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Title: Potential model calculations and predictions for heavy quarkonium

Abstract

We investigate the spectroscopy and decays of the charmonium and upsilon systems in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which allows us to compare the results for both perturbative and nonperturbative treatments of the potential. As well as comparing the mass spectra, radiative widths and leptonic widths with the available data, we include a discussion of the errors on the parameters contained in the potential, the effect of mixing on the leptonic widths, the Lorentz nature of the confining potential, and the possible cc interpretation of recently discovered charmoniumlike states.

Authors:
 [1];  [2]
  1. Department of Physics, State University of New York at Brockport, Brockport, New York 14420 (United States)
  2. Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824 (United States)
Publication Date:
OSTI Identifier:
21020291
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.75.074031; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHARMONIUM; COMPARATIVE EVALUATIONS; CORRECTIONS; KINETIC ENERGY; LEPTONS; MASS SPECTRA; MESON SPECTROSCOPY; PARTICLE DECAY; PARTICLE WIDTHS; POTENTIALS; RELATIVISTIC RANGE; VARIATIONAL METHODS; WAVE FUNCTIONS

Citation Formats

Radford, Stanley F., and Repko, Wayne W. Potential model calculations and predictions for heavy quarkonium. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.074031.
Radford, Stanley F., & Repko, Wayne W. Potential model calculations and predictions for heavy quarkonium. United States. doi:10.1103/PHYSREVD.75.074031.
Radford, Stanley F., and Repko, Wayne W. Sun . "Potential model calculations and predictions for heavy quarkonium". United States. doi:10.1103/PHYSREVD.75.074031.
@article{osti_21020291,
title = {Potential model calculations and predictions for heavy quarkonium},
author = {Radford, Stanley F. and Repko, Wayne W.},
abstractNote = {We investigate the spectroscopy and decays of the charmonium and upsilon systems in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which allows us to compare the results for both perturbative and nonperturbative treatments of the potential. As well as comparing the mass spectra, radiative widths and leptonic widths with the available data, we include a discussion of the errors on the parameters contained in the potential, the effect of mixing on the leptonic widths, the Lorentz nature of the confining potential, and the possible cc interpretation of recently discovered charmoniumlike states.},
doi = {10.1103/PHYSREVD.75.074031},
journal = {Physical Review. D, Particles Fields},
number = 7,
volume = 75,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}
  • A theoretical explanation of the observed splitting among the [ital P] states of charmonium is given with the use of a nonsingular potential model for heavy quarkonia. We also show that the recently observed mass difference between the center of gravity of the [sup 3][ital P][sub [ital J]] states and the [sup 1][ital P][sub 1] state of [ital c] [bar c] does not provide a direct test of the color hyperfine interaction in heavy quarkonia. Our theoretical value for the mass of the [sup 1][ital P][sub 1] state is in agreement with the experimental result, and its [ital E]1 transitionmore » width is 341.8 keV. The mass of the [eta][sub [ital c]][sup [prime]] state is predicted to be 3622.3 MeV.« less
  • We investigate the spectroscopy and decays of the charm-strange quarkonium system in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections, and the complete perturbative one-loop quantum chromodynamic short distance potential. The unperturbed wave functions of the various states are obtained using a variational technique. These are then used in a perturbative treatment of the potential to fit the mass spectrum of the cs system and calculate the radiative decay widths. Our results compare well with the available data for the spectrum of D{sub s} states. We includemore » a discussion of the effect of mixing and investigation of the Lorentz nature of the confining potential.« less
  • An interquark potential proposed recently to describe cc-bar and bb-bar systems is used to calculate some properties of the tt-bar system, for m/sub t/ = 40 and 45 GeV/c/sup 2/. It is shown how these properties (notably the 2S-1S spacing and the ratio GAMMA(2S..-->..e/sup +/e/sup -/)/GAMMA(1S..-->..e/sup +/e/sup -/ )) can be used to test the correctness of the underlying nonrelativsitic QQ-bar potential, allowing one to return to relativistic corrections in cc-bar and bb-bar bound states with improved confidence.
  • The inclusive light hadronic decays of {sup 1}D{sub 2} heavy quarkonia are studied within the framework of the nonrelativistic QCD at the leading order in v and up to the order of {alpha}{sub s}{sup 3}. With one-loop QCD corrections, the infrared divergences and Coulomb singularities in the decay amplitudes are proved to be absorbed by the renormalization of the matrix elements of corresponding nonrelativistic QCD operators, and the infrared finite short-distance coefficients are obtained through the matching calculations. By taking the factorization scale to be 2m{sub Q}, the light hadronic decay widths are estimated to be about 274, 4.7, andmore » 8.8 KeV for {eta}{sub c2}, {eta}{sub b2}, and {eta}{sub b2}', respectively. Based on the above estimates, and using the E1 transition width and dipion transition width for {eta}{sub c2} estimated elsewhere, we get the total width of {eta}{sub c2} to be about 660-810 KeV, and the branching ratio of the E1 transition {eta}{sub c2}{yields}{gamma}h{sub c} to be about (44-54)%, which will be useful in searching for this missing charmonium state through, e.g., {eta}{sub c2}{yields}{gamma}h{sub c} followed by h{sub c}{yields}{gamma}{eta}{sub c}.« less