Continuous Monitoring of STAR\u27s Main Time Projection Chamber

STAR refers to the Solenoidal Tracking instrument At RHIC (the Relativistic Heavy Ion Collider). For momenta above 500 MeV/c charged kaons are not separated from pions within STAR\u27s Main TPC (Time Projection Chamber) by track density alone and they are poorly separated below 500 MeV/c, even when using information from other sources like the vertex tracker. Within the TPC large numbers of kaons and pions decay into muons (and undetected neutrinos). Earlier work has shown parent pions and kaons whose decays are detected within a TPC may be distinguished uniquely from each other in a two-dimensional plot of muon-emission angle versus momentum difference (between each parent meson and its decay muon). Since pions and kaons have zero spin, each muon decay-product emerges isotropically in its parent meson\u27s rest frame. Identification of particle type provides the parent meson\u27s rest mass and, thus, its total energy. This means the measurement of each decay event is kinematically complete. Thus, Lorentz Transformations may be used to transform each component of the decaying muon\u27s laboratory four-momentum into the rest frame of its parent meson, where the muon decay is isotropic. An aggregated plot of muon directions from many parent rest frames will be isotropic in each (selected) sub-volume of the TPC unless there is a problem within the TPC or in its tracking algorithms. Continuous monitoring of a TPC is possible using this subset of detected charged particles

Rotational Symmetries of Nuclear States: Spin Determinations in Advanced Laboratory

An advanced laboratory experiment is described which shows the connection between the rotational symmetries of nuclear states and the assignments of spins to discrete nuclear states. Standard angular correlation methods were used to study the two sequential gamma ray transitions in each ⁶⁰Ni nucleus, populated by unobserved beta decays from a weak radioactive ⁶⁰Co source. The chosen electronics and detectors were inexpensive and easy to operate. This experiment was extended to introduce students to real-world data acquisition, using finite-geometry detectors, which resulted in enormously larger coincident data rates

Coplanarity Test for Selecting a Pair of Charged-Particle Tracks Resulting from a Single Neutral-Particle Decay

It is hard to determine directly the position of a neutral subatomic particle, but when such a particle decays into a pair of charged particles, it is easy to determine the positions of the charged decay particles and thereby infer the position of the parent particle at the time of its decay. A minimum of two coordinate points for each of the two decay particles is needed to reconstruct the position of the parent vertex. The mathematics of the reconstruction process is inherently interesting, and it can be used to demonstrate to students the utility of some of the most fundamental ideas of vector analysis

Curing a Summing Error That Occurs Automatically When Fitting a Function to Binomial or Poisson Distributed Data

Without special precautions a sum-rule error occurs automatically when a chi-squared procedure is used to fit a funtion to binomial or Poisson distributed histogram data if the function has at least one linear parameter. Since the square of the variance per channel is equal to the mean population, errors are usually approximated using (G2~=yi\u3e0)}; this choice for approximating the variance gives a per-channel error weighting of 1/yi that automatically results in a sum-rule error. This sum-rule error consistently and systematically underestimates the total sum of the data points by an amount equal to the value of %*, resulting in Zjyj-Zjfj= J& where %i = £j(vi - QVyi an^ f\u27i= f(Xj,{parameters}). In contrast, using {o\u27-f=(¦\u3e()} gives the error weighting per channel of 1/fj that automatically results in a less well known sum rule error. This sum-rule error which is only half as large but opposite insign consistently and systematically overestimates the total sum ofthe data X? points by an amount equal to half the value of %?, that is, itresults in - Zjf- =- L y ,where Xr = (vi \u27i) \u27/\u27i- The good news is a combination of error weightings may be constructed which completely eliminates the otherwise automatically cocuring sum-rule error by taking advantage of cancellations occuring between the two sum-rule errors implicit in the two above-mentioned approaches to error-weighting per channel. This fortunitous linear combination ofsum-rule error swill combine and cancel ifthe fitting funtion is a sufficiently viable choice so that Xr= Xy = v (number ofdegrees of freedom); 1 2 consequently a weighted linear combination of these two definitions may be used, X 2 = 3 Xy + !%?• This choice for X = is 1 1 2 equivalent to choosing an error weighting of „\u27_\u27 = 3yj +:\u27\u3e(; ,and it essentially eliminates summing errors so that Xjyi- Zjf-. An alternate method is presented and proven for {jLt; = f-}infitting a function using Maximum Likelihood

Separating K+/- from Pi+/- using In-Flight Decays to Mu+/- + Nu

A method is presented for completely distinguishing between charged kaons and charged pions by using their charged muon (plus neutrino) decays (with neutrinos undetected) for meson laboratory momenta up to 1000 MeV/c. When either a charged kaon or a charged pion decays into a muon and a neutrino, momentum-energy (four-momentum) conservation will be used to provide unique kinematic trajectories for distinguishing kaon decays from pion decays when the change in three-momentum of the muon from that of either parent kaon or pion is measured (or simulated). Ina magnetic field, observation of a tracked particle showing a kink and/or a change in helicity indicates the decay of the parent particle into a similarly charged muon product. Unique kinematic separation between each parent kaon and parent pion is possible for each parent particle\u27s momentum up to 1000 MeV/c. Curvature-radius of the helical path in a magnetic field is used to determine each charged particle\u27s momentum, whether it be a kaon, a pion or a muon. A weak field is adequate for making this determination since momentum (curvature radius) need only be measured to an accuracy of about 10%. Monte Carlo calculations of the kineatic trajectories have been carried out for primary meson momenta between 0 and 1000 MeV/c and for a range of emission angles (or kinks ) between 0° and 180°. Monte Carlo results from these in-flight decay kinematic calculations show a complete separation is possible for pion decays from kaon decays for laboratory momenta up to 1000 MeV/c because these two classes of meson decays cluster into completely separated 2-D regions of difference-momentum (x)muon-angle space. The most difficult region for separating primary particles occurs for small-kink decays within less than 5°. Decay halflife and time dilation require an efficient time projection chamber to be fairly large, because kaons are strongly favored over pions at the higher laboratory momenta and for the smaller time projection chamber geometries

