Nucleon and Nuclear Structure Function Measurements in the ...
Nucleon and Nuclear Structure Function Measurements in the ...
Nucleon and Nuclear Structure Function Measurements in the ...
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<strong>Nucleon</strong> <strong>and</strong> <strong>Nuclear</strong> <strong>Structure</strong> <strong>Function</strong><br />
<strong>Measurements</strong> <strong>in</strong> <strong>the</strong> resonance region at<br />
low Q 2<br />
Eric Christy<br />
Hampton University<br />
Workshop on Intersections of <strong>Nuclear</strong> Physics with<br />
Neutr<strong>in</strong>os <strong>and</strong> Electrons<br />
JLab – May 4, 2006
JLab has a large program of structure function<br />
measurements <strong>in</strong> <strong>the</strong> resonance region at low Q 2 .<br />
This talk will focus on unpolarized structure function<br />
measurements <strong>in</strong> Hall C <strong>and</strong> specifically ...<br />
Longitud<strong>in</strong>al <strong>and</strong> Transverse (L/T) separated structure<br />
functions, F 1 , F L , <strong>and</strong><br />
F 2 = (2xF 1 + F L )/(1+M 2 x 2 /Q 2 ),<br />
for nucleons <strong>and</strong> <strong>in</strong> nuclei<br />
=> learn about medium modifications / nuclear effects<br />
(ie. dist<strong>in</strong>guish various models of EMC)
3<br />
Reduced crosssection:<br />
Fit reduced cross<br />
section l<strong>in</strong>early with<br />
at fixed W 2 <strong>and</strong> Q 2<br />
(or x, Q 2 ).<br />
L<strong>in</strong>ear fit yields:<br />
σL = Slope<br />
σT = Intercept<br />
Extraction of F 2 depends on<br />
R = L / T <strong>and</strong> !<br />
Rosenbluth Separation<br />
1<br />
Γ<br />
dσ<br />
=<br />
dΩdE'<br />
σ<br />
α<br />
T<br />
( 2 ) ( 2<br />
x, Q + εσ x, Q )<br />
F1<br />
L<br />
α<br />
F2<br />
{ α FL
4<br />
Proton L/T Separated SFs (E94-110)<br />
Large body of high precision resonance data ( 0.3 < Q 2 < 4.5) l<strong>in</strong>ks smoothly to DIS data set.<br />
Duality observed <strong>in</strong> both transverse <strong>and</strong> longitud<strong>in</strong>al structure functions.<br />
Hardly any L/T for nuclear targets at <strong>the</strong> JLab k<strong>in</strong>ematics.<br />
Resonance region fit to T AND L available ....
5<br />
Photoproduction<br />
Energy dependent BreitWigners with current best guess<br />
of dom<strong>in</strong>ant resonances, <strong>in</strong>clud<strong>in</strong>g decay modes <strong>and</strong><br />
branch<strong>in</strong>g fractions.<br />
T constra<strong>in</strong>ed by photoproduction.<br />
Fit typically good to better than 3%.<br />
Fit available at www.jlab.org/~christy/cs_fits/cs_fits.html
6<br />
(Q2 c )<br />
Duality Averaged Proton Data<br />
2 Q = 3 c<br />
2 Q = 0.75<br />
Δ<br />
2 Q = 5 Δ<br />
Fix x <strong>and</strong> move to common<br />
Q<br />
Average over this x-b<strong>in</strong><br />
2 2 at us<strong>in</strong>g Q dependence<br />
of DIS fits.<br />
=> 'DIS-like' data
Global Fitt<strong>in</strong>g of DIS + Ave. Resonance data<br />
F<strong>in</strong>ite mass nucleon => modification of scal<strong>in</strong>g limit structure functions.<br />
F2 x ,Q 2 x 2<br />
3 F 2<br />
bg M<br />
2 6<br />
Q 2<br />
x 3<br />
1<br />
bg M<br />
dx ' F 4<br />
2 x ' 12 4<br />
Q 4<br />
Prescription due to Geogi & Politzer '76<br />
With <strong>the</strong> M=0 structure function given<br />
by M=0 2 bg<br />
F = x F2<br />
2<br />
M=0 2 Parameterize F (x,Q ) <strong>and</strong> fit F2 (x,Q 2<br />
2 ) to<br />
world data set<br />
(duality averaged data used to constra<strong>in</strong> large x)<br />
7<br />
procedure similar to radiative unfold<strong>in</strong>g<br />
x 4<br />
5<br />
1<br />
dx '<br />
1<br />
x '<br />
bg<br />
dx ' ' F 2 x ' '
8<br />
Even at Q 2 = 9 TM is ~7%<br />
effect at x = 0.7!<br />
M=0<br />
Fit results provide both F2 <strong>and</strong> full F2 .<br />
Full data set fit covers<br />
0.3 < Q 2 < 250 GeV<br />
x 2 /dof = 0.98
9<br />
F1 <strong>and</strong> FL F ...<br />
For F 1 only L/T separated data are fit (much more limit data set).<br />
Need L/T separated data for x < 0.2 <strong>and</strong> Q 2 > 3!<br />
F L is determ<strong>in</strong>ed from F 2 & F 1 fits.
