Nuclear DualityNuclear Duality(and related topics…)(and related topics…)

Cynthia Keppel

Hampton University / Jefferson Lab

First Workshop on Quark-Hadron DualityFirst Workshop on Quark-Hadron DualityFrascati, ItalyFrascati, Italy

June 2005June 2005

A Program of Inclusive Structure Function Measurements in Hall C at Jefferson Lab

• E94-110: L/T Hydrogen Resonance Region

• E99-118: L/T Low x, Q2 A-Dependence

• E00-002: L/T Low Q2 Deep Inelastic H, D

• E00-116: High Q2 H,D• E04-001: L/T Nuclear

Dependence, Neutrino Modeling

• E02-109: L/T Deuterium Resonance Region

• E02-109: x>1, A-Dependence• E03-103: EMC effect

InclusiveInclusive e + p e + X Scattering Scattering

Alternatively:

)(' LTdEdd

εσσσ

+Γ=Ω

Where: Γ = flux of transversely polarized virtual photonsε = relative longitudinal polarization

)/)2/(tan2/( 212' MFF

dEdd

mott θνσσ+=

Ω

12xFF

R L

T

L ==σσ

122

222)41( xFF

QxMFL −+=

longitudinallongitudinal

TransverseTransverse

mmIIxxEEdd

Rosenbluth:

dσ/d

ΩdE

/Γ

(nb/

sr/G

eV)

(All data for Q2 < 9 (GeV/c)2)

R = σL/σT

R = σL/σT

<<

High Precision DataHigh Precision Data

E94-110 Example: 180+ L/T’sE94-110 Example: 180+ L/T’s

σσ ~ 1.6%~ 1.6%

Example Precision Proton Structure Function: FExample Precision Proton Structure Function: FLL

Smooth transition from DIS (solid squares) to resonance region

Resonances oscillate about leading order curves

Q2 dependence same for leading order scaling, resonances

Target mass corrections large and important

Alekhin NNLOMRST NNLOMRST NNLO withBarbieri Target Mass Corrections

Duality in F2…let the nucleus do the averaging

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

Duality and the EMC EffectDuality and the EMC Effect

J. Arrington, et al., submitted

Red = resonance region data

Blue, purple, green = deep inelastic data from SLAC, EMC

Medium modifications to the structure functions are the same in the resonance region as in the DIS

Cross-over can be studied with new data

C/D

Fe/D

Au/D

Momentum Sum Rule M2(Q2) = ∫dx F2(x,Q2)

I. Niculescu, et al, in preparationI. Niculescu, et al, in preparation

Fe data = Fe data = data :) data :)

Fe curve = Fe curve = 26p + 30n26p + 30n****

d from e-d d from e-d data (sum = data (sum = 0.31)0.31)

p from p from hydrogenhydrogen

**n = d-p **n = d-p (sum rule (sum rule = 0.14)= 0.14)…….elastic .elastic

contributionscontributions

11

00

More quantitatively…..More quantitatively…..

Momentum sum rule Momentum sum rule from iron agrees with from iron agrees with simple sum p,n to simple sum p,n to within 5% (not very within 5% (not very sensitive to neutron sensitive to neutron excess) excess)

EMC effect is a EMC effect is a redistribution, not redistribution, not additional, additional, momentum of quarksmomentum of quarks

Where is the nuclear binding?Where is the nuclear binding? 7 MeV / nucleon / 7 MeV / nucleon / 938 MeV ~ expect 6% difference!938 MeV ~ expect 6% difference!

