Proton Form Factor Ratio, GPE/GPM
From
Double Spin Asymmetries
Spin
Asymmetries of the
Nucleon
Experiment
( E07-003)
Analysis Updates
Anusha Liyanage
Hall C User Meeting
(January 25, 2013)
Outline
 Introduction
 Physics Motivation
 Experiment Setup
 Polarized Target
 Elastic Kinematic
 Data Analysis &
MC/SIMC Simulation
 Conclusion
2
Introduction
Nucleon Elastic Form Factors
•
•
•
•
Defined in context of single-photon exchange.
Describe how much the nucleus deviates from a point like particle.
Describe the internal structure of the nucleons.
Provide the information on the spatial distribution of electric charge (by electric form
factor,GpE) and magnetic moment ( by magnetic form factor, GpM) within the proton.
• Can be determined from elastic electron-proton scattering.
• They are functions of the four-momentum transfer squared, Q2
The four-momentum transfer
squared,

Q 2  q 2  4 EE  sin 2  
2
E  E  Q
2
2M
3
General definition of the nucleon form factor is
é m N 2
mn qn
N
2 ù
N ( P¢) J EM ( 0) N ( P ) = u ( P¢) êg F1 (Q ) + is
F2 (Q )úu ( P )
ë
û
2M
m
Sachs Form Factors
GE = F1 - t F2 ; GM = F1 + F2
;
Q2
t=
4M 2
F1 – non-spin flip (Dirac Form Factor) describe the charge distribution
F2 – spin flip (Pauli form factor) describe the magnetic moment distribution
At low | q 2 |
GE (q ) » GE (q ) = ò e r (r )d r
2
2
iq×r
3
GM (q 2 ) » GM (q 2 ) = ò eiq×r m (r )d 3r
At q 2  0
ò
(0) = ò
G Ep (0) =
G Mp
r (r )d 3r =1
m (r )d 3r = mP = +2.79
Fourier transforms of the charge,  (r )
and magnetic moment,  (r ) distributions
in Breit Frame
p
 GE
G Mp
1
4
Form Factor Ratio Measurements
1. Rosenbluth separation method.
• Measure the electron - unpolarized proton elastic scattering cross section at
fixed Q2 by varying the scattering angle, θe.
• Strongly sensitive to the radiative corrections.
a E¢ cos2
2
qe
é 2 t 2ù
ds
2
=
G E + GM ú
ê
û
dW 4(1+ t )E 3 sin 4 q e ë
e
2
s Mott
(1+ t )
ds e (1+ t )
×
= GE2e + t GM2
dW s Mott
Y =mX+C
The gradient = GE2 , The Intercept = t GM2 ,
Q2 = 2EE¢(1- cosqe )
Q2
t=
4M p2
-1
é
2 qe ù
e = ê1+ 2(1+ t )tan ú
ë
2û
E - Incoming electron energy
E/ - Outgoing electron energy
θe- Outgoing electron’s scattering angle
Mp - Proton mass
5
2. Polarization Transfer Technique.
• Measure the recoil proton polarization components from elastic scattering of
polarized electron-unpolarized proton.
• Ratio insensitive to absolute polarization, analyzing power.
• Less sensitive to radiative correction.
( )
(E + E¢)tan q e
2
GE
PT
=GM
PL
2M p
PL = M P-1 (E + E¢) t (1+ t )GM2 tan 2 (qe / 2)
PT = 2 t (1+ t )GEGM tan (qe / 2)
PN = 0
E - Incoming electron energy
E/ - Outgoing electron energy
θe– Outgoing electron’s scattering angle
