Instanton-induced contributions to hadronic form factors.

1. Talk given at Nucleon05. Frascati October 2005. Instanton-induced contributions to hadronic form factors. Pietro Faccioli Universita’ degli Studi di Trento, I.N.F.N., Gruppo Collegato di Trento, E.C.T.* A list of present and past collaborators: E. Shuryak (SUNY, Stony Brook), T.DeGrand, J.Negele (M.I.T) M.Cristoforetti (Trento), M.Traini(Trento)

2. Two messages from high Q2 form factors 1) There are short-range non perturbative correlations Pion form factor: Proton GE/GM ratio: The asymptotic perturbative QCD (pQCD) prediction is very far from data at the highest available Q2

3. Such non-perturbative short-range interactions are • channel-dependent DIS structure functions: *0transition form factor: In these processes pQCD predictions are very accurate for Q2 ≥ 1GeV2.

4. Strong non-perturbative correlations: Pion form-factor Proton form factors OZI violations (scalar ch.) Scalar diquarks .... “Mild” non-perturbative correlations: *0 transition D.I.S. structure functions OZI rule (vector ch.) Vector diquarks Generalizing….. The channel dependence of non-perturbative interactions appears to be quite a general feature of light hadron physics

5. Some conclusions from these data: Large high Q np-effects: Channel dependence: • There is short-range (dl~1/GeV) non-perturbative interaction in QCD • 2. Equivalently: there are small non-perturbative structures in the QCD vacuum 1. Such np-interaction has well defined flavor-spin structure 2. There is some effective small parameter at work even in the non-perturbative sector

6. Consequences • We should expect non-perturbative • effects at the GeV scale • The dynamical origin of chiral • symmetry breaking and the solution • of the U(1) problem must be • understood simultaneously instantons What dynamics is at work? The non-perturbative dynamics of light-quarks in QCD is characterized by an important separation of scales: Pert. QCD Mρ ~ 1 GeV ~ Mη’ ΛQCD

7. Digression:Lattice QCD and the role of instantons

8. Near zero-modes and chiral dynamics Spectral decomposition of the quark propagator: NB: Near zero-modes relate to the quark condensate: ( Banks-Casher ) Small eigen-values  Chiral Dynamics This connection provides a tool for investigating chiral dynamics in lattice QCD

9. Role of chiral dynamics in hadrons, from LQCD From a variety of lattice tests it has emerged that when one restricts to very low eigenmodes (chiral dynamics) • String tension desappear • (no more confinement) • Lowest-lying light Hadrons survive unchanged The nucleon properties are determined by chiral dynamics, while confinement plays only a (very) marginal role Example:. Light ps meson 2point fnct.

10. Test 1: Isolating the gauge configuration in the Path-Integral which lead to low-lying eigen-modes Problem: how can we identify the gauge configurations responsible for near-zero modes? Solution (Gattringer): use fermionic representation of Fμν: Eigen-modes of Dirac Operator Gluon stress tensor

11. Results: Action Density: Top. Charge Density: Gattringer, Phys.Rev.Lett. 88 (2002) 221601

12. R(t) 1 Test 2: Quark chirality flips and instantons Isolated instantons induce sudden flips of quarks chirality. Define chirality flip correlator: ) Ampl. ( R:= ) Ampl.( Prediction of the instanton picture: 2nd inst. 1st inst. t L R L PF, T.DeGrand, Phys. Rev. Lett. 91:182001,2003

13. Instanton Liquid Model of the QCD vacuum • One assumes the QCD vacuum is saturated by an ensemble • of instantons and anti-instantons… • …and determines phenomenologically their density and size (Shuryak, 1982). NB: Small diluteness: (virial expansion!) !!!

14. Virial expansion and single-instanton approximation ‘t Hooft interaction: L R • Chirality flipping • Flavor dependent Selection rules (hard to find in a non-pt theory) R L Shuryak, NPB, 1982 PF and Shuryak PRD. 2001 PF PhD thesis 2002 The o(κ) term in the virial expansion is equivalent to the Single Instanton Approximation (SIA): Many-instanton (infrared) degrees of freedom can be integrated out into one effective parameter: m* Effective theoryof the instanton vacuum valid in the ultraviolet Corrections are o(κ2)~1/10

15. R R R or L ?? R L L R L L =0 The channel-dependence of the instanton-induced interaction Analyze the strength of non-perturbative correlations in terms of the κ-expansion: Example: (Pion form factor) (*0transition form factor)

16. Strong non-perturbative correlations: Pion form-factor Proton form factors Flavor mixing scalar Scalar diquarks o(κ) “Mild” non-perturbative correlations: *0 transition D.I.S. structure functions Flavor mixing vector Vector diquarks o(κ2) Possible explanation of channel dependence of short-range non-perturbative correlations The SIA allows to identify the processes in which instanton effects are strongest (i.e. o(κ)). This provides a possible explanation of the observed channel dependence of non-perturbative correlations in hadrons

17. Proton Form Factors: PF, Phys. Rev. C69: 065211,2004 N.B.: No parameter fitting

18. Pion Form Factor PF, A.Schwenk, E.V Shuryak, Phys. Rev. D67:113009, 2002 N.B.: No parameter fittingc

19. Consistent description of delay of onset of pQCD based on a mechanism supported by LQCD Good agreement with data with no parameter fitting Strange E/M form factors DIS moments ConclusionsOutlook