254 research outputs found
Quarkonium Wave Functions at the Origin
We tabulate values of the radial Schr\"{o}dinger wave function or its first
nonvanishing derivative at zero quark-antiquark separation, for ,
, and levels that lie below, or just above, flavor
threshold. These quantities are essential inputs for evaluating production
cross sections for quarkonium states.Comment: 9 pages, RevTeX, no figure
Spacings of Quarkonium Levels with the Same Principal Quantum Number
The spacings between bound-state levels of the Schr\"odinger equation with
the same principal quantum number but orbital angular momenta
differing by unity are found to be nearly equal for a wide range of power
potentials , with . Semiclassical approximations are in accord with this behavior. The
result is applied to estimates of masses for quarkonium levels which have not
yet been observed, including the 2P states and the 1D
states.Comment: 20 pages, latex, 3 uuencoded figures submitted separately (process
using psfig.sty
Prospects for the Bc Studies at LHCb
We discuss the motivations and perspectives for the studies of the mesons of
the (bc) family at LHCb. The description of production and decays at LHC
energies is given in details. The event yields, detection efficiencies, and
background conditions for several Bc decay modes at LHCb are estimated.Comment: 20 pages, 5 eps-figure
Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics
Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics
have been successfully applied to obtain a covariant nonperturbative
description of QED and QCD bound states. Coulomb-type potentials in these
applications lead naively in other approaches to singular relativistic
corrections at short distances that require the introduction of either
perturbative treatments or smoothing parameters. We examine the corresponding
singular structures in the effective potentials of the relativistic
Schroedinger equation obtained from the Pauli reduction of the TBDE. We find
that the relativistic Schroedinger equation lead in fact to well-behaved wave
function solutions when the full potential and couplings of the system are
taken into account. The most unusual case is the coupled triplet system with
S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the
effective S-state potential would become attractively singular. We show how
including the tensor coupling is essential in order that the wave functions be
well-behaved at short distances. For example, the S-state wave function becomes
simply proportional to the D-state wave function and dips sharply to zero at
the origin, unlike the usual S-state wave functions. Furthermore, this behavior
is similar in both QED and QCD, independent of the asymptotic freedom behavior
of the assumed QCD vector potential. Light- and heavy-quark meson states can be
described well by using a simplified linear-plus-Coulomb-type QCD potential
apportioned appropriately between world scalar and vector potentials. We use
this potential to exhibit explicitly the origin of the large pi-rho splitting
and effective chiral symmetry breaking. The TBDE formalism developed here may
be used to study quarkonia in quark-gluon plasma environments.Comment: 23 pages, 4 figure
Mesons with Beauty and Charm: Spectroscopy
Applying knowledge of the interaction between heavy quarks derived from the
study of and bound states, we calculate the
spectrum of mesons. We compute transition rates for the
electromagnetic and hadronic cascades that lead from excited states to the
ground state, and briefly consider the prospects for
experimental observation of the spectrum.Comment: 32 pages + 2 uuencoded PostScript figures Fermilab-Pub-94/032-
Nonet Symmetry and Two-Body Decays of Charmed Mesons
The decay of charmed mesons into pseudoscalar (P) and vector (V) mesons is
studied in the context of nonet symmetry. We have found that it is badly broken
in the PP channels and in the P sector of the PV channels as expected from the
non-ideal mixing of the \eta and the \eta'. In the VV channels, it is also
found that nonet symmetry does not describe the data well. We have found that
this discrepancy cannot be attributed entirely to SU(3) breaking at the usual
level of 20--30%. At least one, or both, of nonet and SU(3) symmetry must be
very badly broken. The possibility of resolving the problem in the future is
also discussed.Comment: 9 pages, UTAPHY-HEP-
Relative entropy, Haar measures and relativistic canonical velocity distributions
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS)
entropy is reconsidered by combining elements from group and measure theory.
Our analysis starts by noting that the BGS entropy is a special case of
relative entropy. The latter characterizes probability distributions with
respect to a pre-specified reference measure. To identify the canonical BGS
entropy with a relative entropy is appealing for two reasons: (i) the maximum
entropy principle assumes a coordinate invariant form; (ii) thermodynamic
equilibrium distributions, which are obtained as solutions of the maximum
entropy problem, may be characterized in terms of the transformation properties
of the underlying reference measure (e.g., invariance under group
transformations). As examples, we analyze two frequently considered candidates
for the one-particle equilibrium velocity distribution of an ideal gas of
relativistic particles. It becomes evident that the standard J\"uttner
distribution is related to the (additive) translation group on momentum space.
Alternatively, imposing Lorentz invariance of the reference measure leads to a
so-called modified J\"uttner function, which differs from the standard
J\"uttner distribution by a prefactor, proportional to the inverse particle
energy.Comment: 15 pages: extended version, references adde
Space-Time Evolution of the Oscillator, Rapidly moving in a random media
We study the quantum-mechanical evolution of the nonrelativistic oscillator,
rapidly moving in the media with the random vector fields. We calculate the
evolution of the level probability distribution as a function of time, and
obtain rapid level diffusion over the energy levels. Our results imply a new
mechanism of charmonium dissociation in QCD media.Comment: 32 pages, 13 figure
Neutrino Interactions at Ultrahigh Energies
We report new calculations of the cross sections for deeply inelastic
neutrino-nucleon scattering at neutrino energies between 10^{9}\ev and
10^{21}\ev. We compare with results in the literature and assess the
reliability of our predictions. For completeness, we briefly review the cross
sections for neutrino interactions with atomic electrons, emphasizing the role
of the -boson resonance in interactions for neutrino
energies in the neighborhood of 6.3\pev. Adopting model predictions for
extraterrestrial neutrino fluxes from active galactic nuclei, gamma-ray
bursters, and the collapse of topological defects, we estimate event rates in
large-volume water \v{C}erenkov detectors and large-area ground arrays.Comment: 32 pages, 11 figures, uses RevTeX and boxedep
NEUTRINOS FROM PRIMORDIAL BLACK HOLES
The emission of particles from black holes created in the early Universe has
detectable astrophysical consequences. The most stringent bound on their
abundance has been obtained from the absence of a detectable diffuse flux of
100 MeV photons. Further scrutiny of these bounds is of interest as they, for
instance, rule out primordial black holes as a dark matter candidate. We here
point out that these bounds can, in principle, be improved by studying the
diffuse cosmic neutrino flux. Measurements of near-vertical atmospheric
neutrino fluxes in a region of low geomagnetic latitude can provide a
competitive bound. The most favorable energy to detect a possible diffuse flux
of primordial black hole origin is found to be a few MeV. We also show that
measurements of the diffuse flux is the most promising to improve
the existing bounds deduced from gamma-ray measurements. Neutrinos from
individual black hole explosions can be detected in the GeV-TeV energy region.
We find that the kilometer-scale detectors, recently proposed, are able to
establish competitive bounds.Comment: 19 pages plus 9 uuencoded and compressed postscript figure
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