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MEG実験の全データを用いた
μ → e γ 探索
The analysis of μ → e γ search in
MEG experiment with all statistics
東京大学 素粒子物理国際研究センター
金子大輔 他、MEGコラボレーション
Daisuke Kaneko, on behalf of the MEG collaboration
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μ+→e++γ search in MEG experiment
𝜇+ → 𝑒 + + 𝛾
Forbidden decay in the Standard Model
Extremely low probability even with ν oscillation
Well motivated new theories (SUSY etc.)
predict sizable probability (10-12 ～ 10-14).
Latest result
Phys. Rev. Lett. 110, 201801 (2013)
2009 – 2011 data
B (𝜇+ → 𝑒 + + 𝛾) < 5.7×10-13 (90%CL)
We finished data taking 2013, and
analyze all data in this study with
doubled amount of statistics.
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S ~ 7.7×10-13
S ~ 5×10-13
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MEG experiment
Signal Event
tγ
Eγ
γ
te
μ+
e+
Ee
Θeγ 3×107 /s
E γ = E e = mμ / 2
tγ = te , Θeγ = π
Radiative
Muon Decay
Accidental
Background
(Dominant)
γ
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μ+
RMD γ
μ+
γ
e+
νe
μ+
e+
e+ or
γ
e-e+
AIF γ
Status of physics analysis
It is taking longer time than expectation
● Refinement of improved analysis
・e+ annihilation in flight
・Missing turn identification
● Target alignment issue
μ+ stopping target turned out to be slightly deformed
Strategy is decided.
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BG event by Annihilation in Flight (AIF)
Accidental coincidence of γ from AIF and e+ from normal μ+ decay.
About 1/3 of all γ are from AIF which have possibility to detect by our tracker.
The fraction of AIF γ is higher than RMD γ near signal region.
AIF Observables
ΔθAIF, ΔφAIF, ΔtAIF :
Comparison of e+ & γ
target
Δθ,φ,tAIF
Liquid
Xenon
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R,φ,ZAIF
Drift
Chamber
RAIF, ZAIF, φAIF :
Where AIF occurred
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Inclusion of AIF observables
ℒ 𝑁sig , 𝑁RD , 𝑁BG
𝑒 −𝑁 −
=
𝑒
𝑁obs !
𝑁BG − 𝑁BG 2
𝑁RD − 𝑁RD 2
−
2
2
2𝜎BG
2𝜎RD
𝑒
×
PDFs for AIF observables
𝑁obs
(𝑁sig 𝑆 𝑥𝑖 𝑆AIF(𝑦𝑖 ) + 𝑁RD 𝑅 𝑥𝑖 𝑅AIF(𝑦𝑖 ) + 𝑁BG 𝐵 𝑥𝑖 𝐵AIF(𝑦𝑖 ))
𝑖=1
BAIF : Use sideband data directly
ΔθAIF
Signal RD
simulate
correct
AIF pair
ΔφAIF
ΔtAIF
random
AIF pair
SAIF, RAIF : Only “wrong AIF pair”, but pure data cannot be obtained.
How to make ? → Simulate by shuffling γ and e+ combination
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Multi-Variate Analysis (MVA)
AIF observables are implemented to the likelihood function via MVA.
Red : BAIF
Blue : SAIF & RAIF
← AIF-like
No-AIF-events are stored in
the exceptional bin
MVA (BDT) index
Correct AIF pair
Expected improvement in sensitivity is 5 – 10%.
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Target alignment
We get initial e+ information by extrapolating track to target
→ The relative position of target and tracker is very important
MEG muon stopping target
Target
r = 10cm, Δp = 1mm
→ 10 mrad
e+
Alignment is done by
Target hole : by positron track data
Cross mark : by theodolite survey
Drift Chamber
Hit distribution
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Target bowing
Target cross measurement with theodolite
In 2012 and 2013 data, target
found to be deformed.
In 2009 and 2010 it was
consistent with flat. In 2011,
[mm]
deformation was small.
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Parabolic fit of target cross measurements
X and Y coordinates of 4 central target holes
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Survey by theodolite and hole
analysis are in good
agreement.
1
-10
2009
-5
[cm]
0
5
10
-3
0
3
0
5
10
-3
0
3
1
0
1
-10
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2013
-5
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Countermeasure to target issue
We measured the target with 3D
scanner in 2014 (after DAQ finished)
3
beam spot
Result is basically consistent with
survey, but found to be more
complex shape.
