# Presentation: 656920

## Measurement of spin structure functions with CLAS at Jefferson Lab

*Vipuli Dharmawardane*

-                       OUTLINE
- Formalism and experimental setup
- What can we learn at Jefferson Lab kinematics?
- Q2 evolution of SSFs in and above the resonance region
- Spin physics at large *x*
- Quark-hadron duality
- Spin structure of nuclei?

## Inclusive electron scattering

-   =  -1

-   = +1

-  = 0

-  = - 1⁄2

- Virtual photon         Nucleon

- Virtual photon asymmetries

## Double polarized inclusive electron scattering

- Longitudinally polarized beam and target

*F**1*

*Unpolarized structure function*

## Continuous Electron Beam Accelerator Facillity (CEBAF)

**A**

**C**

**B**

- Superconducting accelerator provides beams of unprecedented quality, with energies up to 6 GeV.

- Continuous Electron Beam Accelerator Facillity (CEBAF)

- Typical beam polarization ~80%

- Each of the three halls offers complementary experimental capabilities and allows for large equipment installations to extend scientific reach.

## Continuous Electron Beam Accelerator Facillity (CEBAF)

**A**

**C**

**B**

- Superconducting accelerator provides beams of unprecedented quality, with energies up to 6 GeV.

- Continuous Electron Beam Accelerator Facillity (CEBAF)

- Typical beam polarization ~80%

**HALL A**
- Two high-resolution 4 GeV spectrometers
**HALL B**
- Large acceptance spectrometer electron/photon beams
**HALL C**
- 7 GeV spectrometer, 1.8 GeV spectrometer,
- large installation experiments

**CLAS**

## Jefferson Lab after the energy upgrade

- Ten-fold increase in luminosity for large-acceptance electron beam measurements

- Double the beam energy

- CLAS12

## CEBAF Large Acceptance  Spectrometer (CLAS)

- Drift
- chambers

- Cerenkov
- counters

- em. calorimeters

- TOF
- counters

- CEBAF Large Acceptance  Spectrometer (CLAS)

**Event in CLAS**

- Depending on the torus field electrons bend inward or outward

- Large kinematical coverage
- Detection of charged and neutral particles
- Multi particle final states

**Notes:**
Include CLAS

## Polarized target

- Polarized NH3 and ND3
- 5 Tesla Magnetic field
- 1K LHe cooling bath
- 12C and He targets to measure target dilution factor

- Target insert

- Target insert houses four cells
- Each of the four cells is moved onto the electron beam using a stepping motor

**Ammonia**
**beads**

## Target polarization

- Beam was rastered over 12 mm diameter at the center **→** Only this portion was depolarized by beam-induced radiation damage
- NMR coils are located on the outside of the cell  **→** Primarily sensitive to the polarization of material outside the beam spot

- NMR coil

- 12 mm

- 15 mm

- Target polarization was extracted using data
- For elastic scattering A|| is known
*Donnelly and Raskin Ann. Phys., 169 247 (1986)*

- deuteron

- _For deuteron_
- quasi-elastic peak

- proton polarization 70-80 % deuteron polarization 25-35%

## Background subtraction

- a and b were determined by fitting limited statistic 15N data with high statistic 12C data

- Fit to 15N data

- Second target insert was used to collect data on solid 15N

## Asymmetry analysis

- Models
-  A2 →  Wandzura-Wilczek relation in the DIS region and the code MAID 2000 in the resonance region
-  F1 → Fit to world data

- A2

- unmeasured

- 0.27 < Q2(GeV2) < 0.32

## Experimental status of SSF g1

*Interesting physics in this relatively unmeasured region*

**JLAB**

- Existing data → Large Q2, small to moderate x
- JLab → Large x precision measurements
- JLab → Spin structure in non-perturbative regime

**JLAB**
**@ 6 GeV**

**JLAB**
**@ 12 GeV**

## Spatial resolution of virtual photon

- Structure we observe by probing the nucleon by the virtual photon depends on the virtuality or Q2 of the photon

-          **small distances              medium distances           large distances**
**       ****elementary quarks        constituent quarks              Nucleon**

- Deep Inelastic Scattering

- λ

- Q2

- Inelastic electron nucleon scattering can be viewed as the incoherent elastic scattering of the electron from free quarks withing the nucleon

## Inclusive Electron Scattering

- Need to measure exclusive processes in full phase space to separate resonances from each other and from non-resonant contributions.

