Bi-Event Subtraction Technique at Hadron Colliders

We propose the Bi-Event Subtraction Technique (BEST) as a method of modeling and subtracting large portions of the combinatoric background during reconstruction of particle decay chains at hadron colliders. The combinatoric background arises when it is impossible to know experimentally which observed particles come from the decay chain of interest. The background shape can be modeled by combining observed particles from different collision events and be subtracted away, greatly reducing the overall background. This idea has been demonstrated in various experiments in the past. We generalize it by showing how to apply BEST multiple times in a row to fully reconstruct a cascade decay. We show the power of BEST with two simulated examples of its application towards reconstruction of the top quark and a supersymmetric decay chain at the Large Hadron Collider.Comment: 4 pages, 4 figure

Spectral Solution with a Subtraction Method to Improve Accuracy

This work addresses the solution to a Dirichlet boundary value problem for the Poisson equation in 1-D, d2u/dx2 = f using a numerical Fourier collocation approach. The order of accuracy of this approach can be increased by modifying f so the periodic extension of the right hand side is suffciently smooth. A proof for the order is given by Sköllermo. This work introduces a subtraction technique to modify the function\u27s right hand side to reduce the discontinuities or improve the smoothness of its periodic extension. This subtraction technique consists of cosine polynomials found by using boundary derivatives. We subtract cosine polynomials to match boundary values and derivatives of f. The derivatives need only be calculated numerically and approximately represent derivatives at the boundaries. Increasing the number of cosine polynomials in the subtraction technique increases the order of accuracy of the solution. The use of cosine polynomials matches well with the Fourier transform approach and is computationally efficient. Implementation of this technique results in a solution with variable accuracy depending on the number of collocation points and approximated boundary derivatives. Results show that the technique can be up to 14th order accurate

Confining potential in momentum space

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations

Study of stop and sbottom at LHC

In supersymmetric models a gluino can decay into $tb\tilde{\chi}^{\pm}_1$ through a stop or a sbottom. The decay chain produces an edge structure in the $m_{tb}$ distribution. Monte Carlo simulation studies show that the end point and the edge height would be measured at the CERN LHC by using a sideband subtraction technique. The stop and sbottom masses as well as their decay branching ratios are constrained by the measurement. We study interpretations of the measurement.Comment: 3 pages, 2 eps files, style files are included, talk at PASCOS'03, Mumbai, India, January 3-8, 200

A higher-order singularity subtraction technique for the discretization of singular integral operators on curved surfaces

This note is about promoting singularity subtraction as a helpful tool in the discretization of singular integral operators on curved surfaces. Singular and nearly singular kernels are expanded in series whose terms are integrated on parametrically rectangular regions using high-order product integration, thereby reducing the need for spatial adaptivity and precomputed weights. A simple scheme is presented and an application to the interior Dirichlet Laplace problem on some tori gives around ten digit accurate results using only two expansion terms and a modest programming- and computational effort.Comment: 7 pages, 2 figure