0
0
-3
[cm] -10
-2
-5
0
+2
5
10
Target shift and bowing is corrected
raw + Δ 𝜙 + Δ
Δ𝜙𝑒𝛾 = 𝜙𝑒𝛾
𝑝0 𝑒𝛾
para 𝜙𝑒𝛾
We introduced two new nuisance parameters, and profile with the parameters.
𝜇𝜙 = Δ𝑝 𝜙𝑒𝛾 + Δ3D 𝜙𝑒𝛾 − Δpara 𝜙𝑒𝛾 ⋅ 𝑠
𝜇𝜃 = Δ𝑝 𝜃𝑒𝛾 + Δ3D 𝜃𝑒𝛾 − Δpara 𝜃𝑒𝛾 ⋅ 𝑠
Expected deterioration of sensitivity by target issue is a few percents.
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Summary
We are analyzing data for final physics result with all data amount.
Expected sensitivity is 5×10-13 (last result 7.7×10-13)
Newly developed items and problems are being finalized.
2-3 months before unblinding
We would like to present our result by summer of this year.
~1 month to calculate confidence region, etc.
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An example of SUSY seesaw
S. Antusch, et.al. JHEP 0611 (2006) 090
規格化因子 (×1012)
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5
4
3
2
1
0
2009
2010
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2011
2012
2013
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Signal & BG
BackGround Event
Signal Event
tγ
Eγ
γ
te
μ+
e+
Radiative
Muon
Decay
μ+
γ
Ee
e+
Θeγ
True μ → e+ γ event
Accidental
Background
Normal (Michel) decay e+
νe
μ+
e+
Eγ = Ee = mμ / 2
tγ = te
γ
μ+
e+
or
γ
e- e+
Θeγ = π
RMD γ
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AIF γ
Strategy of physics analysis
Calculate number of signal (Nsig) by most likelihood fitting, from
observables (Eγ, Ee …) which is obtained in experiment.
ℒ 𝑁sig , 𝑁RD , 𝑁BG
−𝑁
=
𝑒
𝑒
𝑁obs !
−
𝑁BG − 𝑁BG 2
𝑁RD − 𝑁RD 2
−
2
2
2𝜎BG
2𝜎RD
𝑒
Branching ratio
𝑁obs
×
(𝑁sig 𝑆 𝑥𝑖 + 𝑁RD 𝑅 𝑥𝑖 + 𝑁BG 𝐵 𝑥𝑖 )
𝑖=1
𝑁sig
ℬ=
𝑘
k : Normalization factor, calculate from data
Set confidence interval (upper limit) from many Toy-MC experiment with
Feldman-Cousin approach.
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RAIF
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ZAIF
AIF
RMD
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Implementation to analysis
We developed the way to implement AIF to MEG physics analysis
PDF type
value
entry
comment
Projection
3×1D
Binning
▲Cannot treat correlation between AIF
observables
3D Binning
1×3D
Binning
▲Much statistics needed for multi
dimension
3D Fit
1×3D
Fitting
▲It is difficult to model distribution is whole
analysis area
MVA
1×1D
Binning
● Correlation can be considered
● Less statistics needed because 1D
Data flow
e+ tracker
γ detector
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Signal BG
training
AIF
rec.
AIF
result
MVA
Calc.
MVA
index
Likelihood
Function
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ｙ
φ
Δy
Δp
Δy =tanφ×Δp
assumed
true
position position
hole #2
Y-hole [cm]
φ
0.4
c 2 / ndf
Prob
4.555 / 6
0.602
Y-hole [cm] -0.272 ± 0.01098
0.3
D P [cm]
-0.2357 ± 0.02644
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-30 -20 -10 0
10 20 30 40 50
phi [degs]
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Using 50 μm errors!
Target major axis
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Target minor axis
2-3 months
Schedule from now
● AIF (1.5- 2.5 months)
・Finalize AIF
・Decide MVA
・PDF preparation
● Target (3weeks)
・Review PDF parameters
・Test modified fitting
● Missing turn (2 weeks)
ー Re-process data (2-6 weeks)
1 month
● Check before Unblind (1-2 weeks)
ー Unblind data
● After unblind
・ Likelihood fit, event check
・ Sensitivity, Confidence interval calculation
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missing turn
Sometimes positron runs more
than 1 turns before exit drift
chamber.
If 1st and 2nd turn are
reconstructed as individual e+, the
initial vector of the 2nd turn makes
wrong vertex.
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1st
2nd