duality: recent and future results ioana niculescu james madison university hall c “summer”...
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Duality: Recent and Future Results
Ioana Niculescu
James Madison University
Hall C “Summer” Workshop
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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
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Q2 :Four-momentum transferx : Bjorken variable (=Q2/2Mn)n : Energy transferM : Nucleon massW : Final state hadronic mass
L
T
U
Inclusive Electron Scattering
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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
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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
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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
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Duality observed in all unpolarized structure functions
(E94110)
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p
Fe
d
= 2x[1 + (1 + 4M2x2/Q2)1/2]
…and in Nuclei (F2)
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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
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What is new…
E00-002: “F2N at Low Q2”
E00-116: “Duality at Intermediate Q2”
E00-108: “Duality in Meson Electroproduction”
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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
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Kinematic coverage
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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”
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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
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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
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Why large x ?Integral Ratio Res /
Scaling
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QuantificationLarge x Structure
Functions
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Kinematic coverage
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“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
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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)
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LH2 target
Quark-parton prediction
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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