MP - Proton mass
Polarization along q
Polarization perpendicular to q
(in the scattering plane)
Polarization normal to scattering
plane.
6
3. Double-Spin Asymmetry.
• Measure the double asymmetry between even (++, --) and odd (+-, -+)
combinations of electron and proton polarization.
• Different systematic errors than Rosenbluth or proton recoil polarization
methods.
• The sensitivity to the form factor ratio is similar to that of the Polarization
Transfer Technique.
 br sin  * cos  *  a cos  *
AP 
r2  c
G Ep
b
b2
a
*
*
2 *
2 *
*
=
sin
q
cos
f
±
sin
q
cos
f
cos
q
-c
p
2
GM
2Ap
4Ap
AP
Here, r = GpE /GpM
a, b, c = kinematic factors
*, *= pol. and azi. Angles between q and
q 
S
Ap = The beam - target asymmetry
7
Physics Motivation
• Dramatic discrepancy between
RSS (Jlab)
Q2 = 1.50 (GeV/c)2
SANE
2.06
5.17 6.25
Q2 (GeV/c)2
Dramatic discrepancy !
Rosenbluth and recoil polarization
technique.
• Multi-photon exchange considered
the best candidate for the
explanation
• Double-Spin Asymmetry
is an independent
technique to verify
the discrepancy
8
Experiment Setup
• BETA for coincidence electron
detection
• Central scattering angle: 40 °
• Over 200 msr solid angle
coverage
Hall C at
Jefferson Lab
Elastic (e , e’p) scattering from
a polarized NH3 target using a
longitudinally polarized electron
beam
(Data collected from Jan – March, 2009)
• HMS for scattered
proton or electron
detection
• Central angles are
22.3° and 22.0°
• Solid angle ~10 msr
9
Polarized Target
The Polarized Target Assembly
• C, CH2 and NH3
• Dynamic Nuclear Polarization (DNP) polarized the
protons in the NH3 target up to 90% at
1 K Temperature
5 T Magnetic Field
• Temperature is maintained by immersing the entire target
in a liquid He bath
• Used microwaves to excite spin flip
transitions
(55 GHz - 165 GHz)
• Polarization measured using NMR
coils
• To maintain reasonable target
polarization, the beam current
 was limited to 100 nA and
 uniformly rastered.
10
Polarized Target Magnetic Field
ΘB = 80°
ΘB = 180°
( 80 and 180 deg )
•
Used only perpendicular magnetic field configuration for the elastic data
• Average target polarization is ~ 70 %
• Average beam polarization is ~ 73 %
11
Elastic Kinematics
( From HMS Spectrometer )
Spectrometer
mode
Coincidence
Coincidence Single Arm
HMS Detects
Proton
Proton
Electron
E Beam
GeV
4.72
5.89
5.89
PHMS
GeV/c
3.58
4.17
4.40
ΘHMS
(Deg)
22.30
22.00
15.40
Q2
(GeV/c)2
5.17
6.26
2.06
Total Hours
(h)
~40
(~44 runs)
~155
(~135 runs)
~12
(~15 runs)
Elastic Events
~113
~1200
~5x104
12
Data Analysis
Electrons in HMS
Θ
E’
E
By knowing,
the incoming beam energy, E,
scattered electron energy, E¢
and
the scattered electron angle, 
 
