86 research outputs found
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 Corrections in a Three-Boson System of Equal Masses
Three-body systems of scalar bosons are described in the framework of
relativistic constraint dynamics. With help of a change of variables followed
by a change of wave function, two redundant degrees of freedom get eliminated
and the mass-shell constraints can be reduced to a three-dimensional eigenvalue
problem.
In general, this problem is complicated, but for three equal masses a drastic
simplification arises at the first post-Galilean order: the reduced wave
equation becomes tractable, and we can compute a first-order correction beyond
the nonrelativistic limit. The harmonic interaction is displayed as a toy
model.Comment: 16 pages, no figure. Several points clarified, one typo corrected.
References added. To appear in Physical Review
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
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
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