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International Conference On The Structure of Baryons
Glasgow, June 2013
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P. González Universitat de València and IFIC (SPAIN)
HEAVY QUARKONIA DESCRIPTION FROM AN ENERGY DEPENDENT POTENTIAL P. González Universitat de València and IFIC (SPAIN)
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12 New Neutral Charmonium States since PDG 2000
9 X States (7 + 2 ? Unconventional) J. Beringer et al. (PDG)PRD 86, (2012)
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Conventional States S. Godfrey, N. Isgur PRD 32, 189 (1985)
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X states : Close-below or Above their First S-wave M-M Threshold
DD*|S(1++) X(3872) D*D*| S(2++) X( ) X(4350) DD1|S, DD1|S X(4260) X(4360) D*D*0|S X(4660) X(3915) X states : Close-below or Above their First S-wave M-M Threshold
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Unconventional States
Decay properties very different from conventionally expected Conventional description: with parallel properties to However decay properties completely different Conventional description: or However aan order of magnitude higher than expected
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Quark-Antiquark effective (screened) potential States ?
What are they ? Quark-Antiquark effective (screened) potential States ? Molecular Sates ? Tetraquarks (compact states) ? Quark-Antiquark + Molecular States ? Hybrid (Quark-Antiquark + Gluon) States ?
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Can we explicitly implement threshold effects
within a quark-antiquark model framework?
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INDEX Quenched versus Threshold-Unquenched Quark-Antiquark Ground State Energy from Latttice. Quark Model Static Approach: Cornell Potential versus Energy Dependent Potential. Extended Quark Model. Heavy Quarkonia Description. Summary.
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Quenched vs Threshold-Unquenched Quark-Antiquark GSE
G. S. Bali, Phis. Rep. 343,1 (2001) G. S. Bali et al., PRD 71, (2005)
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Extended Quark Model (EQM) : Energy Dependent Potential
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Heavy Quarkonia Description
The lowest lying spectrum is described by the Cornell potential Calculated masses differing at most 30 MeV (60 MeV) for bottomonium (charmonium).
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Additional states + Attraction
Threshold Effects Additional states + Attraction results from the attraction produced by on the Cornell state
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Additional states + Attraction
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EQM : Non Overlapping Thresholds
The threshold has no effect below and above
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Effective Thresholds (ET)
When two or more thresholds are almost degenerate there are overlapping effects which can be implemented through ET.
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and are Interthreshold States
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EQM Spectrum
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X(4660) X(4350) X(4360) X(4260) X(4140-60) X(3940) X(3915) X(3872)
DD*|S(1++) X(3872) D*D*| S(2++) X(4350) DD1|S, DD1|S X(4260) X(4360) D*D*0|S X(4660) X( ) X(3915)
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EQM Spectrum
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S. Godfrey, N. Isgur PRD 32, 189 (1985) BB1 B*B* (2++) BB* (1++)
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EQM Eigenstates Eigenstates from different energy regions are not orthogonal Generator States DD*|S(1++) results from the attraction produced by on the Cornell state
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results from the attraction produced by on the Generator state
Generator Potential :
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The Generator-Threshold Approximation
Strong Decays The Generator-Threshold Approximation Assumption: The decay takes place, through light quark-antiquark creation, via the virtual generator-threshold state Cornell Threshold In general Generator Threshold
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Conventional Decay Mechanisms
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Summary There is a puzzle concerning experimentally unexpected charmonium states. There is a plausible universal explanation for this puzzle based on an Energy Dependent Potential (EDP) resulting from threshold effects. The Extended Quark Model (EQM) corresponding to this EDP may allow for a general description of hadrons (mesons and baryons) once spin dependent and other relativistic corrections are implemented.
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Examples Mesons:
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Baryons: S. Capstick, N. Isgur PRD 34, 2809 (1986)
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Meson-baryon Thresholds:
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Generator - Threshold Approximation
Consider a system of 1 confined channel (3q) in interaction with 1 free channel (meson-baryon). Hamiltonian Matrix: with
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The couple channel solutions correspond to the eigenvalues of :
With a = 75 MeV all the anomalous masses can be reproduced within their experimental error bars.
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P. Gonzalez, J. Vijande, A. Valcarce , PRC 77, 065213 (2008)
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THE END
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Unquenched Lattice-QCD ab initio calculation
A. Bazavov et al. (MILC) Rev Mod. Phys. 82, 1349 (2010)
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We expect the short range part of the wave function to be only changed by normalization:
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