Hadron 2007 Frascati, October 12 th, 2007 P.Faccioli, M.Cristoforetti, M.C.Traini Trento University & I.N.F.N. J. W. Negele M.I.T. P.Faccioli, M.Cristoforetti, M.C.Traini Trento University & I.N.F.N. J. W. Negele M.I.T. Chiral Symmetry, Hadron Spectrum and Instantons

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 What are the dominant correlations in Hadrons ? 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 T. De Grand, 2001 Small eigen-values of the Dirac Operator  Chiral Dynamics Light 0 - meson 2-point fnct. Conclusion: Physics of light hadrons is strongly affected by chiral dynamics Physics of heavy hadrons is not.

Dirac eigenvalues filtering Cooling Gauge Configurations responsible for chiral symmetry breaking in QCD C. Gattringer PRL (2002) 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

Tests of the instanton picture against LQCD t R(t) 1 1 st inst. 2 nd inst. LLR PF, T.DeGrand, Phys. Rev. Lett. 91:182001,2003 Prediction of the instanton picture: Probability of chirality flip for quarks propagating in the vacuum

4 important features of instanton-induced dynamics Spontaneous Chiral symmetry breaking and anomalous U(1) breaking. The IILM contains Chpt as low-energy EFT Link between current and constituent quarks Lattice: P.Bowmann et al. PRD (2004) Instantons: Diakonov & Petrov NPB, PL,B (1984) M.Cristoforetti, PF, M.Traini, J.Negele (2007)

Diquark correlations Mass ≈ 500 MeV (“good diquark” channel) Size ~ fm M.Cristoforetti, PF, G.Ripka.M.Traini 2004 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 Lack of Confinement

Instanton forces in light hadrons: Stable states Instanton forces in light hadrons: Stable states Pion and Nucleon

Light hadron spectroscopy: Pion and Nucleon masses Two-point Correlation function Two-point Correlation function Nucleon mass Pion mass Effective mass plot

Light hadron spectroscopy: Pion and Nucleon masses

O(p 4 ) Light hadron spectroscopy: Pion and Nucleon masses

Diquarks Mass, correlations, sizes Diquarks Mass, correlations, sizes Elastic Form Factors of nucleons and pions Elastic Form Factors of nucleons and pions Light hadron Phenomenology : Form Factors, Non Leptonic Hyperons decays, Diquark correlations Light hadron Phenomenology : Form Factors, Non Leptonic Hyperons decays, Diquark correlations Non-leptonic decays of hyperons (ΔI=½ rule) Non-leptonic decays of hyperons (ΔI=½ rule)

Light Hadrons: Resonances Resonances ρ and a 1 Instanton forces in light hadrons: Lowest Resonances Instanton forces in light hadrons: Lowest Resonances

Light hadron spectroscopy: Resonances Light hadron spectroscopy: Resonances Why ρ and a 1 ? 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 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: Pion and Nucleon masses Nucleon mass Pion mass Two-point Correlation function Two-point Correlation function Light hadron spectroscopy: Resonances Spectral representation ?? Effective mass plot

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 a 1 meson

Light hadron spectroscopy: Interacting Instanton Liquid Model

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

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 a 1 resonances exist in the Instanton vacuum Splitting is ok. ρ and a 1 resonances exist in the Instanton vacuum Splitting is ok.

Cartoon Summary of IILM results Identity card: Name: Pion Mass: 138 MeV Status: Stable State Size: 0.6 fm Features: Goldst. boson Decay: N/A Identity card: Name: Nucleon Mass: 940 MeV Status: Stable State Size: 0.8 fm Features: diquark content Decay: N/A Identity card: Name: Rho Mass: ~1000 MeV Status: Resonance Size: N/A Decay: constituents Identity card: Name: a1 Mass: ~1500 MeV Status: Resonance Size: N/A Decay: constituents These results provide a picture which is very different from the SU(6) Quark Model view -Dominance of chiral dynamics in light hadrons -Diquarks

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 ChPT prediction: For N f =2, m q =0 the density of eigenvalues of the Dirac Spectrum should become flat near the origin IILM

Interacting Instanton Liquid Model: In the chiral regime Spectrum of the Dirac Operator: finite-mass corrections IILM Consistent with ChPT constant prediction for m q < 80 MeV

Light hadron spectroscopy: Pion and Nucleon masses I box: x 5.9 fm 4 m q =21 MeV m q =30 MeV II box: x 5.9 fm 4 m q =50 MeV m q =70 MeV m q =90 MeV