JLab Hall C E89-JLab Hall C E89-009009

E02-109 x>1: E02-109 x>1: (2004) (2004) H,D,3He,4He,C,H,D,3He,4He,C,Cu,AuCu,Au

E03-103 EMC E03-103 EMC effect: (2004) effect: (2004) H,D, 3He, 4He,C, H,D, 3He, 4He,C, Cu, AuCu, Au

Extraction of Nuclear MomentsExtraction of Nuclear Moments

22

22

22

ML(n) = s(Q

2){ 4M2(n) + 2c∫dx xG(x,Q2)}

3(n+1) (n+1)(n+2)

Preliminary

For F2, QPM gives:(1/3)2(0.17) + (2/3)2(0.34) = 0.17

~50% of momentum carried by quarks - the rest, assumably, by the glue

FL gives a direct measurement of the glueBut, we get 0.70 (preliminary) - also different from pdfs

Proton Momentum Sum RuleProton Momentum Sum Rule

F2, F1 in excellent agreement with NNLO + TM above Q2 = 2 GeV2

Very small (or canceling) higher twists

Yet, dominated by large x and resonance region

Remove known HT (a bit novel), the elastic, and there is no more down to Q2 = 0.5 GeV2

The case looks different for FL (data or curve?)

n = 2 Cornwall-Norton Proton Moments n = 2 Cornwall-Norton Proton Moments

FF22

FFLL

2xF2xF11

D. Dolgov, et al., Phys.Rev.D66:034506, 2002

““Neutron” - Proton Moments: Compare to LatticeNeutron” - Proton Moments: Compare to Lattice

n-p reduces n-p reduces sea, higher sea, higher twist effectstwist effects

Need to wait for BONUS,,,,,,,Need to wait for BONUS,,,,,,,

Parton Distribution Functions not well known at large x largely due to uncertainties associated with neutron

extraction from deuterium

CTEQ u,d(x) uncertainty bands

Similar for HERA, note also glue important still at large x (scaled by factor of 20!)

Need to get scaling curves for p, n Need to get scaling curves for p, n at large xat large x

Duality implies nucleus averaging Duality implies nucleus averaging to scaling, small higher twistto scaling, small higher twist

Use duality-averaged curve to get Use duality-averaged curve to get neutronneutron

Fix range in Fix range in , average data, obtain , average data, obtain curvecurve

……………………………….let’s see…..let’s see….

DD

PP

Being Being bold…..bold…..

FF22

Naïve SU(6) Naïve SU(6) quark model, quark model, d/u = 1/2d/u = 1/2

Helicity Helicity conservation, conservation, d/u = 1/5d/u = 1/5

1 gluon 1 gluon exchange. d/u exchange. d/u = 0= 0

A Prediction from Duality and Large x p,d Data: A Prediction from Duality and Large x p,d Data: Helicity Conservation and d/u = 1/5 Helicity Conservation and d/u = 1/5

Challenges / Issues / Physics at Low Q2

• NEED L/T separations to extract inclusive structure functions F1, FL, and F2

• Low Q2 behavior• Photonuclear absorption:

resonances less apparent in nuclei than in the proton (beyond Fermi)

• Nuclear moment analyses indicate higher twist occur at smaller Q2

higher twistshigher twists

current conservationcurrent conservation

At low QAt low Q22, L/T Separations are , L/T Separations are CrucialCrucial….…. 1) F2 is sometimes referred to as the “transverse” SF.

2) F2 can’t be obtained precisely independent of R and L/T

separations

3) Behaviour of F2 at low Q2 is not actually well determined (F2 0 at Q2 0).

4) R must be small for Q2 < 1 (R = 0 at the photon point, Q2 = 0).

In fact F2 σL + σT

Except at ε= 1 or Q2 large, F2 extracted from cross sections requires knowledge of R.

This has not yet been observed in the data - in fact, quite the opposite…..

Just an example….Just an example….At WAt W22 = 4 = 4 GeVGeV22 and and Q2 < 1 Q2 < 1 GeVGeV22, F, F22 will vary by will vary by 15%15% depending depending on the on the choice of R choice of R = 0 or R = = 0 or R = 0.2. At 0.2. At higher Q2, higher Q2, this can be this can be as much as as much as 20%.20%.