Q 2  4 EE  sin 2  
2
e- p
e- p
W 2  M 2  Q 2  2M ( E  E)
13

Momentum Acceptance
(
hsdelta = P - Pc
Pc
)
=
dp
p
P -Measured momentum in HMS
Pc-HMS central momentum
hsdelta (%)
The elastic data are outside of
the usual delta cut +/- 8%
Use -8% <
dp
p
<10%
&
Invariant Mass, W (GeV/c2)
Use 10% <
dp
p
<12%
14
Extract the electrons
•
Used only Electron selection cuts.
# of Cerenkov photoelectrons > 2 - Cerenkov cut
Esh
-8% <
p
> 0.7
d p < 10% and 10% < d p <12%
p
p
-
Calorimeter cut
-
HMS Momentum Acceptance cuts
Here,
E sh - Total measured shower energy
of a chosen electron track by
HMS Calorimeter
P - Detected electron momentum/
energy at HMS
d p - Relative momentum deviation
p
from the HMS central
momentum
-8% <d p< 10% 10% < d p< 12%
p
3.5 x 104
p
1.5 x 104
15
Extracted the Asymmetries …..
The raw asymmetry, Ar
N  N
Ar  
N  N
Ar 
-8% <
dp
p
2 N

N

(N   N  ) (N   N  )
< 10%
N+ / N- = Charge and live time normalized
counts for the +/- helicities
∆Ar = Error on the raw asymmetry
10% <
dp
p
<12%
16
Extracted the Asymmetries …..
Need
dilution factor, f
in order to determine the
physics asymmetry,
Ap 
Ar
 NC
fPB PT
and GpE/GpM
(at Q2=2.2 (GeV/c)2 )
PBPT = Beam and target polarization
Nc = A correction term to eliminate the contribution from quasi-elastic scattering on polarized
14N under the elastic peak (negligible in SANE)
Use MC/DATA comparison for NH3 target to extract the dilution factor…..
17
MC for C run
Srast x offset=-0.4 cm
Srast y offset=0.1 cm
18
MC with NH3
 Generated N, H and He separately.
 Added Al coming from target end caps and 4K shields as well.
 Calculated the MC scale factor using the data/MC luminosity
ratio for each target type.
 Added all targets together by weighting the above MC scale factors.
 Used 60% packing fraction.
 Adjusted acceptance edges in Y and Y’ by adjusting the horizontal beam
position.
 Adjusted the vertical beam position to bring the elastic peak to W = 0.938GeV.
srastx = -0.40 cm
srasty = 0.10 cm
19
Determination of the Dilution Factor
What is the Dilution Factor ?
The dilution factor is the ratio of the yield from scattering
off free protons(protons from H in NH3) to that from the
entire target (protons from N, H, He and Al)
Each target type contributions
(Top target)
Dilution Factor,
YieldData -YieldMC( N+He+Al )
F=
YieldData
-8% <
Invariant Mass, W (GeV/c2)
dp
p
< 10%
Invariant Mass, W (GeV/c2)
20
 MC
Background contributions (Only He+N+Al)
 Calculate the ratio of
YieldData/YieldMC for the
region 0.7 < W <0.85
and MC is normalized
with this new scaling factor.
 Used the polynomial fit
to N+ He+Al in MC
and
 Subtract the fit function
from data
Invariant Mass, W (GeV/c2)
21
10% < d p < 12%
p
Each target type contributions
(Top target)
Invariant Mass, W (GeV/c2)
Invariant Mass, W (GeV/c2)
Invariant Mass, W (GeV/c2)
22

The relative Dilution Factor
Dilution Factor,
F=
YieldData -YieldMC( N+He+Al )
YieldData
• We have taken data using
both NH3 targets, called
NH3 top and NH3 bottom.
• NH3 crystals are not
uniformly filled in each
targets which arise two
different packing fractions
and hence two different
dilution factors.
The relative dilution factor for
two different targets, top and bottom for
two different delta regions,
-8% <
dp
p
< 10% and 10% <
dp
p
<12%
Invariant Mass, W (GeV/c2)
23
Beam /Target Polarizations
COIN data
Single arm electron data
24

The Physics Asymmetry
dp
dp
p
< 12%
Phys. Asym., AP
p
10% <
< 10%
Phys. Asym., AP
-8% <
Invariant Mass, W (GeV/c2)
Invariant Mass, W (GeV/c2)
25
 The beam - target asymmetry, Ap
AP 
 br sin  cos   a cos 
r2  c
*
*
*
Here, r = GE /GM
a, b, c = kinematic factors
* *= pol. and azi. Angles between q and
,
q
S
GE
b
b2
a
*
*
2 *
2 *
*
=sinq cos f +
sin
q
cos
f
cos
q
-c
2
GM
2Ap
4Ap
AP
 Error propagation from the experiment
From the HMS kinematics, r2 << c
b sin * cos *r a cos *
AP 