- N**’**

- Resonances are spin or momentum excited states of the nucleon
- Three major resonance regions
- About 20 known resonances

- e

- e’

**Notes:**
Change this

## Resonance region

- For a resonance A1 and g1 can be written in terms of helicity amplitudes

- Transition matrix elements between the ground nucleon state and the 3-quark configuration

-   **CLAS**
**Preliminary**

- PhD
- Thesis
- K. Park

- For a resonance

- N**’**

## Virtual photon asymmetry A1 : resonance region 

- Virtual photon asymmetry A1 : resonance region

- N(1520)

- Rapid change of helicity structure from A3/2 dominance at small Q2 to A1/2 dominance at high Q2

- For a resonance

## Virtual photon asymmetry A1 : resonance region 

- (1232)

- A 1  = -0.5

- M 1+

- Pure magnetic dipole transition

- N                    (1232)

- SU(6) → Pure spin flip

- Virtual photon asymmetry A1 : resonance region

## g1

- Spin structure function g1 for the proton

- g1

- x

- Q2 = 0.0592

- Q2 = 0.0844

- Q2 = 0.12

- Q2 = 0.171

- Q2 = 0.244

- Q2 = 0.292

- Q2 = 0.348

- Q2 = 0.416

- Q2 = 0.496

- Q2 = 0.592

- Q2 = 0.707

- Q2 = 1.2

- Q2 = 1.44

- Q2 = 2.05

- Q2 = 2.92 (GeV2)

## 27 Q2 bins

- Spin structure function g1 for the proton

- g1

- x

- Q2 = 0.0592

- Q2 = 0.0844

- Q2 = 0.12

- Q2 = 0.171

- Q2 = 0.244

- Q2 = 0.292

- Q2 = 0.348

- Q2 = 0.416

- Q2 = 0.496

- Q2 = 0.592

- Q2 = 0.707

- Q2 = 1.2

- Q2 = 1.44

- Q2 = 2.05

- Q2 = 2.92 (GeV2)

- 27 Q2 bins
- Q2 = 0.045-5.4 GeV2

## First moment of g1(x,Q2)

- GDH Sum rule

- Closely related to the  spin carried by quarks

- First moment of g1(x,Q2)

- Bjorken Sum Rule

- Elastic contribution excluded

-                   Q2→∞
- Single partons

- pQCD

- Q2 = 0

- GDH slope

- Negative slope

**Dominated by baryon resonance excitations**

*?*

**Notes:**
Change the G1 plot

## Generalized sum rules for 1

- Spin structure function
- g1(x,Q2)  is related to the forward virtual compton scattering amplitude S1

- Parton description
- Operator Product Expansion

- Hadron description
-    Inelastic part of S1

*c* calculable in PT

- Transition between parton and hadron degrees of freedom
**→ **calculable in Lattice QCD

- Calculable         Measurable
- Includes the elastic contribution

- (X. Ji *et al*., J. Phys. G **27**, 127)

- Q2

## First moment 1 for the proton and deuteron

- First moment 1 for the proton and deuteron

- DIS (unmeasured)   Parameterization of world data

- PROTON

- DEUTERON

- Q2 (GeV2)

- 1

- Phenomenological Models
-  Burkert/Ioffe
-             Resonance contribution pion electroproduction analysis
-  Soffer/Teryaev
-             Interpolation of the integral    (g1+g2)dx

- without elastic
- contribution

##   Γ1 for the proton : low Q2

-   Γ1 for the proton : low Q2

- Expand in chiral perturbation theory in a power series of pion mass

- Calculations at next-to-leading order in momenta

- Ji and Osborne (HBPT)

- GDH
- Slope

- 1

- New experiment
- Data taken in 2006

## Spin structure function g1 in DIS 

- Gluon radiation

- Q2

- Q2 → ∞   quarks behave as free particles

- At finite but large Q2 _additional corrections_
- Describable in pQCD
- Distribution functions in DGLAP equations
- Slow logarithmic Q2 dependence

- At moderate Q2  _higher twist effects_
- Interactions between the struck quark and the other quarks in the nucleon
- Inversely proportional to Q2  →  large at small Q2

**+**

## Higher twist effects

- At JLab kinematics higher twist effects are non-negligible

- hTMC are calculable target mass corrections

- Non-perturbative effect and cannot be calculated in a model independent way
- Extract *h *and polarized parton distributions by fitting data
*Analysis performed by Leader, Sidorov and Stamenov (**LSS**) hep-ph/0612360*

