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

A long, long time ago….in Hall C at JLab

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

22*1

22

)(),('

kMpMMArg

ArgEkSdEkddEd

d

AA

iei

QE

),('

),(2,1 EkSdEWkd

dEd

di

npDIS

Spectral function

Same initial state

Different Q2 behavior

e-

e-

MA

M*A-1

QESW2=Mn

2

e-

e-

MA

M*A-1

DIS

W2≥(Mn+Mπ)2

3He

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

Inclusive Electron Scattering

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

JLab, Hall C, 1998

pbj M

Qx

2

2

A useful kinematic variable:

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

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

||

22

2

)(2

)()(

1),(

y

np

kdkkn

qyMNZdd

dyF

q

q

Deuterium

22*1

22

)(),('

kMpMMArg

ArgEkSdEkddEd

d

AA

iei

QE

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

||

22

2

)(2

)()(

1),(

y

np

kdkkn

qyMNZdd

dyF

q

q

22*1

22

)(),('

kMpMMArg

ArgEkSdEkddEd

d

AA

iei

QE

Short Range Correlations => nucleons with high momentum

Independent Particle Shell Model :

S 4 S(Em, pm )pm2 dpm(Em E )

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

2N SRC3N SRC

Short Range Correlations

Deuteron

CarbonNM

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

A

jjj QxAa

jAQx

1

22 ),()(1

),(

),()(2

222 QxAa

A

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....),()(

32

33 QxAaA

)(2

2 AaA D

A

)(3

33

AaA

He

A

P_ m

in (

GeV

/c)

x

Egiyan et al, PRL 96, 2006

Short Range Correlations – Results from CLAS

Egiyan et al, Phys.Rev.C68, 2003

No observation of scaling for Q2<1.4 GeV2

E02-019: 2N correlations in ratios to Deuterium

18° data

Q2=2.5GeV2

E02-019: 2N correlations in ratios to Deuterium

18° data

Q2=2.5GeV2

R(A, D)3He 2.08±0.014He 3.44±0.02

Be 3.99±0.04

C 4.89±0.05

Cu 5.40±0.05

Au 5.37±0.06

A/D Ratios: Previous Results

18° data

Q2=2.5GeV2

R E02-019 NE33He 2.08±0.014He 3.44±0.02

Be 3.99±0.04

C 4.89±0.05

Cu 5.40±0.05

Au 5.37±0.06

3.87±0.12

5.38±0.17

4He

56Fe

E02-019 2N Ratios

3He

12C

3He

12C

W

MW

M

Mq 22 41

2

22

2N correlations in ratios to 3He

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

A measure of probability of finding a 2N correlation:

)(

)(),(),(

112

2212121

Np

Np

NZA

NZAAARAAr

In the example of 3He:

)(3

)2(),(),(

11

131

31

Np

Np

NZ

AHeARHeAr

Hall B results (2003) E02-019

statistical errors only

2N correlations in ratios to 3He

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

E02-019 Ratios

• 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

E02-019 Ratios

• 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

E02-019 Kinematic coverage

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)

Au

Jlab, Hall C, 2004

x ξ

F2A

)4

11(

2

2

22

QxM

x

• In the limit of high (ν, Q2), the structure functions simplify to functions of x, becoming independent of ν, Q2.

• As Q2 ∞, ξ x, 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

2.5<Q2<7.42.5<Q2<7.4

On the higher Q2 side of things

Jlab, E89-008

SLAC, NE3

Q2 -> 0.44 – 3.11(GeV/c2)

Q2 -> 0.44 - 2.29 (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?

)4

11(

2

2

22

QxM

x

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

)4

11(

2

2

22

QxM

x

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

)(12

)(6

)(),( 254

44

242

32)0(

232

22

2

grQ

xMh

rQ

xMF

r

xQxF TMC

Schienbein et al, J.Phys, 2008

1

2

2)0(22

2

),(),(

u

QuFduQh

1

2

2)0(22

2

),()(),(

v

QvFvdvQg

• We want F2(0), the massless limit structure

function as well as its Q2 dependence

How do we get to SFQ distributions

Iterative Approach

• 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)

Q2(x=1) θHMS

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)

Q2

• 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

3/)log(2 2

211)log(0 pQeppQp

• Use the QCD evolution to redo the F2

0 fit at fixed Q2 and to add more data (specifically SLAC)

ξ=0.5

ξ=0.75

F20 fit with a subset of E02-

019 and SLAC data

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

Final fit at Q2=7 GeV2

• 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)

Putting it all Together

Final step: fit exp(-sξ) to F20 and

compare to BCDMS and CCFR

s=15.05±0.5

CCFR

BCDMS

CCFR – (Q2=125GeV2)

s=8.3±0.7

BCDMS – (Q2: 52-200 GeV2)

s=16.5±0.5

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

Analysis repeated for other targets

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