The Time of Flight (TOF) system of the Solenoidal Tracker at RHIC (STAR) at the Relativistic Heavy Ion Collider (RHIC) consists of two different subsystems: the start detector and the stop detector. Described in this thesis is the design, construc tion, and operation of a new start detector for STAR. This new start detector, called the Upgraded Pseudo Vertex Position Detector (upVPD) provides many improvements to the old start detector, called the Pseudo Vertex Position Detector (pVPD). The upVPD is expected to have better efficiency per event and better start timing and primary vertex location resolution compared to the pVPD, which will improve the performance of the STAR TOF and STAR Trigger systems. Timing offsets and the slewing effect smear the raw data read-out by the detectors and require offline calibration. The general approach and a few possible algorithms for such calibrations are also described. The analysis results from both the pVPD and the upVPD detectors are presented. Additional cosmic ray tests of the upVPD detectors were also performed, and the calibration results from these data are also discussed.

We have searched for evidence of $W\sp\prime \to e\nu$ and $Z\sp\prime \to ee$ in data collected with the DO detector at the Tevatron during the 1992-1993 $p\bar p$ collider run at $\sqrt{s}$ = 1.8 TeV. We set an upper limit at the 95% confidence level on the cross section times branching ratio for $W\sp\prime \to e\nu,$ assuming that the neutrino from $W\sp\prime$ decay is stable and has a mass significantly less than $m\sb{W\sp\prime},$ and an upper limit on $Z\sp\prime \to ee.$ We exclude the existence of a $W\sp\prime$ of mass less than 610 GeV and a $Z\sp\prime$ of mass less than 490 GeV at the 95% confidence level, assuming standard model couplings to quarks and leptons.

I have designed and constructed a muon hodoscope/veto counter for E-683 at Fermilab. Preliminary tests indicate that the efficiency of each scintillator is $\approx$99.9%, allowing the hodoscope layers to be used in coincidence mode. The calibration of the modules in the E-683 main calorimeter has been studied using muons from the 1987-88 parasitic run. Preliminary calibration reveals that the calorimeter's response is within the parameters observed in E-609. Further, new information reveals the response of calorimeter modules to different physical triggers. The response of the calorimeter modules to different voltage thresholds, neighbor cuts, and gate timings has been analyzed. Results from the 1990 parasitic run indicate that the gate timing should precede the signal by 80 ns. After developing a new program to analyze the data from the entire calorimeter, I have begun muon balancing of all the modules. (Abstract shortened with permission of author.)

The analysing power A$\sb{\rm N}$ of inclusively produced charged pions is measured using 13.3 and 18.5 GeV/c polarized protons from the Brookhaven AGS. The measurement was performed at the Multiparticle Spectrometer in early 1986, in conjunction with a measurement of inclusively produced $\Lambda$ particles. There are two possible theoretical explanations for the data. A baryon exchange model is discussed in light of the previous measurements of the pion analysing power. This model is dependent on the scanty backward $\pi$p elastic data that is available at lower energies. A more modern quark recombination model which uses SU(6) symmetry and the idea that the spin of the quarks is preserved in the scattering and recombination process is used to make specific predictions concerning the analysing power of inclusively produced particles. The quark model predicts that A$\sb{\rm N}$ should be positive for $\pi\sp{+}$ and negative for $\pi\sp{-}$ in the beam fragmentation region. The data analysis consists of pattern recognition and track reconstruction of the tracks in the spectrometer, and identification of the pions. The background consists of particles that did not originate in the target, and particles which may have passed through the edges of drift chamber frames. Minimal cuts are applied to the data, requiring that the pions come from the target and pass through the drift chamber active areas. The acceptance of the apparatus was verified by Monte Carlo calculation. The measured vertical component of the beam polarization P$\sb{\rm N}$ was 0.379 $\pm$ 0.020 at 18.5 GeV/c. At 13.3 GeV/c, P$\sb{\rm N}$ was measured to be 0.5900 $\pm$ 0.0130. The analysing power for $\pi\sp{-}$ over the range of 0.1 $\leq$ X$\sb{\rm F}$ $\leq$ 0.7 was found to be almost negligible, with a value of 0.0037 $\pm$ 0.0036 at 13 GeV/c when calculated for all transverse momenta. A$\sb{\rm N}$ for $\pi\sp{-}$ is observed to be negative in the highest X$\sb{\rm F}$-P$\sb{\rm T}$ bin measured. The $\pi\sp{+}$ analysing power is found to be positive, increasing approximately linearly with increasing X$\sb{\rm F}$, and is observed to have a flat dependence upon P$\sb{\rm T}$, with a value of 0.047 $\pm$ 0.0034 when averaged over all P$\sb{\rm T}$ and X$\sb{\rm F}$. Our measurement is found to be in qualitative agreement with the predictions of the quark recombination model.

