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x>1: Short Range Correlations and “Superfast” Quarks Jlab Experiment 02-019

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x>1: Short Range Correlations and “Superfast” Quarks

Jlab Experiment 02-019

Nadia Fomin

University of Tennessee

User Group Meeting

Jefferson Lab

June 9th, 2010

E02-019 Overview

- Inclusive Scattering only the scattered electron is detected, cannot directly disentangle the contributions of different reaction mechanisms.
- Inclusive Quasielastic and Inelastic Data allows the study of a wide variety of physics topics
- Duality
- Scaling (x, y, ξ, ψ)
- Short Range Correlations – NN force
- Momentum Distributions
- Q2 –dependence of the F2 structure function

- E02-019 ran in Fall 2004
- Cryogenic Targets: H, 2H, 3He, 4He
- Solid Targets: Be, C, Cu, Au.
- Spectrometers: HMS and SOS (mostly HMS)
- Concurrent data taking with E03-103 (EMC Effect – Jason Seely & Aji Daniel)

The inclusive reaction

e-

e-

e-

e-

M*A-1

M*A-1

MA

MA

Same initial state

Different Q2 behavior

DIS

QES

W2=Mn2

W2≥(Mn+Mπ)2

Spectral function

3He

Inclusive Electron Scattering

(x>1)x=1 (x<1)

The quasi-elastic contribution dominates the cross section at low energy loss, where the shape is mainly a result of the momentum distributions of the nucleons

As ν and Q2 increase, the inelastic contribution grows

A useful kinematic variable:

JLab, Hall C, 1998

Fraction of the momentum carried by the struck parton

A free nucleon has a maximum xbj of 1, but in a nucleus, momentum is shared by the nucleons, so 0 < x < A

Deuterium

- Usually, we look at x>1 results in terms of scattering from the nucleon in a nucleus and they are described very well in terms of y-scaling (scattering from a nucleon of some momentum)
- Quasielastic scattering is believed to be the dominant process

Deuterium

- Usually, we look at x>1 results in terms of scattering from the nucleon in a nucleus and they are described very well in terms of y-scaling (scattering from a nucleon of some momentum)
- Quasielastic scattering is believed to be the dominant process

Short Range Correlations => nucleons with high momentum

Independent Particle Shell Model :

For nuclei, Sα should be equal to 2j+1 => number of protons in a given orbital

However, it as found to be only ~2/3 of the expected value

The bulk of the missing strength it is thought to come from short range correlations

- NN interaction generates high momenta (k>kfermi)
- momentum of fast nucleons is balanced by the correlated nucleon(s), not the rest of the nucleus

Short Range Correlations

2N SRC

Deuteron

3N SRC

Carbon

NM

Short Range Correlations

- To experimentally probe SRCs, must be in the high-momentum region (x>1)

- To measure the probability of finding a correlation, ratios of heavy to light nuclei are taken
- In the high momentum region, FSIs are thought to be confined to the SRCs and therefore, cancel in the cross section ratios

P_min (GeV/c)

x

Short Range Correlations – Results from CLAS

Egiyan et al, Phys.Rev.C68, 2003

No observation of scaling for Q2<1.4 GeV2

Egiyan et al, PRL 96, 2006

18° data

Q2=2.5GeV2

18° data

Q2=2.5GeV2

R(A, D)

18° data

Q2=2.5GeV2

4He

R E02-019 NE3

3.87±0.12

56Fe

5.38±0.17

3He

3He

12C

12C

Can extract value of plateau – abundance of correlations compared to 2N correlations in 3He

2N correlations in ratios to 3He

A measure of probability of finding a 2N correlation:

Recently learned that this correction is probably not necessary (pn >>pp)

In the example of 3He:

Hall B results (2003) E02-019

statistical errors only

Q2 (GeV2)

CLAS: 1.4-2.6

E02-019: 2.5-3

- Excellent agreement for x≤2
- Very different approaches to 3N plateau, later onset of scaling for E02-019
- Very similar behavior for heavier targets

Q2 (GeV2)

CLAS: 1.4-2.6

E02-019: 2.5-3

For better statistics, take shifts on E08-014

- Excellent agreement for x≤2
- Very different approaches to 3N plateau, later onset of scaling for E02-019
- Very similar behavior for heavier targets

- E02-019 ran in Fall 2004
- Cryogenic Targets: H, 2H, 3He, 4He
- Solid Targets: Be, C, Cu, Au.
- Spectrometers: HMS and SOS (mostly HMS)
- Concurrent data taking with E03-103 (EMC Effect – Jason Seely & Aji Daniel)