c
c
æ GE ö
c
Dr = D ç
DAp
÷=
*
*
è GM ø bsinq cosj
æ GE ö
D ( mr ) = D ç m
÷
G
è
M ø
Where , μ – Magnetic Moment of the Proton=2.79
26
Preliminary …..
-8 < d p < 10
10 < d p < 12
Top Ap±eAp
-0.212±0.022
-0.150±0.032
Bot Ap±eAp
-0.216±0.027
-0.161±0.040
Avg. Ap±eAp
-0.213±0.017
-0.154±0.025
p
q
* (Deg)
*
45.68
(Deg)
190.49
Q2 (GeV/c)2
μGE/GM
p
2.2
1.927
0.477±0.190
0.928±0.279
0.75
0.775
-0.188
-0.174
Pred. μGE/GM
Pred. Ap
Q2 (GeV/c)2
Wei. Avg. μGE/GM
2.06
0.62±0.157
27
Coincidence Data
(Electrons in BETA and Protons in HMS)
Definitions :
X/Yclust - Measured X/Y positions on
the BigCal
• X = horizontal / in-plane coordinate
• Y = vertical / out – of – plane
coordinate
Eclust - Measured electron energy at the
BigCal
By knowing
the energy of the polarized electron
beam, EB
and
the scattered proton angle, ΘP
Yclust
Xclust
e’
P
e
We can predict the
• X/Y coordinates - X_HMS, Y_HMS and
( Target Magnetic Field Corrected)
•The Energy - E_HMS
of the coincidence electron on the BigCal
28
Elastic Kinematics
( From HMS Spectrometer )
Spectrometer
mode
Coincidence
Coincidence Single Arm
HMS Detects
Proton
Proton
Electron
E Beam
GeV
4.72
5.89
5.89
PHMS
GeV/c
3.58
4.17
4.40
ΘHMS
(Deg)
22.30
22.00
15.40
Q2
(GeV/c)2
5.17
6.26
2.06
Total Hours
(h)
~40
(~44 runs)
~155
(~135 runs)
~12
(~15 runs)
e-p Events
~113
~1200
~5 x 104
29
Fractional momentum difference
dp
PHMS - PCal
=
p
Pcent
Data
MC
PCal 

2
 2 M

Q2

2M
4M 2 E 2 cos 2 
Q  2
M  2ME  E 2 sin 2 
2
dp
p
PHMS – Measured proton momentum by HMS
Pcal - Calculated proton momentum by knowing the beam energy, E and the proton
angle,Θ
Pcent – HMS central momentum
30
X/Y position difference
X position difference
Data
MC

