Nuclear Duality, electron scattering,and neutrino scattering:

Nucleon Resonance Region

P. BostedAugust 1 2006

Quark-Hadron duality in F1, F2, g1, and semi-inclusive DIS

Nuclear dependence: what’s new

PV electron scattering in the resonance region

Why I got interested

Needed for radiative correction calculations.

Needed to get “dilution factor” in experiments using NH3 or ND3 targets to measure g1 (inclusive exclusive, SIDIS)

Needed to predict PV asymmetry in ep inelastic scattering (background to Moller scattering and DIS tests of Standard Model

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Duality and the Transition to Perturbative Duality and the Transition to Perturbative QCDQCD

Asymptotically Free Quarks: regime of pQCD

Long Distance Physics: hadronic observables

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Textbook Example: eTextbook Example: e++ee- - hadronshadrons

Only evidence of hadrons produced is narrow states oscillating around step function

determined by quark color, charge.

R =

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.First observed ~1970 by Bloom and Gilman at SLAC by comparing resonance production data with deep inelastic scattering data using ad hoc variable

.Integrated F2 strength in nucleon resonance region equals strength under scaling curve.

.Resonances oscillate around curve - for Q2>1 or so

Shortcomings:

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

’ = 1+W2/Q2

Q2 = 0.5 Q2 = 0.9

Q2 = 1.7 Q2 = 2.4

F 2

F 2

Bloom-Gilman Duality

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Bloom-Gilman Duality in FBloom-Gilman Duality in F2 2 proton Todayproton Today

• F2 DIS well-measured over several orders of magnitude in x, Q2

• QCD established theory• Perturbative predictions

(based on extracted PDF’s, evolution) available

• Target mass prescription• Quark-Hadron Duality

quantifiable (more later….)• Show to hold to better than

5% above Q2 ~ 0.5 GeV2

• F2 average• Q2 dependence

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Bloom-Gilman Duality in FBloom-Gilman Duality in F2 2 TodayToday

Difference between Alekhin NNLO curve (formed from lepton-nucleon scattering only) and resonance data, integrated for many spectra

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Experimental Status of L/T Separated Structure Functions: 2xFExperimental Status of L/T Separated Structure Functions: 2xF11

Smooth transition from DIS (solid squares) to resonance region

Resonances oscillate about perturbative curves

Target mass corrections large and important (subject of much recent theory work - Steffens, Melnitchouk, Qiu, Reno, Kretzer,…)

Alekhin NNLOMRST NNLOMRST NNLO withBarbieri Target Mass Corrections

Data from JLab E94-110 (nucl-ex/0410027)

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Experimental Status of L/T Separated Structure Functions: Experimental Status of L/T Separated Structure Functions:

FFLL

Smooth transition from DIS (solid squares) to resonance region

Resonances oscillate about perturbative curves for Q2>1 GeV2

Target mass corrections large and important

Alekhin NNLOMRST NNLOMRST NNLO withBarbieri Target Mass Corrections

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Duality in QCDDuality in QCD• Moments of the Structure Function

Mn(Q2) = ∫ dx xn-2F(x,Q2)

If n = 2, this is the Bloom-Gilman duality integral!

• Operator Product Expansion

Mn(Q2) = (nM02/ Q2)k-1 Bnk(Q2)

higher twist logarithmic dependence

(pQCD)

• Duality is described in the Operator Product Expansion as higher twist effects being small or cancelling DeRujula, Georgi, Politzer (1977)

0

1

k=1

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0

1

Mn(Q2) = dx xn-2F(x,Q2)

Need data covering wide range in x, at

fixed Q2

Large x increasingly important at

large n

+ elastics……

F2

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Preliminary

n = 2 Cornwall-Norton Moments n = 2 Cornwall-Norton Moments F2FLFT F2, F1 in excellent

agreement with NNLO + TM above Q2 = 2 GeV2

No (or canceling) higher twists

Yet, dominated by large x and resonance region

Remove known HT ( elastic), and there are no more down to Q2 = 0.5 GeV2

The case looks different for FL (target mass larger issue - still under study)

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Duality Works even better in Nuclei, (F2)

p

Fe

d

= 2x[1 + (1 + 4M2x2/Q2)1/2]•Data in resonance region, spanning Q2 range 0.7 - 5 GeV2

•GRV curve

•The nucleus does the averaging

•For larger A, resonance region indistinguishable from DIS

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Duality (F2) in Deuterium

Resonantstructure mostly gone for W>1.4 GeV

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Duality and the EMC EffectDuality and the EMC Effect

J. Arrington, et al., submitted

Medium modifications to the structure functions are the same in the resonance region as in the DIS for Q2>2 GeV2 or so.

