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Polarized d+d elastic scattering at Ed=231.8 MeV
IUCFA. Micherdzinska, C.E. Allgower, A.D. Bacher, C. Lavelle,
H. Nann, J. Olmsted, T. Rinckel, E.J. StephensonW. Michigan U. P.V. Pancella
Minnesota State U. M.A. Pickar Ohio U. J. Rapaport
Hillsdale College A. Smith
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Talk sketch
• Motivation• Experimental setup
• Measurement plan for Tkq and cross section
for
• Tkq and cross section data and theoretical calculations (A. Fonseca)
• Summary
ddDd 2
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π0
CHARGE SYMMETRY (CS)
Physics is unchanged when protons and neutrons are interchanged
d + d 4He + π0
d + d d + d
To calculate this we need to describe entrance channel interaction.
To do this, we measured σ(Θ), Tkq(Θ) for
MOTIVATION
Ed=231.8 MeV
The observation (E. Stephenson et al. Phys. Rev. Lett. 91 (2003) 142302) demonstrates that CS is broken
Ed=231.8 MeV
π0 is odd under CS
?d
d
4He
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2002 IUCF
Completed data taking in search for d + d 4He + π0
Last week of beam time was spent for d + d d + d at 231.8 MeV (changing experimental setup)
PINTEX detector system
Ideal Polarization Valuespy pyy required RF transition 1 1 MF 3:4 and SF 2:6-1 1 MF 1:4 and WF 0 1 MF 1:4 and SF 2:6 0 -2 MF 1:4 and SF 3:5 0 0 none CIPIOS can produce these
values with an efficiency of 80-90%.
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2002 IUCF
d beam
WC1
WC2
KE
V
F Si Barrel
target (D2, H2 or HD)
Si Barrel
PINTEX detector system
dddd
pd d,dpd,d
pdpd
Det. Thickness Radius
(mm) (mm)
F 1.5 203
K 153 423
E 103 369
Si Barrel – 3 rings of 6 Si detector, each 28 strips
1st ring: 1mm
2nd ring: 1mm
3rd ring: 0.5mm
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σdp(θ) K. Ermisch Phys. Rev C68 051001 (2003)
We can find Py, Pyy
pd d,dpd,d
pdpd
dddd
We know: Tkq K. Sekiguchi Phys. Rev C65, 034003 (2002)
We know Py, Pyy
We can find Tkq, unnormalized σdd(θ)
We can find normalization factor Ndd/Ndp
and normalize σdd(θ)
Experimental issues:
unknown beam polarization
unknown luminosity
extrapolated Tkq for 231.8 MeV (theory + experiment)
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pdpd
d beam
H2 target
F
WC1
WC2K E
V2 charged particles registered in forward angles: dp, pp
We have complete energy and angle information
p
d
TRIGGER
H2 target
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d beam
F
WC1
WC2K E
V
d
TRIGGER
1 forward prong in coincidence with at least 1 recoil is Si barrel dd, dp, pp
We can reconstruct azimuthal angle and energy losses
dddd
D2 target
D2 target
d
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pdpd
Particle identification (1-p, 2-d)
If Θ1 > 37o o.k
Else if E1 < E2 switch 1 2
coplanarity
energy cut Ep+Ed=231.8MeV
Extracting dp elastic scattering events
pd kinematic curve
+
+
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pd kinematic curve
pdpd
calcd
datad θθθD
Ntrue= Ntot- F(NL+NR)
F(NL+NR)=NM
Subtraction of dp breakup
for each spin state
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)2cos)(4
3)(
8
1cos)(31)((),( 222011 yyyyy pTpTpiT
yy
y
yy
pTdH
piTdG
pTdF
220
2
0
110
2
0
20
2
0
0
4
32cos)(
3cos)(
]8
11[2)(
Elastic scattering polarized cross section
Cosine portion of Fourier series of azimuthal angle:
Finding Py, Pyy
Solve for Py, Pyy
)2coscos),( HGF
notches
pdpd
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pdpd
)2cos)(4
3)(
8
1cos)(31)((),( 222011 yyyyy pTpTpiT
yy
y
yy
pTdH
piTdG
pTdF
220
2
0
110
2
0
20
2
0
0
4
32cos)(
3cos)(
]8
11[2)(
Elastic scattering polarized cross section
Cosine portion of Fourier series of azimuthal angle:
Finding Py, Pyy
Solve for Py, Pyy
)2coscos),( HGF
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cosΦ cos2Φ Py Pyy
nom. exp exp nom.
