Measurements of R and the Longitudinal and Transverse Structure Functions in the Nucleon Resonance Region and Quark-Hadron Duality Rolf Ent, DIS2004 -Formalism:

Measurements of R and the Longitudinal and Transverse Structure Functions in the Nucleon Resonance Region and Quark-Hadron Duality

Rolf Ent, DIS2004

-Formalism: R, 2xF1, F2, FL

-E94-110: L/T Separation at JLab-Quark-Hadron Duality

-Or: Why does DIS care about the Resonance Region?-If time left: Duality in nuclei/g1

-Summary

Inclusive Inclusive e + p e’ + X scattering scattering

Single Photon Exchange

Elastic Resonance DIS

Alternatively:

)(' LT

dEd

d

onpolarizati allongitudin relative : ε

photons virtualpolarizedely transversofflux :Where

)/)2/(tan2/( 212'

MFFdEd

dmott

12xF

FR L

T

L

)2/(sin4

)2/(cos42

22

Emott 122

22

2)4

1( xFFQ

xMFL

Resonance Region L-Ts Needed ForResonance Region L-Ts Needed For

Extracting spin structure functions from spin asymmetries

/2 –

3/2

1/2

+ 3/2

A1 =

g

1

=

1/2 –

3/2

A1

A1

2T

=F

1(A

1 – A

2)

1 + 2From measurements of F

1 and A

1

extract 1/2

and 3/2

!

(Get complete set of transverse helicity amplitudes)

R (for R small)

_~

_~F

2(1 + R)

1 + R(Only insensitive to R if F2 in relevant (x,Q2)

region was truly measured at = 1)

G0

SOS

HMS

E94-110 Experiment performed at JLab-Hall C

JLab-HALL CJLab-HALL C

Shielded Detector Hut

Superconducting Dipole

Superconducting Quadrupoles

Electron Beam

Target Scattering Chamber

HMS

SOS

Thomas Jefferson National Accelerator Facility

Rosenbluth SeparationsRosenbluth Separations Hall C E94-110: a global survey of longitudinal strength in the resonance region…...

T

L +T

= L T/

(polarization of virtual photon)


Spread of points about the linear fits is Gaussian with ~ 1.6 % consistent with the estimated point-point experimental uncertainty (1.1-1.5%)

a systematic “tour de force”

Hall C E94-110: a global survey of longitudinal strength in the resonance region…...

Rosenbluth SeparationsRosenbluth Separations


World's L/T Separated Resonance DataWorld's L/T Separated Resonance Data

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

R = L/T

<

R = L/T

<


World's L/T Separated Resonance DataWorld's L/T Separated Resonance Data

Now able to study the Q2 dependence of individual resonance regions!

Clear resonant behaviour can be observed!

Use R to extractF2, F1, FL

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

R = L/T

<

R = L/T

E94-110 Rosenbluth Extractions of R E94-110 Rosenbluth Extractions of R ● Clear resonant behaviour is observed in R for the first time!

→ Resonance longitudinal component NON-ZERO.

→ Transition form factor extractions should be revisited.

● Longitudinal peak in second resonance region at lower mass than S 11(1535 MeV)

→ D13(1520 MeV) ? P11(1440 MeV)?

● R is large at low Q high W (low x)

→ Was expected R → 0 as Q2 → 0

→ R → 0 also not seen in recent SLAC

DIS analysis (R1998)

Kinematic Coverage of ExperimentKinematic Coverage of Experiment

● Rosenbluth-type separations where possible (some small kinematic evolution is needed)

● Iteratively fit F2 and R over the entire kinematic range.

2 Methods employed for separating Structure Functions:

R = (d/) =(W

2,Q2) + L(W2,Q2)

Also perform cross checks with elastic and DIS (comparing with SLAC data)

L-T Separated Structure FunctionsL-T Separated Structure Functions

Good agreement between methods ( model available for use!) Very strong resonant behaviour in F

L!

Evidence of different resonances contributing in different channels?


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. Integrated strength (over all ’) is called Bloom-Gilman integral

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

Duality in the F2 Structure Function

’ = 1+W2/Q2

Q2 = 0.5 Q2 = 0.9

Q2 = 1.7 Q2 = 2.4

F 2

F 2


First observed ~1970 by Bloom and Gilman at SLAC

Now can truly obtain F2 structure function data, and compare with DIS fits or QCD calculations/fits (CTEQ/MRST)

Use Bjorken x instead of Bloom-Gilman’s ’

Bjorken Limit: Q2, Empirically, DIS region is

where logarithmic scaling is observed: Q2 > 5 GeV2,

W2 > 4 GeV2

Duality: Averaged over W, logarithmic scaling observed to work also for Q2

> 0.5 GeV2, W2 < 4 GeV2, resonance regime

(note: x = Q2/(W2-M2+Q2) JLab results: Works

quantitatively to better than 10% at such low Q2

Duality in the F2 Structure Function

Numerical Example: Resonance Region F2

w.r.t. Alekhin Scaling Curve(Q2 ~ 1.5 GeV2)


Duality in FDuality in FTT and F and FLL Structure Functions Structure Functions

Duality works well for both FT and FL above Q2 ~ 1.5 (GeV/c)2

MRST (NNLO) + TMMRST (NNLO)

AlekhinSLACE94-110

Also good agreement with SLAC L/T Data


Quark-Hadron Duality

complementarity 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

But why also in limited local energy ranges?