Y position difference
X_HMS-Xclust/ cm
Y_HMS-Yclust/ cm
31
Applied the coincidence cuts
abs(X_HMS-Xclust)<7
X_HMS-Xclust/ cm
Abs( d p )<0.02
p
dp
abs(Y_HMS-Yclust)<10
p
Y_HMS-Yclust/ cm
32
Elastic Events
5.89 GeV data
Y_HMS-Yclust/ cm
Y_HMS-Yclust/ cm
4.72 GeV data
X_HMS-Xclus/ cmt
Raw # ofYields
Raw # ofYields
X_HMS-Xclus/ cmt
Run Number
Run Number
33
Extract the Raw Asymmetries
Raw yields are normalized with
• Total Charge
• charge average +/- life times
Need
dilution factor, f
in order to determine the
physics asymmetry,
Ap 
Ar
 NC
fPB PT
and GpE/GpM
34
Determine The Dilution Factor
• Estimate The Background
dp
p
dp
p
• Get the ratio of data/SIMC_C for the region of 0.03 < d p p< 0.08. (ratio=2.73893)
• Normalized the SIMC_C with that ratio (2.73893) for the region of -0.1 < d p < 0.1 and
p
added SIMC_H3 to it. Compare with the data.
Data/SIMC(H3+2.73893*C) = 0.991536
• Used the Gaussian fit for the SIMC_C (normalized with 2.73893) and subtract it from the
data
• Get the relative dilution factor by taking the ratio of SIMC_C substracted data to data.
the relative df. = (data-SIMC_C)/data
35
• Get The Relative Dilution Factor
Two different target cups
(NH3 Top and NH3 Bottom)
Two different packing
fractions
Need
Two different dilution
factors
36
• The Relative Dilution Factors For
Top Target
Bottom Target
dp
dp
p
37
p
• The Relative Dilution Factor
(Used the Integration Method)
• Because of the low statistics, It is hard to correct the raw asymmetry for the df as a function of d p p
• Just integrate over the d p region of +/- 0.02 for the top and bottom.
p
Top Target
dp
p
Bottom Target
dp
p
The relative D.F = (data-SIMC_C)_top/data_top
= (data-SIMC_C)_bot/data_bot
= 606-130/606
= 541-92/541
= 0.785
= 0.830
Similarly, the relative D.F for 4.72 GeV beam energy is 0.816
38
Beam and Target Polarizations
• Used the runs of beam polarization > 60 % and abs(target polarization) > 55 %
• Used the charge average target and beam polarizations to calculate the physics asymmetries
39
Extract the Physics Asymmetries
Beam
Energy(GeV)
4.72
5.89
Ap±eAp
0.184±0.136
-0.006±0.077
Dilution
Factor, f
0.816
Top (0.785)
Bot. (0.830)
q * (Deg)
102
102
 * (Deg)
0
0
5.17
6.26
-0.032±0.668
0.875±0.424
Q2 (GeV/c)2
μGE/GM
Q2 (GeV/c)2
Wei. Avg. μGE/GM
5.72
0.614±0.358
40
Extract the Proton Form Factor Ratio, GpE/GpM
Preliminary …..
Q2
(GeV/c)2
μGE/GM
2.06
5.72
0.620± 0.614±
0.157
0.358
Q2 (GeV/c)2
41
Conclusion
 Measurement of the beam-target asymmetry in elastic electron



proton scattering offers an independent technique of
determining the GpE/GpM ratio.
This is an ‘exploratory’ measurement, as a by-product
of the SANE experiment.
Extraction of the GpE/GpM ratio from single-arm electron and
coincidence data are shown.
The preliminary data point at Q2=2.06 (GeV/c)2 is very
consistent with the recoil polarization data.
The preliminary weighted average data point of the coincidence
data at Q2=5.72 (GeV/c)2 has large error due to the lack of
elastic events.
42
SANE Collaborators:
Argonne National Laboratory, Christopher Newport U., Florida International U.,
Hampton U., Thomas Jefferson National Accelerator Facility, Mississippi State U., North
Carolina A&T State U., Norfolk S. U., Ohio U., Institute for High Energy Physics, U. of
Regina, Rensselaer Polytechnic I., Rutgers U., Seoul National U., State University at New
Orleans , Temple U., Tohoku U., U. of New Hampshire, U. of Virginia, College of
William and Mary, Xavier University of Louisiana, Yerevan Physics Inst.
Spokespersons: S. Choi (Seoul), M. Jones (TJNAF), Z-E. Meziani (Temple),
O. A. Rondon (UVA)
44
Packing Fraction.
• Packing fraction is the actual amount of target material normalized the
nominal amount expected for the target volume.
• Determined by taking the ratio of data to MC as a function of W.
• Need to determine the packing fractions for each of the NH3 loads used
during the data taking.
Hoyoung Kang’s
work
45

Determine the Packing Fraction
Compared data to SIMC simulation for the NH3 target for 3 different
Packing Fractions.
• Normalized MC_NH3 by 0.93 which is the factor that brings C data/MC
ratio to 1.
•
• Determined the packing fraction
which brings Data/MC ratio to 1
from the plot.
• Packing Fraction=56.3 %
Pf (%)
50
60
70
Data/MC
Ratio
1.00
0.88
0.78
Data/MC
Ratio/0.93
1.075
0.95
0.84
Consistent with Hoyoung kang’s packing fraction determinations !!!!
46