degenerate and non degenerate Anderson impurity models. As applications of the solver, we have combined the method with dynamical mean field theory to explore lattice models like the single orbital Hubbard model, covalent band insulator and the multi-orbital Hubbard model for density-density type interactions in different parameter regimes. The Hund's coupling effects in case of multiple orbitals is also studied. The limitations and quality of results are gauged through extensive comparison with data from the numerically exact continuous time quantum Monte Carlo method (hybridization expansion CTQMC). In general we observe that the agreement with CTQMC results gets better as we move away from particle-hole symmetry. We have integrated MO-IPT with density functional theory based electronic structure methods to study real material systems. As a test case, we have studied the classic, strongly correlated electronic material, SrVO$_3$. A comparison of density of states and photo emission spectrum (PES) with results obtained from different impurity solvers and experiments yields good agreement.Comment: 20 pages, 20 figure

Solution of Abel Integral Equation Using Differential Transform Method

The application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense. Abel integral equation occurs in the mathematical modeling of various problems in physics, astrophysics, solid mechanics and applied sciences. An analytic technique for solving Abel integral equation of first kind by the proposed method is introduced here. Also illustrative examples with exact solutions are considered to show the validity and applicability of the proposed method. Abel integral equation, Differential transform method, Fractional differential transform method