R on the proton…E99-118, E94-110 + world

Note: R still Note: R still not small at not small at low Qlow Q22 as as expected!expected!Precious Precious little nuclear little nuclear data data availableavailable(E99-118 (E99-118 soon high soon high WW22, low Q, low Q22 H,D,C,Al,Cu,H,D,C,Al,Cu,Au)Au)

E99-118 Ratio RD / RH

Very Very limited limited previous previous datadata

RRDD ~ 0.7 R ~ 0.7 RH H

(within(within large large uncertainty)uncertainty)

V. Tvaskis, PhD Thesis, Vrije Universiteit, 2004V. Tvaskis, PhD Thesis, Vrije Universiteit, 2004

LOTS of new, L/T separated, LOTS of new, L/T separated, low Qlow Q22 nuclear data en route… nuclear data en route…

Very preliminary Very preliminary data data (just obtained (just obtained January 2005)January 2005)

H,D,C,Al,Cu,Fe,Au H,D,C,Al,Cu,Fe,Au resonance regionresonance region

Models:

D resonance - JLab n/p - d/u = 1/5 EMC - SLAC DIS - F2allm (NMC)

R - JLab e99118

Data will be used for:Data will be used for:

Nuclear dualityNuclear duality

Neutrino modelingNeutrino modeling

Deuterium (neutron) Deuterium (neutron) momentsmoments

R on deuterium in R on deuterium in resonance regionresonance region

A-dependence of A-dependence of structure functions structure functions (and moments) at low (and moments) at low QQ22

Search for nuclear Search for nuclear pions (G. Miller pions (G. Miller prediction)prediction)

Summary• Duality seems to hold even better in the nucleus, where

Fermi motion naturally averages the structure function over resonances

• EMC effect in resonance region same as deep inelastic regime• Fe momentum sum rule constructed from (d-p),p to within 5%• Use duality and the deuteron to extract

• n-p structure function moments (lattice comparison)• n/p at large x (helicity conservation)

• Challenges at low Q2

• Need L/T separations• When do R, F2 approach 0?• Nuclear Effects

• *LOTS* of new data “in the can”…exciting times…

• Moments of the Structure FunctionMn(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 (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

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

Why is IGDH(Q2) interesting?

Extended Baldin Sum Rule QQ22 = 0, photoproduction = 0, photoproduction

νν

σσπ

κν

de

M ∫∞ −

=−0

2/32/12

22

24∫

∞ +=+

02

2/32/124

1)(ν

νν

σσπ

βα dN

GDH Sum RuleGDH Sum Rule

QQ22 > 0, electroproduction > 0, electroproductionExtended GDH Sum RuleExtended GDH Sum Rule

Baldin Sum RuleBaldin Sum Rule

Extended Baldin Sum RuleExtended Baldin Sum Rule * *

∫

∫=

=−∞

0

0

012

2

2

22

2

4x

TT

dxgQM

dKe

M νν

σνπ

κν

∫

∫=

=+∞

0

0

014

2

22

2

21)(

x

TN

dxxFQMe

dK

π

ννσ

νπβα

ν

Where Where κκ : anomalous magnetic moment of the nucleon. : anomalous magnetic moment of the nucleon. αα, , ββ: electric and magnetic polarizabilities respectively: electric and magnetic polarizabilities respectively νν00 : pion photoproduction threshold : pion photoproduction threshold

* D. Drechsel, B. Pasquini, M. Vanderhaeghen hep-ph/0212124 Dec 2002* D. Drechsel, B. Pasquini, M. Vanderhaeghen hep-ph/0212124 Dec 2002

Need L/T Need L/T separated separated data!data!

Multiply with Q4/2M to emphasize transition of Baldin Sum Rule to Perturbative DIS Region

~ 2xF1 MomentAgain, smooth transition

Duality (F2) in Deuterium

Resonance region and DIS F2 same, with same Q2 dependence, other than at smallest W