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We describe an example of an exact, quantitative Jeopardy-type quantum mechanics problem. This problem type is based on the conditions in one-dimensional quantum systems that allow an energy eigenstate for the infinite square well to have zero curvature and zero energy when suitable Dirac delta functions are added. This condition and its solution are not often discussed in quantum mechanics texts and have interesting pedagogical consequences., Comment: 8 pages, 3 figures, requires graphicx and epsfig packages. Additional information, including individual files containing the Worksheet and a Worksheet template, are available at http://webphysics.davidson.edu/mjb/jeopardy/

We extend the standard treatment of the asymmetric infinite square well to include solutions that have zero curvature over part of the well. This type of solution, both within the specific context of the asymmetric infinite square well and within the broader context of bound states of arbitrary piecewise-constant potential energy functions, is not often discussed as part of quantum mechanics texts at any level. We begin by outlining the general mathematical condition in one-dimensional time-independent quantum mechanics for a bound-state wave function to have zero curvature over an extended region of space and still be a valid wave function. We then briefly review the standard asymmetric infinite square well solutions, focusing on zero-curvature solutions as represented by energy eigenstates in position and momentum space., Comment: 17 pages, 5 .eps figures

We provide simple examples of closed-form Gaussian wavepacket solutions of the free-particle Schrodinger equation in one dimension which exhibit the most general form of the time-dependent spread in position, namely (Delta x_t)^2 = (Delta x_0)^2 + At + (Delta p_0)^2t^2/m^2, where A = <(xhat - _0)(phat - _0) + (phat - _0)(xhat - _0)>_0 contains information on the position-momentum correlation structure of the initial wave packet. We exhibit straightforward examples corresponding to squeezed states, as well as quasi-classical cases, for which A < 0 so that the position spread can (at least initially) decrease in time because of such correlations. We discuss how the initial correlations in these examples can be dynamically generated (at least conceptually) in various bound state systems. Finally, we focus on providing different ways of visualizing the x-p correlations present in these cases, including the time-dependent distribution of kinetic energy and the use of the Wigner quasi-probability distribution. We discuss similar results, both for the time-dependent Delta x_t and special correlated solutions, for the case of a particle subject to a uniform force., Comment: 25 pages, 2 embedded postscript figures

We discuss special k=sqrt{2m(E-V(x))/\hbar^2}=0 (i. e. zero-curvature) solutions of the one-dimensional Schrodinger equation in several model systems which have been used as idealized versions of various quantum well structures. We consider infinite well plus Dirac delta function cases (where E=V(x)=0) and piecewise-constant potentials, such as asymmetric infinite wells (where E=V(x)=V_0>0). We also construct supersymmetric partner potentials for several of the zero-energy solutions in these cases. One application of zero-curvature solutions in the infinite well plus delta-function case is the construction of `designer' wavefunctions, namely zero-energy wavefunctions of essentially arbitrary shape, obtained through the proper placement and choice of strength of the delta-functions., Comment: 13 pages, 2 embedded .eps figures; a slightly shortened version of this manuscript was submitted to Phys. Rev. A as a Brief Report: Fig. 2 was removed in the Phys. Rev. A version, as were some minor details from the text, in order to meet the length requirements for a Brief Report

We studied single Higgs boson production in $\gamma\gamma$ collisions proceeding via the hadronic content of the photon. For SM Higgs masses of current theoretical interest, the resolved photon contributions are non-negligible in precision cross section measurements. We found that production of the heavier Higgs bosons H^0 and A^0 of the MSSM can probe regions of the SUSY parameter space that will complement other measurements. Finally, we showed that associated t H^\pm production in gamma-gamma collisions can be used to make an accurate determination of tan(beta) for low and high tan(beta)by precision measurements of the gamma gamma to H^\pm t +X cross section., Comment: 3 pages, contributed talk to the 2004 DPF Meeting, Riverside CA, Aug 26-31, 2004, Uses ws-ijmpa.cls

