Duality: Recent and Future Results

Ioana Niculescu

James Madison University

Hall C “Summer” Workshop

Quark-Hadron Dualitycomplementarity between quark and hadron descriptions of observables

Hadronic Cross Sectionsaveraged over

appropriate energy range

hadrons

Perturbative Quark-Gluon Theory

=

At high enough energy:

quarks+gluons

Can use either set of complete basis states to describe physical phenomena

Q2 :Four-momentum transferx : Bjorken variable (=Q2/2Mn)n : Energy transferM : Nucleon massW : Final state hadronic mass

L

T

U

Inclusive Electron Scattering

Duality in Inclusive electron Duality in Inclusive electron scatteringscattering

Elastic Resonance

Deep Inelastic

Where : flux of transversely polarized virtual photons : relative longitudinal polarization

FL = F

2 – 2xF

1 + 2M

pF

2F

2

L +

TR =

L /

T =

F

L /

2xF

1

),(),(2'

221 QxFQxxF

dWdE

dL

Duality in F2 Structure Function

’ = 1+W2/Q2

First observed ~1970 by Bloom and Gilman at SLAC by comparing resonance production data with deep inelastic scattering data

Integrated F2 strength in Nucleon Resonance region equals strength under scaling curve.

Shortcomings:

• Only a single scaling curve and no Q2 evolution (Theory inadequate in pre-QCD era)

• No L/T separation F2 data depend on assumption of R = L/T

• Only moderate statistics

Now can obtain “true” F2 data

Compare with DIS fits or QCD calculations/fits (CTEQ/MRST)

Bjorken x instead of ’

Empirically, DIS region is where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2

Duality: Averaged over W, log

scaling observed to work also for Q2 > 0.5 GeV2, W2

< 4 GeV2

JLab results (E94110): Works quantitatively to better than 10%

Duality in the F2 Structure Function

Duality observed in all unpolarized structure functions

(E94110)

p

Fe

d

= 2x[1 + (1 + 4M2x2/Q2)1/2]

…and in Nuclei (F2)

Where we are now…

Experimentally, duality holds in all unpolarized structure functions, in nuclei, and in tested spin structure functions down to surprisingly low Q2

Apparently a non-trivial property of nucleon structure

What is new…

E00-002: “F2N at Low Q2”

E00-116: “Duality at Intermediate Q2”

E00-108: “Duality in Meson Electroproduction”

Low Q2 duality in inclusive electron-nucleon scattering

Measure F2 (p and n) in the region where it drops off Study F2 at low Q2 as a function of x

Kinematic coverage

Duality at Intermediate Q2

“proposed measurements will help answering the question of the nature of power corrections in hard processes as fundamental components in understanding the transition between pQCD and non-pQCD”

Cornwall-Norton moments

)()()( 2,2

2022 QB

Q

nMQAQM kn

k

knn

Logarithmic dependenceHigher twists

.Duality is described in the Operator Product Expansion as higher twist effects being small or canceling

DeRujula, Georgi, Politzer (1977)

dxQxFxQM nn ),()( 2

1

0

22

Moments of F2p @ Low

Q2

Proton Charge(Coulomb Sum Rule)

Elasticcontribution

n = 2

n = 4

n = 6

n = 8

50% of momentum carried by quarks (Momentum Sum Rule)

total

n = 2

elastic

-region

W2 > 4 GeV2 (“DIS”)

S11-region

@ Q2 = 2 (GeV/c)2 30% of M2

comes from the resonance region

Why large x ?Integral Ratio Res /

Scaling

QuantificationLarge x Structure

Functions

Kinematic coverage

“Explore the extent to which the electroproduction of mesons exhibits the same dual behavior between resonance region scattering and scaling region”

At high energies: factorization (pQCD)

),()( 2Qxgzf

quark hadronization hard quark-photon interaction

If duality holds: may see behavior consistent with factorization even at lower energies.

Duality in Meson Electroproduction

Spectra in z at low Q2 and W average to scaling curve (high Q2 and W)?

Q2 behavior of resonant bumps

Relative strength of resonances/ background at different Q2

d/dz iei2qi(x,Q2)Dqi

m(z,Q2) + qi(x,Q2)Dqim(z,Q2)

Duality in meson electroproduction:look for duality in f(z)

LH2 target

Quark-parton prediction

The future…CTEQ currently planning to use duality for large x parton distribution modelingNeutrino community planning to test dualityNeutrino community using duality to predict low energy (~1 GeV) regime Duality provides extended access to large x regimeAllows for direct comparison to QCD Moments

calculated on the latticeMore experiments are plannedNeutronPolarized structure functionsNeutrino scattering