M. A. Doncheski

Fragmentation production of J ψ and ψ′ at the Tevatron

Abstract We present a calculation of the charm and gluon fragmentation contributions to inclusive J ψ and ψ ′ production at large transverse momentum at the Tevatron. For ψ production, we include both fragmentation directly into ψ and fragmentation into χ c followed by the radiative decay χ c → ψ + λ . We find that fragmentation overwhelms the leading-order mechanisms for prompt ψ production at large p T , and that the dominant contributions come from fragmentation into χ c . Our results are consistent with recent data on ψ production from the CDF and D0 experiments. In the case of prompt ψ ′ production, the dominant mechanism at large p T is charm fragmentation into ψ ′. We find serious disagreement between our theoretical predictions and recent ψ ′ data from the Tevatron.

Wigner quasi-probability distribution for the infinite square well: Energy eigenstates and time-dependent wave packets

We calculate and visualize the Wigner quasi-probability distribution for the position and momentum, PW(n)(x,p), for the energy eigenstates of the infinite square well. We evaluate the time-dependent Wigner distribution, PW(x,p;t), for Gaussian wave packet solutions of this system, and illustrate the short-term semi-classical time dependence and the longer-term revival and fractional revival behavior. Our results indicate how the Wigner distribution can be used to examine the highly correlated dynamical position-momentum structure of quantum states. In particular, 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.

Low transverse momentum ψ and production in polarized proton-proton collisions

Abstract We present calculations of the spin-spin asymmetry in the low transverse momentum production of ψs and s in polarized proton-proton collisions. A perturbative QCD approach using quarkonium wavefunctions derived from non-relativistic potential models is employed. The contributions from gg→ χ 0,2 and gg→g 3 S 1 are known to dominate in this approach and we exhibit the sensitivity of the polarization asymmetry to various choices of polarized gluon distribution.

Leptoquark production in ultrahigh-energy neutrino interactions reexamined

The prospects for producing leptoquarks (LQs) in ultrahigh-energy (UHE) neutrino nucleon collisions are reexamined in the light of recent interpretations of DESY 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 {bar {nu}}-N collisions including (i) recent experimental limits on masses and couplings from the CERN LEP and Fermilab 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 that couples mainly to e{sup +}q states, we argue that there are likely other LQ states that couple to neutrinos that are close in mass, due to constraints from precision electroweak measurements. {copyright} {ital 1997} {ital The American Physical Society}

Quantum Mechanical Analysis of the Equilateral Triangle Billiard: Periodic Orbit Theory and Wave Packet Revivals

Abstract 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 =9μ a 2 /4 ħ π where a and μ 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°–60°–60°) triangle, such as the half equilateral (30°–60°–90°) triangle and other “foldings,” which have related energy spectra and revival structures.

Comparing classical and quantum probability distributions for an asymmetric infinite well

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 arise 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 the amount of 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.

Fragmentation production of doubly heavy baryons.

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 Fermilab Tevatron, the CERN LHC, DESY HERA, and the NLC. The production rate is woefully small at HERA and at the NLC, but significant at {ital pp} and {ital p{bar p}} machines. We present distributions in various kinematical variables in addition to the integrated cross sections at hadron colliders. {copyright} {ital 1996 The American Physical Society.}

More on the asymmetric infinite square well: energy eigenstates with zero curvature

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 wavefunction to have zero curvature over an extended region of space and still be a valid wavefunction. 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.

Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum

Abstract 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 ( τ ) is also dramatic, having the special limiting case of τ →∞ 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 fourth 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.

Resolved photon contributions to leptoquark production in e+ e- and e gamma collisions

We calculate the resolved photon contribution to leptoquark production at [ital e][gamma] colliders for the center-of-mass energies [radical][ital s] =500 GeV and 1 TeV. We also calculate the resolved photon contribution to leptoquark production at [ital e][sup +][ital e][sup [minus]] colliders for the center of mass energies [radical][ital s] =1 and 2 TeV. In both cases we find that these contributions are considerably larger than the standard contributions considered in the literature. In addition we find that polarized electron beams would be able to determine the chirality of the leptoquarks and therefore be crucial for the determination of the type of leptoquark discovered.