A study has been made of 400 GeV proton-nucleus collisions using a large acceptance calorimeter. The targets used were LH$\sb2$, He, Be, C, Al, Cu, Sn and Pb. A geometrically unbiased trigger efficient at selecting hadronic jet events was utilized. The A-dependence of the production of jet-like events is like that seen in high transverse momentum single- and di-hadron production. The dependence upon A of high E$\sb{\rm T}$ production is found to weaken with increasing planarity and when the observed event p$\sb{\rm T}$ balance improves. The flow of energy in the events is found to have a number of features in common with soft high-energy proton-nucleus collisions.

We formulate a systematic, nonperturbative expansion for the effective potential of $\lambda\phi\sp4$ theory. At first order it gives the Gaussian effective potential (GEP), which itself contains the 1-loop and leading-order $1\over N$ results. Here, we compute the second-order terms and hence obtain the post-Gaussian effective potential (PGEP) in 1, 2, 3, and 4 spacetime dimensions. The renormalization procedure, including the calculation of the physical mass, is discussed in detail. The results in lower dimensions agree well with the GEP when the comparison is made for the same values of the bare parameters. In 4 dimensions the divergent integrals are calculated using coordinate-space methods combined with dimensional regularization. (Difficulties with other regularizations are briefly discussed). The PGEP for the "precarious" $\lambda\phi\sp4$ theory is obtained in manifestly finite form. Remarkably, the final result takes the same mathematical form as the GEP, with only some numerical co-efficients being changed. Indeed, when parametrized in terms of the physical mass and the renormalized coupling constant, only a single coefficient is changed, from 1 to 1-1/(N + 3)$\sp2$. The "autonomous" version of the 4-dimensional theory refuses to work in this approach: one obtains indeed an autonomous-like theory, but it is unbounded below for a certain range of the parameters. The influence of fermions on scalar systems is also investigated in the post-Gaussian approximation. For the simple case of an Yukawa-type coupling with no scalar self-interaction terms the results turn out to be the same as in the Gaussian approximation.

The calibration of an electromagnetic-hadronic calorimeter is discussed in the larger context of the physics goals of the experiment in which it was used. Descriptions of the experimental apparatus are given. The methods employed for balancing electromagnetic response are discussed, including cuts on data integrity and fiducial cuts on energy distributions, and the reliability of the balancing algorithm. Results for energy resolution are given and are found to be in reasonable agreement with expectation. Extension of these balancing methods to hadronic response is discussed along with preliminary results. The ratio of hadronic to electromagnetic response is considered and is found to be in reasonable agreement with expectation. Methods of measuring and correcting for the calorimeter's evolution through time are briefly discussed.

The Gaussian effective potential (GEP), a non-perturbative approach to study quantum field theory, is applied to scalar and scalar-fermion models. We study the scalar $\phi\sp6$ field coupled to fermions through g$\sb{\rm B}\phi\overline{\psi}\psi$ or g$\sb{\rm B}\phi\sp2\overline{\psi}\psi$ in 2 and 3 space-time dimensions. In addition, we derive the finite temperature (T $>$ 0) GEP from first principles and apply it to study these models at T $>$ 0. Also the Autonomous $\lambda\phi\sp4$, coupled to fermions through a Yukawa term (g$\sb{\rm B}\phi\overline{\psi}\psi$), is examined in 4 dimensions at T $>$ 0. In all these models, in order to obtain stable theories, it is found that g$\sb{\rm B}$ must vanish as 1/log(M$\sb{\rm uv}$), 1/M$\sb{\rm uv}$ or 1/M$\sbsp{\rm uv}{2}$ in 2, 3 or 4 dimensions respectively, M$\sb{\rm uv}$ being an ultraviolet cutoff which is sent to infinity. The contribution of fermions to the GEP, however, is nonvanishing. It is also found that for the class of theories discussed, symmetry, if broken, is restored above a critical temperature. The coupling constant parameter space for each model is studied carefully, and regions where symmetry breaking occurs are determined both at zero and finite temperature.