Note use of xi, not x!

(approximates TM)

C/D

Fe/D

Au/D

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And these results just in…

C/D 4He/D

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Duality in g1

Data both p and d oscillate round NLO PDF curves with TM corrections.

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Average g1 (over M<W<2 GeV) agrees very well with PDF fits with TM corrections down to about 1.5 GeV2. Power law (HT) deviations clear at lower Q2. Adding elastic peak seems to help in this case.

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Locally, Delta(1232) region systematically low, 1.5 GeV region high

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Duality in Meson ElectroproductionDuality in Meson Electroproductionhadronic description quark-gluon description

TransitionForm Factor

DecayAmplitude

Fragmentation Function

Requires non-trivial cancellations of decay angular distributions If duality is not observed,

factorization is questionable

Duality and factorization possible for Q2,W2 3 GeV2 (Close and Isgur, Phys. Lett. B509, 81 (2001))

The Origins of Quark-Hadron Duality – Semi-Inclusive Hadroproduction

Destructive interference leads to factorization and duality

Predictions: Duality obtained by end of second resonance region Factorization and approximate duality for Q2,W2 < 3 GeV2

F. Close et al : SU(6) Quark ModelHow many resonances does one need to average over to obtain a complete set of states to mimic a parton model? 56 and 70 states o.k. for closure

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Missing mass of pions in ep->e’X

Duality question: will factorization work if Mx<2 GeV, even though Delta(1232) reonanceVisible? For pi-, guess need Mx>1.4 GeV.

- 0

+n

0

++

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Z-Dependence of cross sections

Good agreement with prediction using CTEQ5M PDFs and Binnewies fragmentation functions, except for z>0.7, or Mx>1.4 GeV. X=0.3, Q2=2.5 GeV2, W=2.5 GeV

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Rpd+

Rpd-

Both ratios agree PDF models for z<0.7 (Nx>1.4 GeV)

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Summary so far

• Duality useful at O(10%) for Q2>1 to 2 GeV2

– Spin-averaged structure functions– Tested spin structure functions

• Duality observed in Nuclei– Even displays EMC effect

• Duality in semi-inclusive meson production

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Questions raised• How to extend to low Q2

– M. Eric Christy et al have excellent empirical fit to all F1, F2 data covering M<W<5 GeV, 0<Q2<10 GeV2. Duality used in determining functional form

– No good fit to deuteron at low Q2 (in progress though).

– Nuclear dependance. New data 15N/C

What is nuclear depeance of specific final statesin resonance region (good direction for future work: data exist but not analyzed.

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Hall C VERY PRELIMINARYDATA

TYPICALMODEL

Inelastic scattering on deuteron

To study problem further, used large sample (about 10 billion scattered electrons) of data from CLAS Eg1b experiment using CLAS in Hall B at Jlab.

Targets filled with ND3 or NH3 (plus some liquid helium) were alternated frequently (so acceptance cancels) and electrons were detected 10<<40 degrees for beam energies 1.7, 2.5, 4.2, 5.7 GeV.

Inelastic scattering on deuteron

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Curves using Eric Christy for p and Steve Rock fit d

Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3

Inelastic proton/deuteron ratio in Resonance Region

Q2=0.12

Q2=0.6 Q2=1.0 Q2=1.8

Q2=0.2 Q2=0.4

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Curves using Eric Christy for p and D2MODEL_IOANA fit d

Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3

Inelastic proton/deuteron ratio in Resonance Region

Q2=0.12

Q2=0.6 Q2=1.0 Q2=1.8

Q2=0.2 Q2=0.4

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Curves using Eric Christy for p and E665 fit for d

Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3

Inelastic proton/deuteron ratio in Resonance Region

Q2=0.12

Q2=0.6 Q2=1.0 Q2=1.8

Q2=0.2 Q2=0.4

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Curves using E665 fit for both p and d

Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3

Inelastic proton/deuteron ratio in Resonance Region

Q2=0.12

Q2=0.6 Q2=1.0 Q2=1.8

Q2=0.2 Q2=0.4

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Looks like what works best among available models is E665 fit (A. V. Kotwal, January 1994) , hich makes assumption n=0.76p in the resonance region.

