This document discusses models of exotic hadron states beyond conventional quark-antiquark mesons and three-quark baryons. It summarizes the tetraquark model where a tetraquark is composed of a diquark and antidiquark binding together. Other models discussed include uncorrelated quark models and meson-meson molecules. The document concludes that tetraquarks remain an active area of research, various models cannot be distinguished by spectroscopy alone, and diquarks are an important concept in non-perturbative quantum chromodynamics.

1. ON SOME MODELS OF THE EXOTIC
HADRON STATES
Siniša R. Ignjatović1
and Vesna Borka Jovanović2
1
Department of Physics, University of Banja Luka
2
Institute of Nuclear Sciences Vinča, Belgrade
1. Introduction
2. Tetraquark as a diquark-antidiquark bound state
3. Other models

2. 1. Introduction
•
first detailed analysis – Jaffe (1977)
•
first experimental evidence – 2003
•
pentaquark evidence refuted
•
some mesons difficult to interpret as conventional mesons
•
Conventional hadrons:
• mesons: quark+antiquark
• baryons: 3 quarks (antiquarks)
•
Unconventional hadrons allowed by the quark model
(and QCD)

3. Exotic mesons:
•
Glueballs and hybrids (“ordinary” states)
•
Multiquarks and meson-meson molecules (“extraordinary” or
flavor-exotic states)
Models of extraordinary mesons:
•
tetraquark as bound state of diquark and antidiquark
•
tetraquark constituted of uncorrelated quarks
•
meson-meson molecule
•
states made of mixed conventional and unconventional states
qq
q
q
q
q q
q
q
q
q
q
meson molecule diquark-antidiquark uncorrelated quarks
Cartoon picture of the four-quark states

4. 2. Tetraquark as a diquark-antidiquark bound state
• Lichtenberg model: baryon = diquark + quark (1967)
• tetraquark = diquark + antidiquark (1980’s)
• further applications of diquarks: dibaryons (hexaquarks),
dense quark matter etc.
Diquark – color multiplet – cannot exist outside hadrons
3

5. color SU(3)c
/light flavor SU(3)f
: 3⊗3=3̅⊕6, 3̅⊗3̅=3⊕6̅
SU(4)f
: 4⊗4=6̅⊕10, 4̅⊗4̅=6⊕1̅0̄̅̃̄̅̆̅
antitriplet flavor (spin singlet, i. e. scalar) states lie
~200 MeV below sextet (vector) ones
Making light-flavor tetraquarks:
(3̅⊕6)⊗(3⊕6̄̅)=3̅⊗3⊕3̅⊗6̅⊕6⊗3⊕6⊗6̅
3̅⊗3=8⊕1 lowest-lying (perhaps the only observable?)

6. Methods
All methods used in the non-perturbative QCD:
• Chiral perturbation theory
• Lattice QCD
• Lattice QCD-inspired models
• QCD sum rules
• Constituent quark model with hyperfine interactions
• Heavy quark effective theory

7. 3. Other models of four-quark states
1. Uncorrelated quarks
– Constituent quark model with hyperfine interactions:
•spin-color or spin-flavor
– Different hamiltonians lead to essentially same masses
2. Meson-meson molecules
– predates quark model itself
– within QCD from 1976
– resonances near threshold
– forces dominated by quark exchange

8. Conclusions
1. unlike pentaquarks, tetraquarks are very active topics
2. revival of hadron spectroscopy due to the exotic states
3. spectroscopy alone is insufficient to discern between the
various models
4. diquarks are an important concept in non-perturbative QCD