A polarized proton beam incident on a Beryllium target was used for inclusive $\Lambda$(1116 meV) production at beam momenta of 13.3 GeV and 18.5 GeV. The beam polarization was transverse to the beam direction with magnitude 0.63(0.40) at 13.3(18.5)GeV. The trigger condition favoured forward produced $\Lambda$'s with moderately high p$\sb{\rm T}$(p$\sb{\rm T}\sim$ 1GeV). The $\Lambda$ polarization was measured and found to be in agreement with results from earlier experiments which used unpolarized proton beams. Analyzing power (A) and depolarization (D$\sb{\rm NN}$) of the $\Lambda$'s were both measured and compared with a hyperon polarization model in which the polarization arises from a Thomas precession effect. There is good agreement with its predictions: A = 0 and D$\sb{\rm NN}$ = 0. In particular, our measurement of D$\sb{\rm NN}$ = $-$0.009 $\pm$ 0.015 supports the idea that the valence quarks carry all of the hadron spin, since this assumption is implicit in the model's use of SU(6) wave functions to form final state hadrons from beam fragments and sea quarks. The analyzing power of K$\sb{\rm s}$ was also measured at 13.3(18.5)GeV and found to be $-$0.094 $\pm$ 0.012($-$0.076 $\pm$ 0.015). We use the same model to predict A of K$\sb{\rm s}$, taking into account K$\sb{\rm s}$productgion from various sources (K$\sp\circ$, K$\sp\circ$ and K*) and find good agreement with the data. Finally a small sample of $\bar\Lambda$ was isolated from the 18.5GeV sample and was found to have A = 0.03 $\pm$ 0.1, consistent with the model's prediction of zero.

The present work concerns nonperturbative variational studies of the effective potential beyond the Gaussian effective potential (GEP) approximation. In the Hamiltonian formalism, we study the method of non-linear canonical transformations (NLCT) which allows one to perform variational calculations with non-Gaussian trial states, constructed by nonlinear unitary transformations acting on Gaussian states. We consider in detail a particular transformation that leads to qualitative as well as quantitative improvement over the Gaussian approximation. In particular we obtain a non-trivial correction to the Gaussian mass renormalization. For a general NLCT state, we present formulas for the expectation value of the $O(N)$-symmetric $\gamma(\phi\sp2)\sp2$ Hamiltonian, and also for the one-particle NLCT state energy. We also report on the development of a manifestly covariant formulation, based on the Euclidian path integral, to construct lower-bound approximations to $\Gamma\sb{1PI}$, the generating functional of one-particle-irreducible Green's functions. In the Gaussian approximation the formalism leads to the Gaussian effective action (GEA), as a natural variational bound to $\Gamma\sb{1PI}$. We obtain, non-trivially, the proper vertex functions at non-zero momenta, and non-zero values of the classical field. In general, the formalism allows improvement beyond the Gaussian approach, by applying nonlinear measure-preserving field transformations to the path integral. We apply this method to the $O(N)$-symmetric $\lambda(\phi\sp2)\sp2$ theory. In 4 dimensions, we consider two applications of the GEA. First, we consider the N = 1 $\lambda\phi\sp4$ theory, whose renormalized GEA seems to suggest that the theory undergoes SSB, but has noninteracting particles in its SSB phase. Second, we study the Higgs mechanism in scalar quantum electrodynamics (i.e., $O(2)$ $\lambda\phi\sp4$ coupled to a U(1) gauge field) in a general covariant gauge. In our variational scheme we can optimize the gauge parameter, leading to the Landau gauge as the optimal gauge. We derive optimization equations for the GEA and obtain the renormalized effective potential explicitly.