On the higher Q2 side of things

2.5<Q2<7.4

2.5<Q2<7.4

Au

Jlab, Hall C, 2004

F2A

x

ξ

- In the limit of high (ν, Q2), the structure functions simplify to functions of x, becoming independent of ν, Q2.
- As Q2∞, ξx, so the scaling of structure functions should also be seen in ξ, if we look in the deep inelastic region.
- However, the approach at finite Q2 will be different.
- It’s been observed that in electron scattering from nuclei, the structure function F2, scales at the largest measured values of Q2 for all values of ξ

SLAC, NE3

Jlab, E89-008

Q2 -> 0.44 - 2.29 (GeV/c2)

Q2 -> 0.44 – 3.11(GeV/c2)

- Interested in ξ-scaling since we want to make a connection to quark distributions at x>1
- Improved scaling with x->ξ, but the implementation of target mass corrections (TMCs) leads to worse scaling by reintroducing the Q2 dependence

ξ-scaling: is it a coincidence or is there meaning behind it?

- Interested in ξ-scaling since we want to make a connection to quark distributions at x>1
- Improved scaling with x->ξ, but the implementation of target mass corrections (TMCs) leads to worse scaling by reintroducing the Q2 dependence
- TMCs – accounting for subleading 1/Q2 corrections to leading twist structure function

Following analysis discussion focuses on carbon data

From structure functions to quark distributions

- 2 results for high x SFQ distributions (CCFR & BCDMS)
- both fit F2 to e-sx, where s is the “slope” related to the SFQ distribution fall off.
- CCFR: s=8.3±0.7 (Q2=125 GeV/c2)
- BCMDS: s=16.5±0.5 (Q2: 52-200 GeV/c2)

- We can contribute something to the conversation if we can show that we’re truly in the scaling regime
- Can’t have large higher twist contributions
- Show that the Q2 dependence we see can be accounted for by TMCs and QCD evolution

CCFR

BCDMS

How do we get to SFQ distributions

- We want F2(0), the massless limit structure function as well as its Q2dependence

Schienbein et al, J.Phys, 2008

- Step 1 – obtain F2(0)(x,Q2)
- Choose a data set that maximizes x-coverage as well as Q2
- Fit an F2(0), neglecting g2 and h2 for the first pass
- Use F2(0)-fit to go back, calculate and subtract g2,h2, refit F2(0), repeat until good agreement is achieved.

- Step 2 – figure out QCD evolution of F2(0)
- Fit the evolution of the existing data for fixed values of ξ (no good code exists for nuclear structure evolution, it seems)

θHMS

Q2(x=1)

Cannot use the traditional W2>4GeV/c2 cut to define the DIS region

Don’t expect scaling around the quasielastic peak (on either side of x=1)

- Fit log(F20) vs log(Q2) for fixed values of ξ to
- p2,p3 fixed
- p1 governs the “slope”, or the QCD evolution.
- fit p1 vs ξ

ξ=0.5

ξ=0.75

Q2

- Use the QCD evolution to redo the F20 fit at fixed Q2 and to add more data (specifically SLAC)

P1 parameter vs ξ, i.e. the QCD evolution

F20 fit with a subset of E02-019 and SLAC data

Final fit at Q2=7 GeV2

Putting it all Together

- With all the tools in hand, we apply target mass corrections to the available data sets
- With the exception of low Q2 quasielastic data – E02-019 data can be used for SFQ distributions

E02-019 carbon

SLAC deuterium

BCDMS carbon

Putting it all Together

- With all the tools in hand, we apply target mass corrections to the available data sets
- With the exception of low Q2 quasielastic data – E02-019 data can be used for SFQ distributions

E02-019 carbon

SLAC deuterium

BCDMS carbon

| CCFR projection

(ξ=0.75,0.85,0.95,1.05)

Final step: fit exp(-sξ) to F20 and compare to BCDMS and CCFR

BCDMS

CCFR

CCFR – (Q2=125GeV2)

s=8.3±0.7

BCDMS – (Q2: 52-200 GeV2)

s=16.5±0.5

s=15.05±0.5

All data sets scaled to a common Q2 (at ξ=1.1)

Summary

- Short Range Correlations
- ratios to deuterium for many targets with good statistics all the way up to x=2
- different approach to scaling at x>2 in ratios to 3He than what is seen from CLAS
- Future: better/more data with 3He at x>2 in Hall A (E08-014)

- “Superfast” Quarks
- Once we account for TMCs and extract F20 – we find our data is in the scaling regime and can be compared to high Q2 results of previous experiments
- appears to support BCDMS results
- TO DO: check our Q2 dependence against pQCD evolution
- Follow-up experiment approved with higher energy (E12-06-105)

Greater disagreement in ratios of heavier targets to 3He

Show?

F2A for all settings and most nuclei for E02-019