We consider time-dependent Gaussian wave packet solutions of the Schrodinger equation (with arbitrary initial central position, x_0, and momentum, p_0, for an otherwise free-particle, but with an infinite wall at x=0, so-called bouncing wave packets. We show how difference or mirror solutions of the form psi(x,t)-psi(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate _t explicitly which illustrates how the free-particle kinetic (and hence total) energy is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, _t, and momentum, _t, and their relation to the impulsive force during the `collision' with the wall. Finally, the x_0,p_0 --> 0 limit is shown to reduce to a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands on the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form., Comment: 14 pages, 1 embedded .eps figure

We calculate the Wigner quasi-probability distribution for position and momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite well potential, using both x- and p-space stationary-state solutions, as well as visualizing the results. We then evaluate the time-dependent Wigner distribution, P_W(x,p;t), for Gaussian wave packet solutions of this system, illustrating both the short-term semi-classical time dependence, as well as longer-term revival and fractional revival behavior and the structure during the collapsed state. This tool provides an excellent way of demonstrating the patterns of highly correlated Schrodinger-cat-like `mini-packets' which appear at fractional multiples of the exact revival time., Comment: 45 pages, 16 embedded, low-resolution .eps figures (higher resolution, publication quality figures are available from the authors); submitted to American Journal of Physics

The rigid pendulum, both as a classical and as a quantum problem, is an interesting system as it has the exactly soluble harmonic oscillator and the rigid rotor systems as limiting cases in the low- and high-energy limits respectively. The energy variation of the classical periodicity ($\tau$) is also dramatic, having the special limiting case of $\tau \to \infty$ at the 'top' of the classical motion (i.e. the separatrix.) We study the time-dependence of the quantum pendulum problem, focusing on the behavior of both the (approximate) classical periodicity and especially the quantum revival and superrevival times, as encoded in the energy eigenvalue spectrum of the system. We provide approximate expressions for the energy eigenvalues in both the small and large quantum number limits, up to 4th order in perturbation theory, comparing these to existing handbook expansions for the characteristic values of the related Mathieu equation, obtained by other methods. We then use these approximations to probe the classical periodicity, as well as to extract information on the quantum revival and superrevival times. We find that while both the classical and quantum periodicities increase monotonically as one approaches the 'top' in energy, from either above or below, the revival times decrease from their low- and high-energy values until very near the separatrix where they increase to a large, but finite value., Comment: 27 pages, 8 embedded .eps figures; to appear, Annals of Physics

We present quasi-analytical and numerical calculations of Gaussian wave packet solutions of the Schr\"odinger equation for two-dimensional infinite well and quantum billiard problems with equilateral triangle, square, and circular footprints. These cases correspond to N=3, N=4, and $N \to \infty$ regular polygonal billiards and infinite wells, respectively. In each case the energy eigenvalues and wavefunctions are given in terms of familiar special functions. For the first two systems, we obtain closed form expressions for the expansion coefficients for localized Gaussian wavepackets in terms of the eigenstates of the particular geometry. For the circular case, we discuss numerical approaches. We use these results to discuss the short-time, quasi-classical evolution in these geometries and the structure of wave packet revivals. We also show how related half-well problems can be easily solved in each of the three cases., Comment: 46 pages, 6 embedded .eps figures

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by $T_{rev} = 9 \mu a^2/4\hbar \pi$ where $a$ and $\mu$ are the length of one side and the mass of the point particle respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral ($60^{\circ}-60^{\circ}-60^{\circ}$) triangle, such as the half equilateral ($30^{\circ}-60^{\circ}-90^{\circ}$) triangle and other `foldings', which have related energy spectra and revival structures., Comment: 34 pages, 9 embedded .eps figures

We discuss the time development of Gaussian wave packet solutions of the quantum bouncer' (a quantum mechanical particle subject to a uniform downward force, above an impermeable flat surface). We focus on the evaluation and visualization of the expectation values and uncertainties of position and momentum variables during a single quasi-classical period as well as during the long term collapsed phase and several revivals. This approach complements existing analytic and numerical analyses of this system, as well as being useful for comparison with similar results for the harmonic oscillator and infinite well cases., Comment: 20 pages, 7 separate .ps figures

