109 research outputs found
The Relativistic N-body Problem in a Separable Two-Body Basis
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the
relativistic N-body problem in a separable two-body basis in which the
particles interact pair-wise through scalar and vector interactions. The
resultant N-body Hamiltonian is relativistically covariant. It can be easily
separated in terms of the center-of-mass and the relative motion of any
two-body subsystem. It can also be separated into an unperturbed Hamiltonian
with a residual interaction. In a system of two-body composite particles, the
solutions of the unperturbed Hamiltonian are relativistic two-body internal
states, each of which can be obtained by solving a relativistic
Schr\"odinger-like equation. The resultant two-body wave functions can be used
as basis states to evaluate reaction matrix elements in the general N-body
problem. We prove a relativistic version of the post-prior equivalence which
guarantees a unique evaluation of the reaction matrix element, independent of
the ways of separating the Hamiltonian into unperturbed and residual
interactions. Since an arbitrary reaction matrix element involves composite
particles in motion, we show explicitly how such matrix elements can be
evaluated in terms of the wave functions of the composite particles and the
relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe
Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
A large number of treatments of the meson spectrum have been tried that
consider mesons as quark - anti quark bound states. Recently, we used
relativistic quantum "constraint" mechanics to introduce a fully covariant
treatment defined by two coupled Dirac equations. For field-theoretic
interactions, this procedure functions as a "quantum mechanical transform of
Bethe-Salpeter equation". Here, we test its spectral fits against those
provided by an assortment of models: Wisconsin model, Iowa State model,
Brayshaw model, and the popular semi-relativistic treatment of Godfrey and
Isgur. We find that the fit provided by the two-body Dirac model for the entire
meson spectrum competes with the best fits to partial spectra provided by the
others and does so with the smallest number of interaction functions without
additional cutoff parameters necessary to make other approaches numerically
tractable. We discuss the distinguishing features of our model that may account
for the relative overall success of its fits. Note especially that in our
approach for QCD, the resulting pion mass and associated Goldstone behavior
depend sensitively on the preservation of relativistic couplings that are
crucial for its success when solved nonperturbatively for the analogous
two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content
Relativistic Modification of the Gamow Factor
In processes involving Coulomb-type initial- and final-state interactions,
the Gamow factor has been traditionally used to take into account these
additional interactions. The Gamow factor needs to be modified when the
magnitude of the effective coupling constant increases or when the velocity
increases. For the production of a pair of particles under their mutual
Coulomb-type interaction, we obtain the modification of the Gamow factor in
terms of the overlap of the Feynman amplitude with the relativistic wave
function of the two particles. As a first example, we study the modification of
the Gamow factor for the production of two bosons. The modification is
substantial when the coupling constant is large.Comment: 13 pages, in LaTe
Relativistic Generalization of the Gamow Factor for Fermion Pair Production or Annihilation
In the production or annihilation of a pair of fermions, the initial-state or
final-state interactions often lead to significant effects on the reaction
cross sections. For Coulomb-type interactions, the Gamow factor has been
traditionally used to take into account these effects. However the Gamow factor
needs to be modified when the magnitude of the coupling constant or the
relative velocity of two particles increases. We obtain the relativistic
generalization of the Gamow factor in terms of the overlap of the Feynman
amplitude with the relativistic wave function of two fermions with an
attractive Coulomb-type interaction. An explicit form of the corrective factor
is presented for the spin-singlet S-wave state. While the corrective factor
approaches the Gamow factor in the non-relativistic limit, we found that the
Gamow factor significantly over-estimates the effects when the coupling
constant or the velocity is large.Comment: 16 pages, 4 figures in LaTe
Correction Factors for Reactions involving Quark-Antiquark Annihilation or Production
In reactions with production or annihilation, initial-
and final-state interactions give rise to large corrections to the lowest-order
cross sections. We evaluate the correction factor first for low relative
kinetic energies by studying the distortion of the relative wave function. We
then follow the procedure of Schwinger to interpolate this result with the
well-known perturbative QCD vertex correction factors at high energies, to
obtain an explicit semi-empirical correction factor applicable to the whole
range of energies. The correction factor predicts an enhancement for
in color-singlet states and a suppression for color-octet states, the effect
increasing as the relative velocity decreases. Consequences on dilepton
production in the quark-gluon plasma, the Drell-Yan process, and heavy quark
production processes are discussed.Comment: 25 pages (REVTeX), includes 2 uuencoded compressed postscript 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
Vlasov Description Of Dense Quark Matter
We discuss properties of quark matter at finite baryon densities and zero
temperature in a Vlasov approach. We use a screened interquark Richardson's
potential consistent with the indications of Lattice QCD calculations.
We analyze the choices of the quark masses and the parameters entering the
potential which reproduce the binding energy (B.E.) of infinite nuclear matter.
There is a transition from nuclear to quark matter at densities 5 times above
normal nuclear matter density. The transition could be revealed from the
determination of the position of the shifted meson masses in dense baryonic
matter. A scaling form of the meson masses in dense matter is given.Comment: 15 pages 4 figure
The Soft Gluon Emission Process in the Color-Octet Model for Heavy Quarkonium Production
The Color-Octet Model has been used successfully to analyze many problems in
heavy quarkonium production. We examine some of the conceptual and practical
problems of the soft gluon emission process in the Color-Octet Model. We use a
potential model to describe the initial and final states in the soft gluon
emission process, as the emission occurs at a late stage after the production
of the heavy quark pair. It is found in this model that the soft gluon M1
transition, 1S0(8)->3S1(1), dominates over the E1 transition, 3PJ(8)->3S1(1),
for J/psi and psi' production. Such a dominance may help resolve the questions
of isotropic polarization and color-octet matrix element universality in the
Color-Octet Model.Comment: 26 pages, in LaTe
Centers of Mass and Rotational Kinematics for the Relativistic N-Body Problem in the Rest-Frame Instant Form
In the Wigner-covariant rest-frame instant form of dynamics it is possible to
develop a relativistic kinematics for the N-body problem. The Wigner
hyperplanes define the intrinsic rest frame and realize the separation of the
center-of-mass. Three notions of {\it external} relativistic center of mass can
be defined only in terms of the {\it external} Poincar\'e group realization.
Inside the Wigner hyperplane, an {\it internal} unfaithful realization of the
Poincar\'e group is defined. The three concepts of {\it internal} center of
mass weakly {\it coincide} and are eliminated by the rest-frame conditions. An
adapted canonical basis of relative variables is found. The invariant mass is
the Hamiltonian for the relative motions. In this framework we can introduce
the same {\it dynamical body frames}, {\it orientation-shape} variables, {\it
spin frame} and {\it canonical spin bases} for the rotational kinematics
developed for the non-relativistic N-body problem.Comment: 78 pages, revtex fil
Energy and decay width of the pi-K atom
The energy and decay width of the pi-K atom are evaluated in the framework of
the quasipotential-constraint theory approach. The main electromagnetic and
isospin symmetry breaking corrections to the lowest-order formulas for the
energy shift from the Coulomb binding energy and for the decay width are
calculated. They are estimated to be of the order of a few per cent. We display
formulas to extract the strong interaction S-wave pi-K scattering lengths from
future experimental data concerning the pi-K atom.Comment: 37 pages, 5 figures, uses Axodra
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