1. Exploring the Chiral Regime of QCD in the Interacting Instanton Liquid Model M.Cristoforetti P.Faccioli M.C.Traini Università degli studi di Trento ECT* INFN J.W.Negele MIT Cortona 13-ottobre-06

2. Chiral Perturbation Theory, Lattice QCD: Ab initio approaches to investigate hadron phenomenology 1 GeV Perturbative QCD Non-perturbative QCD • Chiral perturbation theory • Lattice QCD

3. Lattice QCD: In the real world the current quark mass is small, this is a problem 0.25 Chiral Extrapolation? 0.15 <x> Phys. point 0.2 0

4. Chiral Perturbation Theory: Could help to connect lattice data to the physical point but … Lattice data available Chiral Regime • What is the behavior with mq in the intermediate mass regime? • What is the radius of convergence of Ch.Pt? • Why is the quark-mass dependence so different? • What is the microscopic dynamical origin of the transition to the chiral regime? <x> Phys. point 0.2

5. Interacting Instanton Liquid Model: As a bridge between the chiral regime and lattice Interacting Instanton Liquid Model We develop a framework to study the behavior of the physical observable in the intermediate regime connecting the lattice points and the physical point Investigate the microscopic dynamical mechanism that characterizes the transition into the chiral regime “What happens at the quark level?”

6. Interacting Instanton Liquid Model: QCD vacuum as an instanton ensamble

7. Interacting Instanton Liquid Model: In the chiral regime 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

8. 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

9. Interacting Instanton Liquid Model: As a bridge between the chiral regime and lattice Chiral Regime IILM <x> Consistent with ChPT Phys. point 0.2

10. Interacting Instanton Liquid Model: Connecting to lattice data Two-point Correlation function Effective mass plot Pion mass Nucleon mass

11. Interacting Instanton Liquid Model: Connecting to lattice data I box: 3.53 x 5.9 fm4 mq=21 MeV mq=30 MeV II box: 3.03 x 5.9 fm4 mq=50 MeV mq=70 MeV mq=90 MeV Agree with lattice results

12. Interacting Instanton Liquid Model: Chiral extrapolation of the nucleon mass • Λ=0.992 GeV (from IILM ρ meson mass evaluation) • Included MN at the physical point in the fit Fitted parameters Input parameters • M0 = 0.856± 0.005 GeV • e1 = 0.91± 0.09 GeV-1 • c1 = -1.35±0.08 GeV-1 • c3 = -6.6± 0.7 GeV-1 • fp = 0.0924 GeV • gA = 1.267 • c2 = 3.2 GeV-1

13. Interacting Instanton Liquid Model: Chiral extrapolation of the nucleon mass O(p4) IILM+CPPACS data MILC+CPPACS data MILC+CPPACS fit Pion-N scattering IILM +CPPACS fit • M0 = 0.89± 0.02 GeV • e1 = 0.86± 0.04 GeV-1 • c1 = -0.7±0.1 GeV-1 • c3 = -1.9± 0.8 GeV-1 • M0 = 0.856± 0.005 GeV • e1 = 0.91± 0.09 GeV-1 • c1 = -1.35±0.08 GeV-1 • c3 = -6.6± 0.7 GeV-1 • c1 = -1.23±0.16 GeV-1 • c3 = -5.94± 0.09 GeV-1

14. Interacting Instanton Liquid Model: Nucleon sigma term

15. Interacting Instanton Liquid Model: As a bridge between the chiral regime and lattice Lattice data available Chiral Regime IILM Consistent with Lattice results <x> Consistent with ChPT Phys. point 0.2

16. Interacting Instanton Liquid Model: As a bridge between the chiral regime and lattice Interacting Instanton Liquid Model We develop a framework to study the behavior of the physical observable in the intermediate regime connecting the lattice points and the physical point We develop a framework to study the behavior of the physical observable in the intermediate regime connecting the lattice points and the physical point Investigate the microscopic dynamical mechanism that characterizes the transition into the chiral regime “What happens at the quark level?”

17. Interacting Instanton Liquid Model: Chiral dynamics The quark propagator in the IILM The fermionic determinant in the IILM Overlap matrix elements Chiral dynamics is encoded in the Szm and Detzm parts For im »‹TIJ› the chiral dynamics becomes suppressed

18. Interacting Instanton Liquid Model: Chiral dynamics For mq »m*~80-100 MeV chiral dynamics in the IILM becomes suppressed • Natural Dynamical Mechanism • Natural scale for the transition into the chiral regime. • Further studies are in progress.

19. Interacting Instanton Liquid Model: Chiral dynamics Zero-mode suppression of the fermionic determinant is regulated by m*= ‹TIJ› We observe that for m>m* the Dirac spectrum stops depending on the quark mass and approaches the quenched limit.

20. The Instanton Liquid Model provides a practical tool to study the transition into the Chiral Chiral Conclusions: • The Instanton liquid model is consistent with ChPT • The Instanton liquid model reproduce Lattice data for large pion masses The IILM provides analytic insight, leading to a natural mechanism for the transition into the chiral regime & a natural scale m*. FURTHER STUDIES ARE IN PROGRESS.