Chiral Symmetry, Hadron Spectrum
and Instantons
P.Faccioli, M.Cristoforetti, M.C.Traini
Trento University & I.N.F.N.
J. W. Negele
M.I.T.
Hadron 2007
Frascati, October 12th , 2007
What are the dominant correlations in Hadrons ?
The SU(6) Quark Model answer:
• Binding of hadrons is entirely due to confinement.
Without confinement, hadrons would not exist
• Residual fine structure from e.g. perturbative gluon
exch. Chiral symmetry plays a sub-leading role
However, we know at leas one exception: the PION would exist even in the
absence of confinement (see e.g. NJL model)
QUESTION: Are there other hadrons for which chiral symmetry
plays the dominant role?
In the last decade, LQCD has provided important new
information about non-perturbative quark-gluon dynamics.
It is important to revisit and address this question
in view of what we know in 2007 from LQCD.
The role of chiral dynamics in hadron spectrum
0 q q 0   lim  ( )
 0
Light 0- meson 2-point fnct.
D       i  
  ( x )  ( x )
S( x , y )   
  im
Small eigen-values of the Dirac Operator
 Chiral Dynamics
H (x)  0 JH (x)JH (0) 0
Conclusion: Physics of light hadrons is strongly affected by chiral dynamics
Physics of heavy hadrons is not.
T. De Grand, 2001
Gauge Configurations responsible for chiral
symmetry breaking in QCD
Dirac eigenvalues filtering
C. Gattringer PRL (2002)
Cooling
Chu, Negele et al. PRD (1993)
Instantons are gauge configurations associated to chiral dynamics
(but Horvath’s group…)
Interacting Instanton Liquid Model (IILM)
QCD vacuum as an instanton ensemble
Theoretical ingredients of the model are derived from
semi-classical arguments (Stream-line construction)
Need a counter-term to parametrize the excluded
ultraviolet physics
Tests of the instanton picture against LQCD
Probability of chirality flip for quarks propagating in the vacuum
Prediction of the instanton picture:
R(t)
1
2nd inst.
1st inst.
L
R
t
L
PF, T.DeGrand, Phys. Rev. Lett. 91:182001,2003
4 important features of instanton-induced dynamics
• Spontaneous Chiral symmetry breaking and anomalous
U(1) breaking. The IILM contains Chpt as low-energy EFT
M.Cristoforetti, PF, M.Traini, J.Negele (2007)
• Link between current and constituent quarks
Lattice: P.Bowmann et al. PRD (2004)
Instantons: Diakonov & Petrov NPB, PL,B (1984)
• Diquark correlations
Mass ≈ 500 MeV (“good diquark” channel)
Size ~ 0.6-0.7 fm
M.Cristoforetti, PF, G.Ripka.M.Traini 2004
• Lack of Confinement
Bad description of long-range non-perturbative correlations
It is legitimate to use it as a tool to investigate the role of
chiral forces in light hadrons
Instanton forces in
light hadrons:
Stable states
Pion and Nucleon
Light hadron spectroscopy:
Pion and Nucleon masses
Two-point
Correlation function
Effective mass plot
Pion mass
Nucleon mass
Light hadron spectroscopy:
Pion and Nucleon masses
Light hadron spectroscopy:
Pion and Nucleon masses
O(p4)
Light hadron Phenomenology:
Form Factors, Non Leptonic Hyperons decays, Diquark correlations
Elastic Form Factors
of nucleons and pions
Non-leptonic decays
of hyperons (ΔI=½ rule)
Diquarks
Mass, correlations, sizes
Light Hadrons:
Instanton
forces in
Resonances
light
hadrons:
Lowest Resonances
ρ and a1
Light hadron spectroscopy:
Resonances
Why ρ and a1 ?
• First excited state: sensitive to both
chiral symmetry
breaking and color confinement
• The splitting between the mass of the two meson due only
to chiral symmetry breaking
Light hadron spectroscopy:
Resonances
Pion and Nucleon masses
Two-point
Correlation function
Spectral
Effectiverepresentation
mass plot
Pion mass
Nucleon mass
?
Light hadron spectroscopy:
ALEPH data effective mass plot
ρ meson
Light hadron spectroscopy:
Interacting Instanton Liquid Model
ρ meson
Light hadron spectroscopy:
ALEPH data effective mass plot
a1 meson
Light hadron spectroscopy:
Interacting Instanton Liquid Model
a1 meson
Light hadron spectroscopy:
Conclusion about lowest-lying resonances
•Vector and Axial vector resonances exist in the model
(surprise: no confinement)
•Mass are found to be some 30% larger.
•Perfect chiral-splitting parameter


MA1  M
MA1  M
 0.23(1)
(exp  0.23)
Conclusions:
Where chiral forces do the job
•The Instanton liquid
model is consistent
with ChPT
•The Instanton-induced
chiral forces reproduce
well pion and nucleon
masses
•ρ and a1 resonances
exist in the Instanton
vacuum
•Splitting is ok.
Cartoon Summary of IILM results
Identity card:
Identity card:
Name:
Pion
Mass:
138 MeV
Status:
Stable State
Size:
0.6 fm
Features: Goldst. boson
Decay:
N/A
Name:
Mass:
Status:
Size:
Decay:
These results provide a picture which is very
different from the SU(6) Quark Model view
Rho
~1000 MeV
Resonance
N/A
constituents
-Dominance of chiral dynamics in light hadrons
-Diquarks
Identity card:
Identity card:
Name:
Nucleon
Mass:
940 MeV
Status:
Stable State
Size:
0.8 fm
Features: diquark content
Decay:
N/A
Name:
Mass:
Status:
Size:
Decay:
a1
~1500 MeV
Resonance
N/A
constituents
Related work not discussed here:
•Exploration of the microscopic origin of chiral logs:
at which quark mass scale does one enter the chiral regime?
(M.Cristoforetti, P.F. M.Traini and J.W.Negele, PRD 2007)
• Instanton correlations in glueballs
(M.Tichy, M.Cristoforetti, P.F., in preparation)
Chiral Dynamics in Interacting Instanton
Liquid Model:
Quantities to compare directly ChPT and IILM are needed
Spectrum of the Dirac Operator
IILM
ChPT prediction:
For Nf=2, mq=0 the density of
eigenvalues of the Dirac Spectrum
should become flat near the origin
Interacting Instanton Liquid Model:
In the chiral regime
Spectrum of the Dirac Operator: finite-mass corrections
IILM
Consistent with ChPT constant
prediction for mq<80 MeV
Light hadron spectroscopy:
Pion and Nucleon masses
I box: 3.53 x 5.9 fm4
II box: 3.03 x 5.9 fm4
mq=21 MeV
mq=30 MeV
mq=50 MeV
mq=70 MeV
mq=90 MeV