• L/T Separation Data: Targets: D, C, Al, Fe - F<strong>in</strong>al uncerta<strong>in</strong>ties 1.6 % pt-pt <strong>in</strong><br />
Targets: D, C, Al, Fe - F<strong>in</strong>al uncerta<strong>in</strong>ties 1.6 % pt-pt <strong>in</strong> ε (2%<br />
normalization) - essentially, duplicate proton data.<br />
10<br />
L/T Separated <strong>Structure</strong> <strong>Function</strong>s on Nuclei<br />
(JLab E02-109, E04-001 <strong>and</strong> E06-009)<br />
Data from Jan '05 Approved future runn<strong>in</strong>g<br />
Low Q<br />
2 L/T separations<br />
where multiple<br />
model<strong>in</strong>g data<br />
energies.<br />
• Targets: H,D, C, Al<br />
• Uncerta<strong>in</strong>ties <strong>in</strong> prelim<strong>in</strong>ary data<br />
estimated at ~3 - 8%<br />
(Much larger RCs <strong>and</strong> rates)
SOS SOS<br />
detection of<br />
positrons<br />
Target Scatter<strong>in</strong>g Chamber<br />
Electron Beam<br />
Superconduct<strong>in</strong>g Dipole<br />
detection of<br />
electrons<br />
Shielded Detector Hut<br />
HMS HMS<br />
Superconduct<strong>in</strong>g Quads
12<br />
Inclusive cross sections <strong>in</strong> Hall C<br />
HMS Momentum<br />
2.75 GeV<br />
2.36 GeV<br />
2.0 GeV<br />
1.75 GeV<br />
<br />
<br />
<br />
dp/p = +/ 8%<br />
<br />
<br />
Efficiency fficiency corrected e- yield HMS<br />
** For cryo targets, subtract empty<br />
target background<br />
Subtract charge symmetric e- yield<br />
(e+ yields measured <strong>in</strong> SOS)<br />
Apply acceptance corrections.<br />
Apply radiative corrections.
13<br />
Prelim<strong>in</strong>ary Cross Section Results<br />
Error bars are statistical only.<br />
Only <strong>in</strong>elastic data shown.<br />
Deuterium: Fits to previous JLab & SLAC resonance<br />
region data.<br />
Heavy targets: fits to DIS data (F 2 & R) + y-scal<strong>in</strong>g QE<br />
model.
14<br />
Low Q 2 Cross Sections<br />
Even for deuterium, we need<br />
better models at low Q2<br />
– P. Bosted talk.<br />
resonance is quite strong <strong>in</strong><br />
nuclei at low Q 2 !<br />
Low Q 2 data ( < 0.15 GeV 2 ) will<br />
provide ~57% cross sections.<br />
resonance is quite strong <strong>in</strong><br />
nuclei at low Q 2 .<br />
Quasielastic data still to be<br />
analyzed.
15<br />
<strong>Nuclear</strong> <strong>Structure</strong> <strong>Function</strong>s<br />
Arr<strong>in</strong>gton, Keppel, Ent, Niculescu PRC73:045206 (2006)<br />
Arr<strong>in</strong>gton, Keppel, Ent, Mammei, Niculescu PRC73: 035205, 2006<br />
ξ = 2x[1 + (1 + 4M 2 x 2 /Q 2 ) 1/2 ]<br />
p<br />
d<br />
Fe<br />
EMC effect is <strong>the</strong> same whe<strong>the</strong>r <strong>in</strong><br />
DIS or resonance region.<br />
<strong>Nuclear</strong> structure functions<br />
follow a s<strong>in</strong>gle curve – shallow<br />
Q 2 dependence, scal<strong>in</strong>g.<br />
In nuclei <strong>the</strong> averag<strong>in</strong>g is nearly<br />
accomplished by Fermi motion.<br />
No low Q 2 or L/T data.
16<br />
New data: Jlab E03-103 – – EMC <strong>in</strong> light nuclei<br />
Ran Fall 2004 <strong>in</strong> Hall C.<br />
Provides precision<br />
data on nuclear SFs/<br />
nuclear modifications <strong>in</strong><br />
light nuclei.<br />
Large k<strong>in</strong>ematic<br />
coverage to study x <strong>and</strong><br />
Q2 dependences.<br />
2 dependences.
17<br />
EMC effect is <strong>the</strong> same <strong>in</strong><br />
resonance region as <strong>in</strong> DIS.<br />
Data will provide precision data<br />
on Adependence of EMC effect<br />
=> help dist<strong>in</strong>guish models of EMC<br />
Can determ<strong>in</strong>e Q 2 at which duality<br />
<strong>in</strong> EMC breaks down.<br />
W 2 ~ 4 GeV 2
18<br />
Summary<br />
Proton L/T separated SFs measured <strong>in</strong> RR for 0.3 < Q 2 < 4.5.<br />
RR cross section fit available for proton data constra<strong>in</strong>ed to<br />
Q 2 = 0.<br />
SF fit performed to world DIS + RR duality data <strong>in</strong>clud<strong>in</strong>g TM.<br />
Prelim<strong>in</strong>ary low Q 2 data for RR L/T SFs <strong>in</strong> nuclei<br />
(larger Q 2 to come)<br />
Prelim<strong>in</strong>ary EMC data for light nuclei shown<br />
=> duality <strong>in</strong> EMC observed.<br />
Will help discrim<strong>in</strong>ate between various models for EMC .