We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum probability distributions agree fairly well, even for relatively small quantum numbers, except for anomalous cases which are due to the unphysical nature of the potential. We are able to derive upper and lower bounds on the differences between the quantum and classical results. We also qualitatively discuss the momentum-space probability densities for this system using intuitive ideas about how much time a classical particle spends in various parts of the well. This system provides an excellent example of a non-trivial, but tractable, quantum mechanical bound state problem where the correlations between the amplitude and curvature of quantum mechanical wavefunctions can be easily compared to classical intuition about particle motion, with quantitative success, but also warning of possible surprises in non-physical limiting cases., Comment: 17 pages, 6 separate .ps figures

We discuss some of the properties of the `collision' of a quantum mechanical wave packet with an infinitely high potential barrier, focusing on novel aspects such as the detailed time-dependence of the momentum-space probability density and the time variation of the uncertainty principle product $\Delta x_t \cdot \Delta p_t$. We make explicit use of Gaussian-like wave packets in the analysis, but also comment on other general forms., Comment: 13 pages, 5 separate .ps figures

The ratio of neutral Higgs field vacuum expectation values, tan beta, is one of the most important parameters to determine in type-II Two-Higgs Doublet Models (2HDM), specifically the Minimal Supersymmetric Standard Model (MSSM). Assuming the energies and integrated luminosity of a future high energy e^+e^- linear collider of sqrt{s}=500, 800, 1000, and 1500 GeV and L=1 ab^{-1} we show that associated t H^+/- production in gamma gamma collisions can be used to make an accurate determination of tan beta for low and high tan beta by precision measurements of the gamma gamma -> H^+/- t + X cross section., Comment: 7 pages, 11 figures, uses REVTEX4

We study the effects of non-commutative QED (NCQED) in fermion pair production, gamma + gamma to f + \bar{f} and Compton scattering, e + gamma to e + gamma. Non-commutative geometries give rise to 3- and 4-point photon vertices and to momentum dependent phase factors in QED vertices which will have observable effects in high energy collisions. We consider e^+ e^- colliders with energies appropriate to the TeV Linear Collider proposals and the multi-TeV CLIC project operating in gamma gamma and e gamma modes. Non-commutative scales roughly equal to the center of mass energy of the e^+e^- collider can be probed, with the exact value depending on the model parameters and experimental factors. The Compton process is sensitive to Lambda_{NC} values roughly twice as large as those accessible to the pair production process., Comment: 9 pages, 5 figures, Talk given at the SUSY 2002 Conference (DESY, Hamburg, Germany, June 2002). To appear in the SUSY 2002 Conference Proceedings

We re-analyze dijet production at hadron colliders (the Tevatron at Fermilab and the Large Hadron Collider, LHC, at CERN), to determine the potential limits on Planck mass in ADD type extra dimensional gravity scenarios. We try a variety of experimental observables in order to maximize the exclusion limits; we find that the $p_{_T}$, $p_{_T}^2$ and $\tau$ distributions give the highest search limits, and these observables provide comparable reaches., Comment: 3 pages, 2 figures, RevTeX 4.0, contributed to APS/DPF/DPB Summer Study on the Future of Particle Physics (Snowmass 2001), Snowmass, Colorado, June 30 to July 21, 2001

We study the effects of non-commutative QED (NCQED) in fermion pair production, $\gamma + \gamma \to f + \bar{f}$ and Compton scattering, $e + \gamma \to e + \gamma$. Non-commutative geometries appear naturally in the context of string/M-theory and gives rise to 3- and 4-point photon vertices and to momentum dependent phase factors in QED vertices which will have observable effects in high energy collisions. We consider $e^+ e^-$ colliders with energies appropriate to the TeV Linear Collider proposals and the multi-TeV CLIC project operating in $\gamma \gamma$ and $e\gamma$ modes. Non-commutative scales roughly equal to the center of mass energy of the $e^+e^-$ collider can be probed, with the exact value depending on the model parameters and experimental factors. However, we found that the Compton process is sensitive to $\Lambda_{NC}$ values roughly twice as large as those accessible to the pair production process., Comment: 3 pages, 2 figures, RevTeX 4.0, contributed to APS/DPF/DPB Summer Study on the Future of Particle Physics (Snowmass 2001), Snowmass, Colorado, June 30 to July 21, 2001