Introduction to Monte Carlo Methods

Monte Carlo computer programming is becoming increasingly popular to those who use it, due to the ease with which complex problems may be formulated and solved. However, the growth of MC programming for small projects is inhibited by a frequent misconception of difficulty, inferred from the high level of complexity of problems solved in High Energy and Nuclear Physics using MC methods. In addition, few students of science and engineering are receiving exposure to the basic issues involved in the Monte Carlo process despite the ease with which MC can be used to solve classical physics problems, especially those problems with little symmetry or unusual geometry. Few upper-division or graduate students have begun to exploit this approach, even in research projects. Thus, an introduction to Monte Carlo methods would be valuable, even for the beginning science or engineering student. The present work introduces integration of area and volume, then expands this effort to include surface and volume integrals of scalar and vector functions. Next, integration over unusual geometries introduces programs which convert the geometries defined by CAD (Computer Aided Design) to geometries convenient to the Monte Carlo process. Finally, Gauss\u27s Law uses MC to calculate the size of an asymmetrically positioned charge and a classic example from Sir Isaac Newton uses MC to calculate the effect of a spherically symmetric shell of mass on an exterior field point where the average force components (Fx ,Fy ,Fz) are calculated. These final examples introduce singularities and convergence problems arising in the Monte Carlo averaging process

Measuring Strangeness Production from Relativisitic Collisions Between Pairs of Nuclei Using a Vertex Time Projection Chamber

At collider energies of 200A-GeV, tracking of charged particle pairs originating from neutrals is dominated by singlystrange KJ.\u27 decays. Counting the number ofsecondary vertex pairs is a method of measuring the strangeness production. The VTX is a four-layer micro-strip gas time projection chamber being designed for use with the STAR instrument in an experiment using the Relativistic Heavy Ion Collider under construction at Brookhaven National Laboratory. Simulated pixel data generated from CERN\u27s Monte Carlo detector-modeling program Geant were put into tables using the TAS sorting structures available from the STAR Collaboration. The response of VTX was mapped for charged pion pairs emerging from each secondary vertex resulting from the decay of a neutral kaon. Grouping each set oftwo charged pions ofopposite sign which originate from a vertex distinct from the collider vertex is the method being presented for measuring strangeness production. This method has three steps: (1) removing all charged particles originating directly from the collider vertex using established methods, (2) identifying which \u3c4 residual pixel tracks in the 4 micro-strip TPC planes belong to which particular individual pion, and (3) grouping these secondary pions into the appropriate pairs. Research presented will concentrate on steps (2) and (3) in idenfifying each K in order to measure strangeness production. Backgrounds were generated as part of the simulation process, and to help in the elimination of backgrounds, rough-set analysis was used to fine tune algorithm parameters using exemplars which are available from simuation data in TAS Tables

User-Interface Coding for the CERN/GEANT Nuclear Physics Program

Explanations will be given of the various user-written routines required by the Monte Carlo detector-modeling program GEANT, developed by CERN, the European Organization for Nuclear Research. User-written routines must be linked with the CERN library to accomplish the researcher\u27s intentions. Examples will illustrate how GEANT passes information to subprograms needed to model events. Various data structures used by GEANT library calls and included in each user routine, are similarly illustrated. Both computational-speed and memory-size limitations need to be factored into the construction of a simulation model. This will constrain the calls used in the user-written routines. Examples are provided of GEANT input data flags, defined by the user to determine simulation parameters and to control various testing choices in GEANT

Energy-Loss Particle Identification in 2-D Silicon Drift Detectors

A relatively new type of transducer known as the Silicon Drift Detector (SDD) has been fabricated onto thin silicon wafers. SDD operates like a miniature, high-resolution, 2-D Time-projection chamber. One of these devices can detect two dimensions of an ionizing particle\u27s position, and its integrated electrical charge output level isproportional to the particle\u27s energy loss through the silicon. An array ofSDD\u27s, arranged in three coaxial cylinders, is being considered as part of an instrument surrounding the beam pipe of highly-relativistic colliding beam facility, where it would be used to simultaneously track individual paths of thousands of charged particles emerging from each primary collision. Energy-loss data from the (x,y) pixels of each track allow individual particle identification as an electron, pion, kaon or proton. CERN\u27s Monte Carlo modeling program, GEANT, is being used to predict energy loss at high statistical accuracy to account for high-energy tailing of the more prevalent pions. GEANT has been installed on a Linux workstation in Little Rock. Speeding up the modeling process is being investigated using parallel virtual memory techniques and groupings of Linux workstations

Monte Carlo Director Modeling and Display, Using the CERN Laboratory

Detectors for high energy nuclear physics experiments are being modeled using programs developed and maintained at CERN, the European Organization for Nuclear Research. These programs include data handling and display routines, as well as those using random-sampling Monte Carlo techniques to calculate energy depositions for high energy particles as they pass through the various parts of the detector system. The complete CERN library has been imported for use with our Workstation computers in a multiple user environment. The enormous CERN Monte Carlo program GEANT(French for GIANT) tracks the progress of a particle through a detector on a simulated event-by-event basis. GEANT is being used to predict energy loss in materials using several different energy-loss assumptions. The energy loss in a silicon slab is calculated for charged particles at moderately relativistic momenta. The response of these calculations is known to result in an asymmetric energy deposition in silicon. Predicted responses are scheduled for examination using test beams at two different accelerator facilities