Next step: add Fermi smearing for deuteron.

Next step: study best transition to DIS region (W>2 GeV): clearly n/p=(1-0.8x) inadequate: need to consider using (1-0.8xi) and also make shadowing corrections.

Inelastic scattering on deuteron

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Presently, apply simple y-scaling-based Fermi smearing model to free neutron and proton fits, plus a Steve Rock fit to “EMC” ratio for x<0.8 to take into account binding and shadowing.

This prescription predicts ratio of 15N to C essentially independent of W in the resonance region.

This seems to be born out by very preliminary ratios measured in CLAS.

Inelastic scattering on nuclei

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Presently, apply simple y-scaling-based Fermi smearing model to free neutron and proton fits, plus a Steve Rock fit to “EMC” ratio for x<0.8 to take into account binding and shadowing.

This prescription predicts ratio of 15N to C essentially independent of W in the resonance region (BUT, not quasielastic!).

This seems to be born out by very preliminary ratios measured in CLAS.

Inelastic scattering on nuclei

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Very preliminary ratios 15N/C (per gm) from CLAS Eg1b

W (GeV)

Curve use DIS limit n/p=(1-0.8x)

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To obtain fraction of events from polarized protons (deuterons) in NH3 (ND3), used recent data for deuteron to carbon ratio in SIDIS from E02-104 (Will Brooks). Few representative points shown. MUCH MORE DATA coming soon over wide kinematic range. Studies quark propogation in cold QCD matter.

CLAS 5.7 GeVPRELIMINARY

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The cross section in terms of electromagnetic, weak and interference contribution

Asymmetry due to interference between Z0 and

Electron can scatter off of proton by exchanging either a virtual photon or a Z0

e’

e P

e’

e P

Z0+

Parity Violating Asymmetry

For inelastic scattering, ARL can be written in terms of response functions

•Isospin symmetry relates weak and EM vector current•Sensitive to axial hadronic current also

Details have so far been worked out only for N→∆(1232)

weakly sensitive to axial vector transition form factor

Resonance Region asymmetry

For an isolated resonance, ARL can be written in terms of response functions

•Isospin symmetry relates weak and EM vector current•Sensitive to axial hadronic current also

Details have so far been worked out only for N→∆(1232)

weakly sensitive to axial vector transition form factor

Resonance Region Asymmetry

•Leading order criteria

DATA NEEDED!

•Duality is satisfied if on average n/p = 2/3

PROTON

SimpleModel

No reliable model for n/p ratio in res. region: use simple toy model

Will data look anything like this?

Duality good to ~5% in F2, our goal is to measure ALR to ~5% locally and <3% globally

DIS model

Resonance model

DUALITY for -Z interference tensor?

•Leading order criteria•Duality is satisfied if on average n/p = 2/3

PROTON

SimpleModel

No reliable model for n/p ratio in res. region: use simple toy model

Will data look anything like this?

Duality good to ~5% in F2, our goal is to measure ALR to ~5% locally and <3% globally

DIS model

Resonance model

DUALITY for -Z interference tensor?

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Study A-dependence of axial contribution

Will duality averaging work similarly to vector hadronic current?

Physics Goals – Nuclear targets

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Neutron / Proton ratio almost constant in the nucleon resonance region.

New data from CLAS and Hall C will soon pin down vector current for proton, neutron, carbon, 15N, and heavier targets from quasi-elastic region up to W-3 GeV and for 0.05<Q2<5 GeV2

Better emipirical fits needed for modeling radiative corrections, neutrino interactions, and many other applications. Duality useful here. Study of specific final states needed for A>1!

Potential for PV electron scattering to constrain axial-vector piece.

CONCLUSIONS