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

2. E 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

3. A long, long time ago….in Hall C at Jefferson Lab
E 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 E (EMC Effect – Jason Seely & Aji Daniel)

4. The inclusive reactionMA
M*A-1 e- MA
M*A-1
Same initial state
Different Q2 behavior
DIS
QES
W2=Mn2
W2≥(Mn+Mπ)2
Spectral function
3He

5. 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

6. 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

7. Short Range Correlations => nucleons with high momentum
Independent Particle Shell Model :
For nuclei, Sα should be equal to 2j => 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

8. Short Range Correlations
2N SRC
3N SRC
Deuteron
Carbon NM

9. 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

10. 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

11. E02-019: 2N correlations in ratios to Deuterium
18° data
Q2=2.5GeV2

12. E02-019: 2N correlations in ratios to Deuterium
18° data
Q2=2.5GeV2
R(A, D)
3He
2.08±0.01
4He
3.47±0.02 Be
4.03±0.04 C
4.95±0.05 Cu
5.48±0.05 Au
5.43±0.06

13. A/D Ratios: Previous Results
18° data
Q2=2.5GeV2
4He
R E NE3
3He
2.08±0.01
4He
3.47±0.02 Be
4.03±0.04 C
4.95±0.05 Cu
5.48±0.06 Au
5.43±0.06
3.92±0.14
56Fe
5.10±0.07
5.42±0.19
Plots by D. B. Day

14. E N Ratios
3He
3He
12C
12C

15. 2N correlations in ratios to 3He
Hall B (statistical errors only)
E02-019

16. Connection between EMC effect and SRC ratios?

17. Connection between EMC effect and SRC ratios?
Very similar behavior with A, including 9Be
Future experiments will further fill in this map

18. E02-019 Ratios 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

19. E02-019 Ratios Q2 (GeV2) CLAS: 1.4-2.6 E02-019: 2.5-3
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

20. Coming soon to Hall A: x>2
3He
4He
12C
40Ca
48Ca

21. 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 E (EMC Effect – Jason Seely & Aji Daniel)

22. On the higher Q2 side of thingsAu
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

23. SLAC, NE3 Jlab, E89-008 Q2 -> 0.44 - 2.29 (GeV/c2)

24. 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

25. 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

26. 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: 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

27. CCFR
BCDMS

28. How do we get to SFQ distributions
Measured structure function
We want F2(0), the scaling limit (Q2→∞) structure function as well as its Q2 dependence
Schienbein et al, J.Phys, 2008

29. 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

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

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

32. P1 parameter vs ξ, i.e. the Q2 dependence
F20 fit with a subset of E and SLAC data
Final fit at Q2=7 GeV2

33. 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 – E data can be used for SFQ distributions
E carbon
SLAC deuterium
BCDMS carbon
| CCFR projection
(ξ=0.75,0.85,0.95,1.05)
Submitted to Phys.Rev. Lett
[arXiv: ]

34. Final step: fit exp(-sξ) to F20 and compare to BCDMS and CCFR
CCFR – (Q2=125GeV2)
s=8.3±0.7
BCDMS – (Q2: GeV2)
s=16.5±0.5
s=15.05±0.5

35. Analysis repeated for other targets
All data sets scaled to a common Q2 (at ξ=1.1)
Submitted to Phys.Rev. Lett
[arXiv: ]

36. x >1 at 12 GeV (E12-06-105) 2H 3He 4He 6,7Li 9Be 10,11B 12C 40CaCu Au

37. 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 (E )

44. Connection between EMC effect and SRC ratios?

45. Connection between EMC effect and SRC ratios?

47. Greater disagreement in ratios of heavier targets to 3He
Show?

48. F2A for all settings and most nuclei for E02-019

51. 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

52. 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