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Transition from QES to DIS at x>1 (Jlab Experiment 02-019). Nadia Fomin University of Tennessee Hall C Summer Workshop August 27 th , 2010. E02-019 Overview.

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Transition from QES to DIS at x>1 (Jlab Experiment 02-019)

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Transition from QES to DIS at x>1

(Jlab Experiment 02-019)

Nadia Fomin

University of Tennessee

Hall C Summer Workshop

August 27th, 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 Jefferson Lab

  • 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


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


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)


A/D Ratios: Previous Results

18° data

Q2=2.5GeV2

4He

R E02-019 NE3

3.92±0.14

56Fe

5.10±0.07

5.42±0.19

Plots by D. B. Day


E02-019 2N Ratios

3He

3He

12C

12C


2N correlations in ratios to 3He

Hall B (statistical errors only)

E02-019


Connection between EMC effect and SRC ratios?


Connection between EMC effect and SRC ratios?

  • Very similar behavior with A, including 9Be

  • Future experiments will further fill in this map


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

E02-019 Ratios

For better statistics at x>2.5, take shifts on Jlab 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


Coming soon to Hall A: x>2

  • 2H

  • 3He

  • 4He

  • 12C

  • 40Ca

  • 48Ca


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)


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 – incoherent sum of quark distributions

  • 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


SLAC, NE3

Jlab, E89-008

Q2 -> 0.44 - 2.29 (GeV/c2)

Q2 -> 0.44 – 3.11(GeV/c2)


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


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


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

Measured structure function

  • We want F2(0), the scaling limit (Q2→∞)structure function as well as its Q2dependence

Schienbein et al, J.Phys, 2008


Iterative Approach

  • Step 1 – obtain F2(0)(ξ,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 Q2 dependence of F2(0)

    • Fit the evolution of the existing data for fixed values of ξ


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 ξto

  • p2,p3 fixed

  • p1 governs the “slope”, or the QCD evolution.

  • fit p1 vs ξ

ξ=0.5

ξ=0.75

Q2

  • Use the extracted Q2 dependence to redo the F20 fit at fixed Q2 and to add more data (specifically SLAC)


P1 parameter vs ξ, i.e. the Q2 dependence

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

Final fit at Q2=7 GeV2


E02-019 carbon

SLAC deuterium

BCDMS carbon

| CCFR projection

(ξ=0.75,0.85,0.95,1.05)

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

Submitted to Phys.Rev. Lett

[arXiv:1008.2713]


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


Analysis repeated for other targets

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

Submitted to Phys.Rev. Lett

[arXiv:1008.2713]


x >1 at 12 GeV (E12-06-105)

  • 2H

  • 3He

  • 4He

  • 6,7Li

  • 9Be

  • 10,11B

  • 12C

  • 40Ca

  • 48Ca

  • Cu

  • Au


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 (in progress)

    • Follow-up experiment approved with higher energy (E12-06-105)


Connection between EMC effect and SRC ratios?


Connection between EMC effect and SRC ratios?


Greater disagreement in ratios of heavier targets to 3He

Show?


F2A for all settings and most nuclei for E02-019


  • 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

Deuterium


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