The TESLA Technical Design Report Part III: Physics at an e+e- Linear Collider, Comment: 192 pages, 131 figures. Some figures have reduced quality. Full quality figures can be obtained from http://tesla.desy.de/tdr. Editors - R.-D. Heuer, D.J. Miller, F. Richard, P.M. Zerwas

We study single Higgs boson production in gamma gamma collisions proceeding via the hadronic content of the photon. These processes complement previous studies of pair and single Higgs production at e^+e^- colliders. For SM Higgs masses of current theoretical interest, the resolved photon contributions are non-negligible in precision cross section measurements. The charged Higgs cross sections are not competitive with the gamma gamma -> H^+ H^- process and at best might offer some information about quark-Higgs couplings. Finally, resolved photon production of the heavier Higgs bosons, H^0 and A^0 of the MSSM, can probe regions of the SUSY parameter space that will complement other measurements. This last process shows some promise in SUSY Higgs searches and warrants further study., Comment: Additional processes considered, references substantially updated, 19 pages including 9 .eps figures. Uses revtex

We report on studies of the sensitivity to extra gauge bosons of the reactions e^+ e^- -> nu nubar gamma and e gamma -> nu q + X to extract discovery limits for W' 's. The discovery potential for a W' is, for some models, comparable to that of the LHC. These processes may be also useful for determining W' and Z' couplings to fermions which would complement measurements made at the Large Hadron Collider., Comment: 3 pages, 2 postscript figures, Presented at the DPF2000 Conference, August 9-12, 2000, The Ohio State University, Columbus, Ohio

We examine the sensitivity of the process e gamma to nu q +X to W' bosons which arise in various extensions of the standard model. We consider photon spectra from both the Weizsacker Williams process and from a backscattered laser. The process is found to be sensitive to W' masses up to several TeV, depending on the model, the center of mass energy, the integrated luminosity, and assumptions regarding systematic errors. If extra gauge bosons were discovered first in other experiments, the process could also be used to measure W' couplings. This measurement would provide information that could be used to unravel the underlying theory, complementary to measurements at the Large Hadron Collider., Comment: 17 pages, 9 figures, uses Revtex and epsfig

In this note, we consider dijet production at gamma gamma colliders as a probe of recently proposed, large extra-dimensional gravity models. The exchange of virtual, spin-2 graviton towers (Kaluza-Klein excitations) significantly modifies the cross section, as compared to the Standard Model predictions. We find that, in order to maximize the value of the effective scale that can be probed at a given center-of-mass energy, a very severe p_T cut should be applied; in general, a p_T equal to approximately 46% of the e^+ e^- beam energy gives the highest reach. We find that we can probe the effective mass scale from about 2.7 TeV to 11.1 TeV, depending on the center-of-mass energy and assumptions about the model., Comment: 14 pages, LaTex, 1 figure (postscript) included in submission

Standard radiation zeros arise from the factorization properties of tree-level amplitudes involving a massless photon and can occur when all charged particles in the initial and final state have the same sign. We investigate how several different processes involving new scalar particles beyond the standard model may exhibit radiation zeros and how this structure might be exploited to probe their electromagnetic structure. We focus on (i) unnoticed aspects of angular zeros in the process e- + e- --> Delta-- + gamma for doubly charged Higgs boson (or any bilepton) production and (ii) the process gamma + e- --> q + S/V for scalar (S) or vector (V) leptoquarks (LQs). We also discuss how factorized amplitudes and radiation zeros may appear in the gauge boson fusion production of non-conjugate leptoquark pairs via gamma + W --> S_i + S_j* in high energy ee reactions and how the zeros affect the production cross-sections for various types of scalar leptoquarks., Comment: 18 pages (LaTeX) plus 5 postscript figures