1 0.68±0.02 0.79±0.05 1
-1 -0.62±0.02 0.58±0.05 1
0 0.00±0.02 0.74±0.05 1
0 -0.00±0.01 -1.85±0.05 -2
pdpd
Py, Pyy
Averaged values of Py and Pyy
Py and Pyy do not depend on the polar angle Ө
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dddd
Particle identification :
Forward detectors
Silicon Barrel –backward ring middle ring forward ring
Extracting dd elastic scattering events
coplanarity
+
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dddd
Breakup subtraction model
total peak with background
dp quasi-elastic peak (from pd breakup data) and dd breakup (model)
dd peak after background subtraction
2 components:
- General background from breakup into dpn or ppnn
- d+p quasi elastic scattering
breakup
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dddd
)2coscos),( HGF
yy
y
yy
pTdH
piTdG
pTdF
220
2
0
110
2
0
20
2
0
0
4
32cos)(
3cos)(
]8
11[2)(
Elastic scattering polarized cross section
yy
y
yy
p
HT
p
GiT
p
FT
3
4
3
2
)1(8
22
11
20
Cosine portion of Fourier series of azimuthal angle:
→
Remove σo in division by unpolarized state, normalized by relative luminosity.
Knowing py and pyy and fitting F, G, H to azimuthal distribution we can find analyzing power
original (with notches)
azimuthal distribution
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dddd
)2coscos),( HGF
yy
y
yy
pTdH
piTdG
pTdF
220
2
0
110
2
0
20
2
0
0
4
32cos)(
3cos)(
]8
11[2)(
Elastic scattering polarized cross section
yy
y
yy
p
HT
p
GiT
p
FT
3
4
3
2
)1(8
22
11
20
Cosine portion of Fourier series of azimuthal angle:
→
Knowing py and pyy and fitting F, G, H to azimuthal distribution
we can find analyzing power
azimuthal distributions divided by
unpolarized spectrum
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dddd
Analyzing power values for each spin state
Do not depend on polarization – good analysis !
Calculation by A. Fonseca
state1
state 2
state 3
state 4
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dddd
Averaged values of analyzing power
Calculation by A. Fonseca
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dddd
dp
dp
dd
dp
dp
dddpdd
N
Nf
d
d
d
d
1
2
2
12
21
1 )(
)()()(
Cross section calculation
Where:
- dp elastic scattering cross section
ε - efficiencies
f – luminosity scaling factor (we know from HD run)
Use data from separate D2 and H2 runs
Efficiency (<90%) d+p d+d
Energy cut 0.79
Notches(φ) 0.865 0.73
Silicon gaps (Ө) 0.63(small Ө) - 0.31 (large Ө)
Others:
coplanarity
Scintillator PID cuts
Silicon PID cuts
Systematic errors: d+d notch 18%
d+d tail 50%
“other” ~10%
TOTAL 54%
)( 22
dd dp
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Summary
dddd
pdpd We analyzed:
pd d,dp d,d
We obtained:
Py, Pyy
Normalization factor
iT11, T22, T20, σ(Θ)
Calculation by A. Fonseca
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pd d,dHDd
dpD
dpH
dpHD
ddD
ddH
ddHD
22
22
bNaNN
bNaNN
Trigger dd:
Trigger dp:
Trigger dp
= a + b
= a + b
Trigger dd