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 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

DIS structure functions: *0 transition form factor:

In these processes pQCD predictions are very accurate for Q2 ≥ 1GeV2.

2) Such non-perturbative short-range interactions are channel-dependent

Generalizing…..

Strong non-perturbativecorrelations:

• 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 evenin 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 ischaracterized by an important separation of scales:

ΛQCD

Mρ Mη’

• We should expect non-perturbativeeffects 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

imxx

yxS

iD

)()(),(

Spectral decomposition of the quark propagator:

NB: Near zero-modes relate to the quark condensate:

)(lim 0

00

qq ( 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, whileconfinement plays only a (very) marginal role

Test 1: Isolating the gauge configuration in thePath-Integral which lead to low-lying eigen-modes

Solution (Gattringer): use fermionic representation of Fμν:

Problem: how can we identify the gauge configurations responsiblefor near-zero modes?

Gluon stress tensorEigen-modes of Dirac

Operator

)]()([)( xDxDTrxF

4

1

Gattringer, Phys.Rev.Lett. 88 (2002) 221601

Results:

][ FFTr

]~

[ FFTr

Action Density:

Top. Charge Density:

Test 2: Quark chirality flips and instantons

t

R(t)

1

1st inst.

2nd inst.

L LR

PF, T.DeGrand, Phys. Rev. Lett. 91:182001,2003

Isolated instantons induce sudden flips of quarks chirality. Define chirality flip correlator:

Ampl. ( 0,|

tdu

Ttdu

,| )

0,|

tdu

)exp( TiHQCD

)exp( TiHQCD

Ttdu

,|

Ampl.( )R:=

Prediction of the instanton picture:

Instanton Liquid Model of the QCD vacuum

parameter expansion n

rate instanton typical fm 1 n

sizeinstanton typical fm 0.3 4-

01.04

• One assumes the QCD vacuum is saturated by an ensemble of instantons and anti-instantons…

• …and determines phenomenologically their density and size (Shuryak, 1982).

!!!

I A

YMfAI

N N

SNNN

niiiILM emDndZ )det()(

1

NB: Small diluteness: (virial expansion!)

Virial expansion and single-instanton approximation

Many-instanton (infrared) degrees of freedom can be integrated outinto one effective parameter: m*

Effective theory of the instantonvacuum valid in the ultraviolet

The o(κ) term in the virial expansion is equivalent to the Single Instanton Approximation (SIA):

Corrections are o(κ2)~1/10

• Chirality flipping• Flavor dependent

L

LR

RSelection rules(hard to find in a non-pt theory)

‘t Hooft interaction:

Shuryak, NPB, 1982PF and Shuryak PRD. 2001PF PhD thesis 2002

The channel-dependence of the instanton-induced interaction

**

5i 5i 5ii

L

L

R

R

R

Example:

(Pion form factor)

L

L

RR 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(κ2)

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: 065211,2004

N.B.: No parameter fitting

PF, A.Schwenk, E.V Shuryak, Phys. Rev. D67:113009, 2002

N.B.: No parameter fittingc

Pion Form Factor

Conclusions Outlook

• 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