Using recent collider data, especially on the hadronic width the Z0, we exclude axigluons in the currently allowed low-mass window, namely axigluons in the mass range 50 GeV < M_A < 120 GeV. Combined with hadron collider data from di-jet production, axigluons with masses below roughly 1 TeV are now completely excluded., Comment: 8 pages, no figures, LaTeX

Collider searches for first-, second-, and third-generation scalar (S) or vector (V) leptoquarks (LQs) focus on the quark-lepton decay modes S,V -> q l. For SU(2)-doublet and -triplet leptoquarks with a sufficiently large splitting between the components, decays involving real W-boson emission (such as S_2^{(+5/3)} -> S_2^{(+2/3)} W^{+} and others) become possible and can change the patterns of leptoquark decays. For third-generation leptoquarks, where these mass splittings might be large, such modes could dominate certain leptoquark decays as they are (if kinematically allowed) guaranteed to be of order g^2 where g is the electroweak coupling. We calculate the decay rates for all such processes involving SU(2)-doublet and triplet, scalar and vector leptoquarks. Standard limits on mass splittings from precision electroweak measurements imply that only such decays involving SU(2)-doublet scalar LQs are likely kinematically possible., Comment: 13 pages, LaTeX, 2 separate postscript figures

The prospects for producing leptoquarks (LQs) in ultrahigh-energy (UHE) neutrino nucleon collisions are re-examined in the light of recent interpretations of HERA data in terms of leptoquark production. We update predictions for cross-sections for the production of first- and second-generation leptoquarks in UHE nu-N and nubar-N collisions including (i) recent experimental limits on masses and couplings from the LEP and TEVATRON colliders as well as rare processes, (ii) modern parton distributions, and (iii) radiative corrections to single leptoquark production. If the HERA events are due to an SU(2) doublet leptoquark which couples mainly to (e+,q) states, we argue that there are likely other LQ states which couple to neutrinos which are close in mass, due to constraints from precision electroweak measurements., Comment: 12 pages, LaTeX, 3 separate postscript figures. Added 1 reference plus discussion, updated another reference

The contribution of axigluons (the massive color-octet gauge bosons in all chiral color models) to top quark pair production in hadronic collisions is considered. The agreement between the experimental values of the ttbar production cross-section at the TEVATRON and recent QCD predictions is used to discuss limits on the axigluon mass. Specifically,intermediate mass axigluons, those in the mass range 50 GeV < M_A < 120 GeV which has not already been excluded, would increase the tree-level qqbar -> ttbar cross-section by a factor of >= 2, thereby increasing the theoretical predictions for sigma_{ttbar} by Delta sigma_{ttbar} = 3.2-3.7 pb (2.7-3.1 pb) using leading-order (next-to-leading order) parton distributions over this mass range, independent of the axigluon decay width. Such an increase is roughly 1.3-1.6 (0.9-1.2) standard deviations larger than that suggested by the apparent good agreement between combined experimental results and recent theoretical calculations and so is not ruled out, but is definitely disfavored. Future high-statistics top-quark production runs will likely make a more definitive statement. The forward-backward asymmetry in ttbar production induced by axigluons in this mass window is also discussed and found to be quite large and so could provide another constraint., Comment: 9 pages, LaTeX, 2 separate postscript files

The effects of light, long-lived gluinos on $2\to 2$ processes at hadron colliders are examined. Such particles can mediate single squark resonant production via $q\glu\to\sq\to q\glu$ which would significantly modify the dijet data sample. We find that squark masses in the range $130

The possibility of studying superstring inspired \mbox{${\rm E}_6$} phenomenology at high energy hadron colliders is investigated. A very simple low energy rank-5 Supersymmetric (N=1) model is considered, which consists of three scalar-Higgses, $H^0_{i=1,2,3}\,$, two charged-Higgses, $H^\pm\,$, one pseudo-scalar-Higgses, $P^0\,$, and an extra vector boson, the $Z^\prime$. The production of charged heavy leptons pairs, $L^+L^-\,$, by gluon-gluon fusion and Drell-Yan mechanisms is discussed. For gluon-gluon fusion an enhancement in the parton level cross-section is expected due to the heavy (s)fermion loops which couple to the gluons. This mechanism is expected to dominate over Drell-Yan for $L^+L^-$ invariant masses above the $Z^\prime$ mass., Comment: 65 pages, LaTeX file, 26 figures, also available at http://www.physics.carleton.ca/~boyce/papers/prd96.ps