- Leading Twist contribution to g1

- Q2 dependence in DGLAP equations

*hep-ph/0612360*

## Higher twist effects

- Improvement in small x @ 12 GeV

- At JLab kinematics higher twist effects are non-negligible

- hTMC are calculable target mass corrections

- Non-perturbative effect and cannot be calculated in a model independent way
- Extract *h *and polarized parton distributions by fitting data
*Analysis performed by Leader, Sidorov and Stamenov (**LSS**) hep-ph/0612360*

- Leading Twist contribution to g1

- Q2 dependence in DGLAP equations

## Q2 dependence of g1/F1

- g1/F1 ratio relatively Q2 independent → Q2 dependence of g1 at fixed x is very similar to F1 in the DIS region

- W = 2 GeV

- No DIS data at large x !

- Q2 dependence of g1/F1

- In DIS, both g1 and F1 show logarithmic Q2 dependence

- _In the resonance region_
- different Q2 dependence
- goes negative at 

## Why study large x ?

- Highest x accessible (DIS) with 6 GeV beam ≈ 0.6
- At 12 GeV can go upto x ≈ 0.8

- HEP data base:
- CTEQ6M parameterization
- Q2 = 8 GeV2

- Valence quarks dominate at large x

- uv

- dv

- Proton

- Deuteron

- AAC parametrization

- DIS

## Virtual photon asymmetry A1 at large x : Theory

- Virtual photon asymmetry A1 at large x : Theory

- Minimal gluon exchanges
- Spectator pair have opposite helicities
-               dominant   A1 → 1
*Farrar and Jackson  PRL  35, 1416 (1975)*

- _x → 1 in pQCD_

- _Hyperfine perturbed quark model_
- makes *S=1* pairs  more energetic than *S=0* pairs
- At large x struck quark carry the spin of the nucleon
-  *N.  Isgur, Phys. Rev. D 59, 34013*

- _SU(6) quark model_

- _Duality_
- suppress transitions to specific resonances in the final state
*Close and Melnitchouk, Phys. Rev. C 68, 035210*

- HFP quark model

- /2

- S1/2

- Symmetric WF

*S=1* and *S=0* equi-probable

## Virtual photon asymmetry A1 

- Virtual photon asymmetry A1

- Hyperfine perturbed QM

- Duality

- World data parameterized at Q2=10 GeV2

- Jlab/
- Hall B

- Proton and deuteron results are in better agreement with the HFP quark model

## Projected errors : 12 GeV upgrade

## Polarized parton distributions at large x

- naïve LO analysis

|  | d/u | u/u | d/d |
| --- | --- | --- | --- |
| SU(6) | 1/2 | 2/3 | -1/3 |
| HFP quark model | 0 | 1 | -1/3 |
| pQCD | 1/5 | 1 | 1 |

- JLab Hall A and Hall B results for d/d _show no indication of a sign change_
- Disagree with pQCD predictions (assumes hadron helicity conservation)

- Not well known at large x

## Polarized parton distributions at large x

|  | d/u | u/u | d/d |
| --- | --- | --- | --- |
| SU(6) | 1/2 | 2/3 | -1/3 |
| HFP quark model | 0 | 1 | -1/3 |
| pQCD | 1/5 | 1 | 1 |

- Not well known at large x

- pQCD

- 1

- -1⁄3

- Hyperfine-perturbed
- Quark model

## NLO analysis of data

- Spin of the nucleon

- NLO analysis (AAC06)
- →  ≈ (27±7) %

*Phys. Rev. D74,*
*14015 (2006)*

- Quark polarization

## Gluon polarization

- g through Q2 evolution

- All DIS data up to 2006 + recent RHIC data (PHENIX)

*Phys. Rev. D74,*
*14015 (2006)*

- (AAC06) fit

- 03

- AAC03G = 0.5±1.27

- AAC06 G = 0.31±0.32

- All DIS data up to 2003

## NLO analysis of CLAS data

- Large increase in the Q2-lever arm allows for a great improvement on the precision of G

*hep-ph/0612360*

- After including CLAS data

- Central values of distributions agree with existing world data

- At JLab kinematics _higher twists are non negligible_

- xg

## Projected errors : 12 GeV upgrade

- Large increase in the Q2-lever arm allows for a great improvement on the precision of G

- xg

- 12 GeV projected errors

- At JLab kinematics _higher twists are non negligible_

## The quark structure of nuclei

- Inclusive electron scattering

- Is the proportion of the spin contributed by its constituents change as the environment around nucleons change ?

