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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 9 th , 2010. E02-019 Overview. - PowerPoint PPT Presentation
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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
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
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