We investigate the possibility of studying E$_6$ phenomenology at high energy hadron colliders. The production of heavy leptons pairs {\it via} a gluon-gluon fusion mechanism is discussed. An enhancement in the parton level cross-section is expected due to the heavy (s)fermion loops which couple to the gluons., Comment: MRST96 Conf. Proc., 10 pages, LaTeX type, macros sprocl.tex included, copy available at http://www.physics.carleton.ca/~boyce/papers/mrst96.ps

Baryons with a single heavy quark are being studied experimentally at present. Baryons with two units of heavy flavor will be abundantly produced not only at future colliders, but also at existing facilities. In this paper we study the production via heavy quark fragmentation of baryons containing two heavy quarks at the Tevatron, the LHC, HERA, and the NLC. The production rate is woefully small at HERA and at the NLC, but significant at $pp$ and $p\bar{p}$ machines. We present distributions in various kinematical variables in addition to the integrated cross sections at hadron colliders., Comment: 13 pages, macro package epsfig needed, 6 .eps figure files in a separate uuencoded, compressed and tarred file; complete paper available at http://www.physics.carleton.ca/~mad/papers/paper.ps

We study the prospects for probing the quark content of the photon using b tagging at high energy electron-photon colliders. We find that heavy quark tagging provides a sensitive and effective probe of the quark content of the photon. Using a 500 GeV $e^+e^-$\ NLC in electron-photon mode, the cross section for $eb_{\gamma}\rightarrow eb$\ can be measured to 10\% with b tagging. This is sufficient to differentiate between the various photon structure functions., Comment: 6 LaTex pages + 3 postscript figures (uuencoded and incorporated with epsfig), postscript version available via anonymous ftp from ftp.physics.carleton.ca in pub/theory/peterson/ocipc9406.ps, Proceedings of MRST-94, OCIP/C 94-6

We study leptoquark production using polarized $e\gamma$ colliders for the center of mass energies $\sqrt s=500$~GeV and 1~TeV. We show that using polarization asymmetries the ten different types of leptoquarks listed by Buchm\"uller, R\"uckl and Wyler can be distinquished from one another for leptoquark masses essentially up to the kinematic limit of the respective colliders. Thus, if a leptoquark were discovered an $e\gamma$ collider could play a crucial role in determining its origins., Comment: 10 pages (plus 10 postscript figures submitted separately), OCIP/C 94-7

Several topics of relevance to low transverse momentum $\psi$ and $\chi_{1,2}(c\overline{c})$ production in polarized proton-proton collisions are discussed. The leading ${\cal O}(\alpha_S^3)$ contributions to the low $p_T$ $\chi_1$ production cross-sections via $gg$, $qg$, and $q\overline{q}$ initial states are calculated as well as the corresponding spin-spin asymmetries. We find that $\chi_1$ production increases relative to direct $\psi$ and $\chi_2$ production, providing up to $25\%$ of the observable $e^+e^-$ pairs arising from $\psi$ decays in $pp$ collisions at $\sqrt{s} = 500\,GeV$. The spin-dependence of $\chi_1$ production, however, is much smaller than for either direct $\psi$ or $\chi_2$ production and so will likely be far less useful than either process in probing the polarized gluon structure function of the proton. A subset of the ${\cal O}(\alpha_S^3)$ radiative corrections to $\chi_2$ production involving initial state quarks are also performed and compared to leading order $gg \rightarrow \chi_2$ predictions., Comment: 21 pages + 5 postscript figures (included), OCIP/C-94-1

