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) Talk given at Nucleon05. Frascati October 2005.

Two messages from high Q 2 form factors 1)There are short-range non perturbative correlations Pion form factor:Proton G E /G M ratio: T he asymptotic perturbative QCD (pQCD) prediction is very far from data at the highest available Q 2

DIS structure functions:  *  0 transition form factor: In these processes pQCD predictions are very accurate for Q 2 ≥ 1GeV 2. 2) Such non-perturbative short-range interactions are channel-dependent

Generalizing….. 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 The channel dependence of non-perturbative interactions appears to be quite a general feature of light hadron physics

Some conclusions from these data: 1.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 Large high Q np-effects:Channel dependence:

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

Digression: Lattice QCD and the role of instantons

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

Example:. Light ps meson 2point fnct. 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

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

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

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

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!)

Virial expansion and single-instanton approximation Many-instanton (infrared) degrees of freedom can be integrated out into one effective parameter: m* Effective theory of the instanton vacuum valid in the ultraviolet The o(κ) term in the virial expansion is equivalent to the Single Instanton Approximation (SIA): Corrections are o(κ 2 )~1/10 Chirality flipping Flavor dependent L LR R Selection rules (hard to find in a non-pt theory) ‘t Hooft interaction: Shuryak, NPB, 1982 PF and Shuryak PRD PF PhD thesis 2002

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

Possible explanation of channel dependence of short-range non-perturbative correlations 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(κ 2 ) 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

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

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

ConclusionsOutlook 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