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
variety of physics topics
Duality
Scaling (x, y, ξ, ψ)
Short Range Correlations – NN force
Momentum Distributions
Q2 –dependence of the F2 structure function
allows the study of a wide
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
e-
e-
e-
e-
Same initial state
DIS
Different Q2 behavior
QES
W2=Mn2
W2≥(Mn+Mπ)2
M*A-1
M*A-1
MA
MA

d DIS
( p ,n )
  dk  dEW1, 2 Si (k , E )
ddE '
Spectral function

d QE
  dk  dE ei Si (k , E ) ( Arg )
ddE '
Arg    M A  M 2  p 2  M A*21  k 2
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:
Q2
xbj 
2 M p
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
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

d QE
  dk  dE ei Si (k , E ) ( Arg )
ddE '
Arg    M A  M 2  p 2  M A*21  k 2
d 2
1
q
F ( y, q) 
dd ( Z  p  N  n ) M 2  ( y  q) 2

 2  n(k )kdk
| y|
Deuteriu
m
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

d QE
  dk  dE ei Si (k , E ) ( Arg )
ddE '
Arg    M A  M 2  p 2  M A*21  k 2
d 2
1
q
F ( y, q) 
dd ( Z  p  N  n ) M 2  ( y  q) 2

 2  n(k )kdk
| y|
Deuterium
Short Range Correlations => nucleons with high momentum
Independent Particle Shell Model :
S  4  S(E m , pm )pm dpm (E m  E )
2
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
3N SRC
Deuteron
Carbon
NM
Short Range Correlations
To experimentally probe SRCs, must be in the high-momentum region (x>1)
A
1
 ( x, Q )   A a j ( A) j ( x, Q 2 )
j
j 1
2

A
a2 ( A) 2 ( x, Q 2 ) 
2
A
a3 ( A) 3 ( x, Q 2 )  ....
3
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
3 A
 a3 ( A)
A  3 He
P_min (GeV/c)
2 A
 a2 ( A)
A D
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)
3He
2.08±0.01
4He
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
4He
Q2=2.5GeV2
R
E02-019
3He
2.08±0.01
4He
3.44±0.02
Be
3.99±0.04
C
4.89±0.05
Cu
5.40±0.05
Au
5.37±0.06
NE3
3.87±0.12
56Fe
5.38±0.17
E02-019 2N Ratios
q   2M
  2
2M
2
2

W

4
M
1 

W





3He
3He
12C
12C
2N correlations in ratios to 3He
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:
r ( A1 , A2 )  R( A1 , A2 ) 
A1 ( Z 2 p  N 2 N )
A2 ( Z1 p  N1 N )
In the example of 3He:
r ( A1 , He )  R( A1 , He ) 
3
Hall B results (2003)
statistical errors only
3
A1 (2 p   N )
Recently learned that
this correction is
probably not necessary
(pn >>pp)
3( Z1 p  N1 N )
E02-019
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
E02-019 Ratios
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 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
F2A
Jlab, Hall C, 2004

x
2x
4M 2 x 2
(1  1 
)
Q2
ξ
•
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
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?

2x
4M 2 x 2
(1  1 
)
2
Q
• 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?

2x
4M 2 x 2
(1  1 
)
2
Q
• 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
2
2 3
4 4
x
6
M
x
12
M
x
TMC
2
( 0)
F2 ( x, Q )  2 3 F2 ( )  2 4 h2 ( ) 
g 2 ( )
4 5
 r
Qr
Qr
F2( 0) (u, Q 2 )
h2 ( , Q )   du

u2
2
1
F2( 0) (v, Q 2 )
g 2 ( , Q )   dv(v   )

v2
2
1
• We want F2(0), the massless limit structure
function as well as its Q2 dependence
Schienbein et al, J.Phys, 2008
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)
ξ=0.5
• Fit log(F20) vs log(Q2) for fixed values
of ξ to

p0  log( Q2 )  p1 1  p2  e log(Q
• p2,p3 fixed
•p1 governs the “slope”, or the QCD
evolution.
ξ=0.75
Q2
• Use the QCD evolution to
redo the F20 fit at fixed Q2 and
to add more data (specifically
SLAC)
• fit p1 vs ξ
2
) / p3

P1 parameter vs ξ, i.e. the
QCD evolution
F20 fit with a subset of E02019 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
Analysis repeated for other targets
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