The difference in production rate between $W^+$ and $W^-$ at hadron colliders is very sensitive to the the difference between up- and down-quark distributions in the proton. This sensitivity allows for a variety of useful measurements. We consider the difference $d_s(x,Q^2) - u_s(x,Q^2)$ in the sea distributions and the difference $\Delta u(x,Q^2) - \Delta d(x,Q^2)$ in the polarized parton distribution functions. In both cases we construct an asymmetry to reduce systematic uncertainties. Although we discuss measurements at the Tevatron and future hadron colliders, we find that the Brookhaven Relativistic Heavy Ion Collider (RHIC) is the most appropriate hadron collider for these measurements., Comment: 19 pages (20 figures available from the authors), MAD/PH/744

Associated production of $J/\psi$ and a $\gamma$ has recently been proposed as clean probe of the gluon distribution. The same mechanism can be used to probe the polarized gluon content of the proton in polarized proton-proton collisions. We study $J/\psi + \gamma$ production at both polarized fixed target and polarized collider energies., Comment: 16 pages (10 figures available from M.A.D.), MAD/PH/745, SNUTP 93-6, YUMS 93-1

It has been suggested that the suppression of $J/\psi$ production in heavy nuclei is a signature of the formation of quark-gluon plasma. We here show that this phenomenon can be understood in terms of conventional physics, {\it i.e.} {\it i)} perturbative QCD, {\it ii)} the parton recombination implementation of shadowing in the initial state, and {\it iii)} final state interactions with the hadronic debris of the nuclear target. Unlike previous calculations we include both the direct $J/\psi$ production and its production via radiative $\chi$ decays ($\chi_J \to J/\psi + \gamma$). We are able to reproduce the experimental data including their small-$x$ behavior. We emphasize the importance of studying the $x_2$-dependence of the ratio $\sigma(b A)/\sigma(b N)$, where $b$ designates the beam and $x_2$ is the momentum fraction of the parton from the nuclear target., Comment: 16 pages (6 figures not included - available from the authors), MAD/PH/742

We study the effects of virtual leptoquark exchange on charged current and neutral current processes at HERA, on di-lepton production at the Tevatron, and on quark pair production at LEP II. We present the areas of parameter space that can be excluded at these colliders by searching for deviations from Standard Model expectations., Comment: 4 pages (+ 2 figures, available by request), LaTex, Presented at the 1992 Meeting of the DPF, Fermilab, November 1992, ANL-HEP-CP-92-126

We examine the spin-dependence of standard model Higgs boson production at large transverse momentum via the processes $gg \rightarrow gH^0$, $qg \rightarrow qH^0$, and $q\overline{q} \rightarrow gH^0$. The partonic level spin-spin asymmetries ($\hat{a}_{LL}$) for these processes are large at SSC/LHC energies., Comment: 10 pages, 4 figures (not included), LaTeX; PSU/TH/113, MAD/PH/709

We study the effects of virtual leptoquarks on charged current and neutral current processes at the $ep$ collider HERA. We present the areas of parameter space that can be excluded at HERA by searching for deviations from Standard Model expectations. The best results are obtained by examining the ratio of neutral current to charged current cross sections, $R=\sigma_{NC}/\sigma_{CC}$, where, with $200\inpb$ of integrated luminosity for unpolarized $e^-$ and $e^+$ beams, HERA can search for leptoquarks with masses up to $\sim 800\gev$, with leptoquark coupling strengths of order $\alpha_{em}$., Comment: 14 pages, 6 figures (not included)

We study the prospects of testing the $WW\gamma$ vertex in $e^- p\to\nu\gamma X$ and $e^+ p\to\nu\gamma X$ at HERA and LEP/LHC. Destructive interference effects between the Standard Model and the anomalous contributions to the amplitude severely limit the sensitivity of both processes to non-standard $WW\gamma$ couplings. Sensitivity limits for the anomalous $WW\gamma$ couplings $\kappa$ and $\lambda$ at HERA and LEP/LHC are derived, taking into account experimental cuts and uncertainties, and the form factor behaviour of nonstandard couplings. These limits are found to be significantly weaker than those which can be expected from other collider processes within the next few years. At HERA, they are comparable to bounds obtained from $S$-matrix unitarity., Comment: 13 pages, 4 figures (not included)