If one integrates over all resonant and non-resonant states, quark-hadron duality should be shown by any model. This is simply unitarity.However, quark-hadron duality works also, for Q2 > 0.5 (1.0) GeV2, to better than 10 (5) % for the F2 structure function in both the N- region and the N-S11 region!(Obviously, duality does not hold on top of a peak! -- One needs an appropriate energy range)

One resonance + non-resonant background

Few resonances + non-resonant background

Why does local quark-hadron duality work so well, at such low energies?

~ quark-hadron transition

Confinement is local ….


Quark-Hadron Duality – Theoretical Efforts

N. Isgur et al : Nc ∞ qq infinitely narrow resonances qqq only resonances

Distinction between Resonance and Scaling regions is spuriousBloom-Gilman Duality must be invoked even in the Bjorken Scaling region

Bjorken Duality

One heavy quark, Relativistic HO

Scaling occurs rapidly!

Q2 = 5

Q2 = 1

F. Close et al : SU(6) Quark ModelHow many resonances does one needto average over to obtain a completeset of states to mimic a parton model?56 and 70 states o.k. for closureSimilar arguments for e.g. DVCS and semi-inclusive reactions

u


Duality ‘’easier” established in Nuclei

The nucleus does the averaging for you!

EMC EffectFe/D

ResonanceRegion Only

( F

e/

D)

IS

(= x corrected for M 0)

Nucleons haveFermi motionin a nucleus


CLAS: N- transition region turns positive at Q2 = 1.5 (GeV/c)2 Elastic and N- transition cause most of the higher twist effects

… but tougher in Spin Structure Functions

g1p

CLAS EG1

Pick up effects of both N and (the is not negative enough….)


Hint of overall negative g1n even in resonance region at Q2 = 1.2 (GeV/c)2

Duality works better for neutron than proton? – Under investigation

… but tougher in Spin Structure Functions (cont.)

g1n

SLAC E143: g1p and g1

d data combined

SummarySummary

Performed precision inclusive cross section measurements in the nucleon resonance region (~ 1.6% pt-pt uncertainties)

R exhibits resonance structure (first observation) Significant longitudinal resonant component observed.

Prominent resonance enhancements in R and FL different from those in transverse and F2 Quark-hadron duality is observed for ALL unpolarized

structure functions. Quarks and the associated Gluons (the Partons) are tightly bound in Hadrons

due to Confinement. Still, they rely on camouflage as their best defense:a limited number of confined states acts as if consisting of free quarks Quark-Hadron Duality, which is a non-trivial property of QCD, telling usthat contrary to naïve expectation quark-quark correlations tend to cancelon average

Observation of surprising strength in the longitudinal channel at Low Q2 and x ~ 0.1


. 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

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

DeRujula, Georgi, Politzer (1977)

QCD and the Operator-Product Expansion

0

1

k=1


Example: e+e- hadrons

Textbook Example

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

R =

E99118

Preliminary: Still R = 0.1 point-to-point(mainly due to bin centering assumptions to x = 0.1)

Model Iteration Procedure Model Iteration Procedure

Starting model is used for input for radiative corrections and in bin-centering the data in θ

σexp is extracted from the data

Model is used to decompose σ exp into F2exp and Rexp

Q2 dependence of both F2 and R is fit for each W2 bin

to get new model

Example SF Iteration Example SF Iteration

Q2

Q2

Measurements at different ε are inconsistent ⇒

started with wrong splitting of strength!

Consistent values of the separated structure functions for all ε !

Iteration results in shuffling of strength

Point-to-Point Systematic Uncertainties for E94-110

Total point-to-Total point-to-point systematic point systematic uncertainty for uncertainty for E94-110 is 1.6%.E94-110 is 1.6%.

Experimental Procedure and CS ExtractionExperimental Procedure and CS Extraction

Cross Section ExtractionCross Section Extraction● Acceptance correct e- yield bin-by-bin (δ, θ).

●Correct yield for detector efficiency.

● Subtract scaled dummy yield bin-by-bin, to remove e- background from cryogenic target aluminum walls.

● Subtract charge-symmetric background from π0 decay via measuring e+ yields.

●bin-centering correction.

● radiative correction.

W2 (GeV2)

Elastic peak not shown

At fixed Ebeam, θc, scan E’ from elastic to DIS. (dp/p =+/-8%, dθ =+/-32 mrad)

Repeat for each Ebeam, θc to reach a range in ε for each W2, Q2.

QCD and the Parton-Hadron Transition

Hadrons Q < s(Q) > 1

Constituent Quarks Q > s(Q) large

Asymptotically Free Quarks Q >> s(Q) small

One parameter, QCD,~ Mass Scale or Inverse Distance Scale where as(Q) = infinity

“Separates” Confinement and Perturbative Regions

Mass and Radius of the Proton are (almost) completely governed by

QCD213 MeV

One parameter, QCD,~ Mass Scale or Inverse Distance Scale where as(Q) = infinity

“Separates” Confinement and Perturbative Regions

Mass and Radius of the Proton are (almost) completely governed by

QCD and the Parton-Hadron Transition

QCD213 MeV

Documents

Measurements of R and the Longitudinal and Transverse Structure Functions in the Nucleon Resonance Region and Quark-Hadron Duality Rolf Ent, DIS2004 -Formalism: