BARYONS 2013

International Conference On The Structure of Baryons

Glasgow, June 2013

HEAVY QUARKONIA DESCRIPTION

FROM AN

ENERGY DEPENDENT POTENTIAL

P. González Universitat de València and IFIC (SPAIN)

12 New Neutral Charmonium States

since PDG 2000

9 X States (7 + 2 ? Unconventional)

J. Beringer et al. (PDG)PRD 86, 010001 (2012)

Conventional States

S. Godfrey, N. Isgur PRD 32, 189 (1985)

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)

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

What are they ?

Quark-Antiquark effective (screened) potential States ?

Molecular Sates ?

Tetraquarks (compact states) ?

Quark-Antiquark + Molecular States ?

Hybrid (Quark-Antiquark + Gluon) States ?

Can we explicitly implement threshold effects

within a quark-antiquark model framework?

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.

Quenched vs Threshold-Unquenched Quark-Antiquark GSE

G. S. Bali, Phis. Rep. 343,1 (2001)

G. S. Bali et al., PRD 71, 11453 (2005)

Extended Quark Model (EQM) : Energy Dependent Potential

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).

Threshold Effects

Additional states + Attraction

results from the attraction produced by on the Cornell state

Additional states + Attraction

EQM : Non Overlapping Thresholds

The threshold has no effect below and above

Effective Thresholds (ET)

When two or more thresholds are almost degenerate there are overlapping effects which can be implemented through ET.

and are Interthreshold States

EQM Spectrum

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)

EQM Spectrum

BB1

BB (0++)

BB* (1++)B*B* (2++)

S. Godfrey, N. Isgur PRD 32, 189 (1985)

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

Generator Potential :

results from the attraction produced by on the Generator state

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

Conventional Decay Mechanisms

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.

Examples

Mesons:

S. Capstick, N. Isgur PRD 34, 2809 (1986)

Baryons:

Meson-baryon Thresholds:

Generator - Threshold Approximation

Consider a system of 1 confined channel (3q) in interaction with 1 free channel (meson-baryon).

Hamiltonian Matrix:

with

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.

P. Gonzalez, J. Vijande, A. Valcarce , PRC 77, 065213 (2008)

THE END

Unquenched Lattice-QCD ab initio calculation

A. Bazavov et al. (MILC)Rev Mod. Phys. 82, 1349 (2010)

We expect the short range part of the wave function to be only changed by normalization: