Updated sensitivity estimate Suguru Shimizu Osaka University Sep. 1, 2007 JPARC TREK Collaboration...
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Updated sensitivity estimate
Suguru ShimizuOsaka University
Sep. 1, 2007JPARC TREK Collaboration meeting at Saskatchewan
(1) Statistical error(2) Systematic error
FOM∝AT√ N was calculated by this formula (see FIFC and PAC reports).
Analyzing power is α=0.38 (at FOM max.)
e+ energy measurement is not so important. Just accept high energy e+ component.
Best e+ angle threshold is about 0.4
Analyzing power and FOM
0.92
0.96
e+
θ
y
cosθ
beam
e+ en
ergy
(MeV
)
cosθ
e + energy (MeV)
cosθ
e + energy (MeV)
e+ angle cut is effective to improve FOM, while e+ energy measurement is less important.
FOM for 0 angle threshold for the 0 fwd/bwd analysis
FOM was determined as a function of cos θπ (see FIFC and PAC reports).
<cos θT >=0.68 (at FOM max.)
π0
θ
Beam axis
cosθπ cosθπ
Summary of FOM studyparameters: e+ energy, e+ angle, 0 angle AT
α<cosT>=0.38<cosT>=0.68
ΔPT=1.2x10-4 is obtained with 2.4G K3 events under the
best FOM condition (only pi0 fwd/bwd analysis).
PT=
Systematic error from B field rotation
1mrad. uncertainty of B field PT = 10-3
fwd
bwd
PN
fwd
PNbwd
spectrometer
Side View End View
PNfwd
PNbwd
Left RightLeft Right
B
π0 fwd 1+ PN
bwd 1 PN
fwd/bwd = 1+2PN ≠1
systematic error
Calibration of the polarimetermisalignment using experimental data is very important.
BPT
fwd PTbwd
π0 fwd 1+ PT
bwd 1 PT
fwd/bwd = 1+2PT
R comp.
Z comp.
Asymmetry
Rot(z) misalignment Rot(r) misalignment
Asymmetry
Offset is generated from R component of muon spin
Systematic error due to misalignments
offset
offset
Offset is generated from Z component of muon spin
R comp.
Z comp.
beam beamideal Bideal B
R comp.
Z comp.
Asymmetry
Rot(z) misalignment Rot(r) misalignment
Introduction of 0
(See E06 technical note No.2)Time integrated e+ left/right asymmetry z sin0 + r cos0
Asymmetry
Offset is generated from R component of muon spin
Systematic error due to misalignments
offset
offset
Offset is generated from Z component of muon spin
R comp.
Z comp.
beam beamideal Bideal B
Time integrated asymmetry
0 : the muon spin phase at t=0
In general, e+ left/right asymmetry can be described by oscillating terms and constant terms(see E06 technote No.2)
KBlack: π0 fwdRed : π0 bwd
0 (deg)
Oscillation terms can be canceled out by the time integration.
0 is determined event by event.
Cancellation mechanism for misalignments
Characteristic θ0 dependence of PT and .
K3 MC, Non-zero PT
π0 fwd
π0 bwd
K3 MC, PT=0, δz=5deg
π0 fwd
π0 bwd
A(0)fwd= A(0)bwd = rcos0zsin0
A(0)fwd≠ A(0)bwd
Cancellation mechanism for misalignments
Characteristic θ0 dependence of PT and .
K3 MC, Non-zero PT K3 MC, PT=0, δz=5deg
Asub
Asum Asum
Asub
Asum=(Afwd+Abwd)/2. = 0
Asub=(Afwd−Abwd)/2. ≠ 0
effect is drastically reduced by Asub .
Effect of misalignments are cancelled out by the θ0 analysis.
Asum ≠ 0
Asub = 0
Separation of PT and misalignments effect
Misalignments are now harmless!
Asum=(Afwd+Abwd)/2.
Asub=(Afwd−Abwd)/2.
Black: no misalignment, non-zero PT
Blue: δz=5deg, non-zero PT
i/o : No misalignmentδ : δz=δr= 5 deg.
AsumAsub
i/o
δi/o
δ
PT (stat)= 1.3 x 10 -4
PT (syst)< 10 -4
with 2.4G K3 events
Estimation of systematic error due to misalignments
Misalignments:Assumption in MC is 5 degree
Misalignments:Real case is ~mrad.
In case of 5 degree,PT
sys = 10-4 x 5deg. /mrad ~ 10-2
PTsys= (2±7)x104 was
obtained in MC
The systematic error is expected to be much smaller than 10-4 .
If PTsys~104 in real case,
should be
compare
Summary of 0 fwd/bwd analysis
• Sensitivity of 0 fwd/bwd analysis:statistical error 1.2x10-4
systematic error <1.0x10-4
in total 1.2x10-4
To improve the sensitivity(1) 0 left/right analysis(2) Can we use high energy 1 detection with veto counter hit events?
PT determination for 0 left/right events
0 left/right analysisPL component are also rotated, together with PT.
PL component can be removed by comparing 0 left and right events.
Beat pattern due to the finite PT can be observed.
0 left/right analysis
Asub=(Aleft-Aright)/2 is calculated before time integration of decay time. Large PL component can be removed by this subtraction.
Black: 0 leftRed: 0 right
e+ asymmetry
Large PL component is seen.
Asub=(Aleft-Aright)/2
PT component can be extracted.
K3 MC, Non-zero PT
0 left/right analysis
• Asub=(Aleft−Aright)/2 is fitted with, cos(t++) : fitting parameter for e+ fwd/bwd analysis /2 for e+ in/out analysis
bwd-fwdbwd+fwd
e+ asymmetry
e+ asymmetry inoutin+out
Asub=(Aleft−Aright)/2.
fwd bwd
in
out
Z
R
e+ detection
e+
black: e+ fwd/bwdred: e+ in/out
dPT = 1.7 x 10 -4 for 2.4G K3 events