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