- Spin of the nucleon

##   Observation that structure functions are altered in nuclei stunned much of the HEP community 23 years ago

**x**

- Origin of the EMC effect

*Demonstrate the change in the quark gluon structure of the nucleon in medium*

- valence quarks dominate

- x > 0.3: A valence quark in a bound nucleon has less momentum than in a free one

## Is the EMC effect a valence 

- Best probe of the sea :
- Drell-Yan experiments

***no clear excess of anti-quarks in nuclei***

- E772

*Is the EMC effect a valence *
*quark phenomenon or *
_*are sea quarks involved?*_

## EMC Effect - Theoretical Explanations

- Multi-quark clusters              dynamical rescaling         combination of Fermi motion
-                                                                                        + nucleonic and pionic d.o.f

- No unambiguously accepted explanation of the EMC effect !

- What is it that alters the quark momentum in the nucleus?

- More than 1000 papers

## The polarized EMC effect : Theory

- Quark-Meson Coupling Model

- Polarized
-  g1p|A/g1p

- Unpolarized

- Valence only

- Valence + Sea

- Chiral Quark-Soliton model

- Valence only

*Cloet, Bentz and Thomas*
*Phys. Rev. Lett.95, 052302 (2005)*

*Smith and Miller*
*Nucl-th/0505048*

- Nuclear matter

- sensitive to quark polarization degrees of freedom

## The polarized EMC effect : Theory

- Valence only calculations consistent with Cloet, Bentz, Thomas calculations
- Same model shows small effects due to sea quarks for the unpolarized case (consistent with data)

- Large enhancement for
- x < 0.3 due to sea quarks

- Sea is not much modified

## Can we measure it?

- Spin-independent case
- Spin-dependent case :
-  Only few (valence) nucleons contribute to nuclear polarization
- Have to do calculations for finite nuclei

- Can scale nuclear matter results

- For J > 1⁄2 new kinds of structure functions appear
*In the Bjorken limit *

*2J+1* quark distributions and structure functions

## Quark distributions in 11B

- Quark distributions in 11B

**multipole structure functions**

*Cloet et al.,*
*Phys. Lett. B642:210 (2006) *

*K* = 1 spin-dependent distributions

*K* = 3 spin-dependent distributions

- Higher multipole distributions are greatly suppressed relative to the leading results

## EMC effect in nuclei : Theory

- unpolarized

- Polarized

*Cloet et al.,*
*Phys. Lett. B642:210 (2006) *

- A dependence of polarized quark distributions

- Helicity 3/2 of the nucleus

- K=1 multipole

- Medium modifications lead to a decrease of the fraction of the spin carried by quarks

## 7LiH as a polarized target

- How to go from g17Li to g1p|7Li ?

- _Shell model_

*Need to know the Polarization of the proton in **7**Li*

- combination of 1 unpaired proton + 2 paired neutrons and a _closed S__1/2__ shell_

- _Cluster model_

- S = 1/2 triton orbiting in an L=1 state about the a cluster

- Net 57% polarization of the proton in 7Li

- Green’s function Monte Carlo algorithm ≈ 59%

## Projected errors 

- Projected errors

- Assumes 11 GeV beam, 40% target polarization, 80% beam polarization and running for 70 days

- Systematic error target is < 5%

## SUMMARY

- With 12 GeV, poised to make a brilliant contribution to our understanding of the Physics of nucleon and Nuclei:
-  Ideally equipped to study the large *x* region and solve the 23-year-old problem of the EMC effect

- A broad physics program to study the spin structure of the proton,  neutron and their excited states in progress at Jefferson Lab
- Unprecedented quality of recent data pushing theory to new frontiers
- Glimpse into unexplored large *x* region of valence quarks
- No sign of hadron helicity conservation in *x*→1 dependence
- JLab@12GeV will resolve 30 year old question about *x*→1 behavior of parton distributions

## ADDITIONAL SLIDES

## Target polarization

- NMR coil

- 12 mm

- 15 mm

- proton

- Comparison with NMR measurements

- anneal

- Annealing the target repairs most of the beam-induced radiation damage

- proton polarization 70-80 % deuteron polarization 25-35%

## Quark-hadron duality

- Complimentarity between quark and hadron description of observables

- Electroproduction of resonances at lower momentum transfers averages smoothly around the scaling curve measured at large momentum transfers
-  Bloom and Gilman PRL 25, 1140 (1970)

- Nachtmann scaling variable

- _Average_ over (strongly Q2 dependent) resonances
-  ≈ Q2 independent scaling function

## Duality and the OPE

- Duality can be understood from an _Operator Product Expansion_ of moments of structure functions

- If F rises above scaling value it must fall at neighboring region to compensate in the moments

- Duality is described in OPE as higher twist effects being small or canceling

- Leading twist

- Higher twists

- Expand moments of structure functions in powers of 1/Q2

- JLab/HallC

## Duality in the g1 structure function

## Duality : Integrated strength

- Q2 (GeV2)

- + elastic

- Scaling curve NLO fits

- The application of OPE requires summing over all final hadronic states

- Does duality work for elastic + resonance region ?

- Local duality : Restricted regions in W

- Including the elastic contribution with the entire resonance region works better

- Elastic and N- transition cause most of the HT effects

## Applications of duality

- If duality works (higher twists are small)
- Properly averaged resonance data can be used to extract leading twist parton distributions
- Duality provides extended access to large x regime
- If duality is violated, and if violations are small
- Can use duality violations to extract higher twist matrix elements
- Learn about non-perturbative quark-quark or quark-gluon correlations

## Double polarized inclusive electron scattering

- Pe

- Pt

- Nucleon

****

- Electron asymmetry

-  Longitudinally and transversely  polarized  targets
- Longitudinally polarized beam
- Inclusive electron scattering

## Experimental Halls

- Each of the three halls offers complementary experimental capabilities and allows for large equipment installations to extend scientific reach.

## Deuteron as a proton+neutron target

- Deuteron can be in a S state or a D state
- In the S state the spin of the proton and the neutron are aligned with the deuteron spin
- The probability of being in the D state ≈ 0.056

## Virtual photon asymmetry A1 

- Virtual photon asymmetry A1

- (1232)

- E 1+ = S 1+ = 0

- M 1+

- Pure magnetic dipole transition

- N                    (1232)

- SU(6) → Pure spin flip

## 1 kinematic coverage

- DIS (unmeasured)   Parameterization of world data

- without elastic
- contribution

- 1 kinematic coverage

- 12 GeV

- 6 GeV

## Chiral perturbation theory

- When the quarks are massless
- QCD lagrangian is Chiral symmetric
-         Right or left handed quarks
-         will retain their handedness

- This exact chiral invariance is spontaneously broken by small quark mass terms allowing left and right handed quarks to mix
-          induce light
-          pseudo-Goldstone bosons

- This allows one to make corrections to the chiral symmetry predictions in a perturbative manner

## World Data on F2p

**World Data on F****2****p**

**World Data on g****1****p**

- In DIS, both g1 and F1 show logarithmic Q2 dependence

## A1 at large x : Duality predictions

- suppress transitions to specific resonances in the final state
-                               states in 56+ and 70-

## NLO analysis of data (AAC)

## Polarized parton distributions at large x

|  | d/u | u/u | d/d |
| --- | --- | --- | --- |
| SU(6) | 1/2 | 2/3 | -1/3 |
| HFP quark model | 0 | 1 | -1/3 |
| pQCD | 1/5 | 1 | 1 |

- Not well known at large x

- no OAM

- with OAM

- BBS/LSS

## Polarized parton distributions at large x

- BBS/LSS without OAM

- BBS/LSS with OAM

- PDF measurements at large x may provide additional information on quark OAM

## QCD and the Parton-Hadron Transition

-  Free Quarks
-             Q >> 
******s**(Q) small

- One parameter, QCD,
- ~  Mass Scale or
-     Inverse Distance Scale
-     where as(Q) = 1
- “Separates” Confinement
-   and Perturbative Regions

- QCD213 MeV

## The polarized EMC effect : Theory

-     *Mainly two groups working on theory*
- Quark-Meson Coupling Model (QMC)           quarks in nucleons (MIT bag, NJL) exchange mesons with nuclear medium
- Chiral Quark Soliton Model (CQSM)              quarks in nucleons (soliton) exchange infinite pairs of pions, vector mesons with nuclear medium,sea

## 7LiH as a polarized target

- Both Li and H are polarized
- 6 GeV polarized target : NMR measurements unreliable

- Use proton elastic data to determine 7Li polarization
- use Equal Spin Temperature theory

- Systematic error 6-7 % on g1