BARYONS 2013 International Conference On The Structure of Baryons Glasgow, June 2013
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BARYONS 2013
International Conference On The Structure of Baryons
Glasgow, June 2013
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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, 010001 (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
2 8 0 0
3 0 0 0
3 2 0 0
3 4 0 0
3 6 0 0
3 8 0 0
4 0 0 0
4 2 0 0
4 4 0 0
4 6 0 0
E (
MeV
)
0 + 1 -- J + + 1 +
X(3940)
D*D*| S(2++)
X(4140-60)
X(4350)
DD1|S, DD1|S
X(4260)
X(4360)D*D*
0|S
X(4660)
X(3915)
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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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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
i) Quenched versus Threshold-Unquenched Quark-Antiquark Ground
State Energy from Latttice.
ii) Quark Model Static Approach: Cornell Potential versus Energy Dependent Potential. Extended Quark Model.
iii) Heavy Quarkonia Description.
iv) 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, 11453 (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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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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2 8 0 0
3 0 0 0
3 2 0 0
3 4 0 0
3 6 0 0
3 8 0 0
4 0 0 0
4 2 0 0
4 4 0 0
4 6 0 0
E (
MeV
)
0 + 1 -- J + + 1 +
X(3940)
D*D*| S(2++)
X(4350)
DD1|S, DD1|S
X(4260)
X(4360)D*D*
0|S
X(4660)
X(4140-60)
X(3915)
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EQM Spectrum
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BB1
BB (0++)
BB* (1++)B*B* (2++)
S. Godfrey, N. Isgur PRD 32, 189 (1985)
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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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Generator Potential :
results from the attraction produced by on the Generator state
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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
i) There is a puzzle concerning experimentally unexpected charmonium states.
ii) There is a plausible universal explanation for this puzzle based on an Energy Dependent Potential (EDP) resulting from threshold effects.
iii) 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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S. Capstick, N. Isgur PRD 34, 2809 (1986)
Baryons:
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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: