Systematic error and

double Gaussian fitting

Toshi Gogami3Apr2014

Contents

Systematic error for binding/excitation energy 12

ΛB(1-,2-) state separation

Different distorted initial matrices

• Distorted matrix sample 6 (dist6)• Distorted matrix sample 7 (dist7)• Distorted matrix sample 8 (dist8)

Differential non-linearity (older sample)

Missing mass [GeV/c2]

12ΛB

7ΛHe 52

ΛV

Before and after the optimization(dist6)

dist6

Standard deviation due to matrices(dist6)

σ = sqrt(σmat+σstat)

σmat = sqrt(σ-σstat)

After matrix optimization

Results for (dist8)(g.s. fitting mean )– Mgen

[keV]A

σmat [keV]

BLambda -4.211.0 21.2Sigma -15.313.0 44.37

ΛHe +44.06.8 23.09

ΛLi -25.435.0 17.510

ΛBe +48.83.3 19.912

ΛB +12.75.8 15.652

ΛCr +65.34.2 5.2

Results for (dist7)(g.s. fitting mean )– Mgen

[keV]A

σmat [keV]

BLambda -2.410.6 6.8Sigma -26.113.1 26.77

ΛHe -11.99.2 16.69

ΛLi -72.37.0 29.110

ΛBe -40.68.1 24.212

ΛB -10.111.1 26.652

ΛCr -61.411.6 27.6

Results for (dist6)(g.s. fitting mean )– Mgen

[keV]A

σmat [keV]

BLambda -11.110.9 32.9Sigma +1.712.5 43.07

ΛHe +20.57.0 32.89

ΛLi -66.15.2 29.210

ΛBe -10.05.2 9.612

ΛB -48.56.2 33.052

ΛCr -19.17.2 37.0

Summary１[Systematic errors]

Fitting mean - Mgen < 80 keV (A: shift of mean value)σmat < 50 keV (B: standard deviation in the interested region)

ΔBmat = sqrt(80*80+50*50) = 94 keVΔEmat = 50 keV

5% of target thickness uncertaintyΛ, Σ0 : < 50 keVHypernucleus : < 20 keV

ΔBmat = 110 keVΔEmat = 50 keV

Decomposition of 1- and 2-

-BΛ[MeV]

Coun

ts

Mean1

Amp1

Amp2

Mean2

Chunhua’s spectrum

Test conditions

Common conditions for testsNpoint = 100Step = 0.002 MeVMean1: -11.45 – Step * i (i<Npoint)Mean2: -11.45 + Step * i (i<Npoint)

Parameters• Chunhua’s spectrum

• σ = 0.231 (fixed)

• Han’s spectrum• σ = 0.300 (fixed)

• Toshi’s spectrum • σ = 0.200 (fixed)

|χ2-1.0| distributionreal data

|χ2-1.0| distribution (Chunhua2009)

Mean1 [MeV]

Mean2 [MeV]

σ = 231 keV (fixed)

paper

Mean1 – Mean2 = 162 keV

Mean1 [MeV]

Mea

n2 [M

eV]

|χ2 -1

.0|

|χ2-1.0|

|χ2-1.0| distribution(Han2009)

Mean1 [MeV]

Mean2 [MeV]

σ = 300 keV (fixed)

paper

Mean1 – Mean2 = 162 keV

Mean1 [MeV]

Mea

n2 [M

eV]

|χ2 -1

.0|

|χ2-1.0|

|χ2-1.0| distribution (Toshi2009)

Mean1 [MeV]

Mean2 [MeV]

σ = 220 keV (fixed)

Mean1 – Mean2 = 162 keV

Mean1 [MeV]

Mea

n2 [M

eV]

|χ2 -1

.0|

|χ2-1.0|

SIMULATION

Test conditions (Simulation)

Npoint = 100Step = 0.002 MeVMean1: -11.32 – Step * i (i<Npoint)Mean2: -11.32 + Step * i (i<Npoint)

Generated dummy data

Assumptions 100 + 600 = 700 events 160 keV separation (-BΛ

g.s. = -11.38 MeV) Gaussian distribution (σ = 0.200 MeV) No background

-BΛ [MeV]

[Cou

nts/

240

keV]

SIMULATION

Fitting results (1)

Mean1 [MeV]

Mean2 [M

eV]

Mean1 [MeV]

Mea

n2 [M

eV]

X

σ = 180 keV σ = 190 keV σ = 200 keV

Assumed width for fitting

Answer

Answer Answer

Mean1 – Mean2 = 160 keV

SIMULATION SIMULATION SIMULATIONAnswer

Fitting results (2)

Mean1 [MeV]Mean2 [MeV]

Mean1 [MeV]

Mea

n2 [M

eV]

X

σ = 210 keV σ = 220 keV σ = 230 keV

Assumed width for fitting

Answer

Answer Answer

Mean1 – Mean2 = 160 keV

SIMULATION SIMULATION SIMULATION

Fitting results (4)

Mean1 [MeV]

Mean2 [MeV]

Mean1 [MeV]

Mea

n2 [M

eV]

X

σ = 240 keV

Answer

Mean1 – Mean2 = 160 keV

SIMULATION

Samples

Answer

Mean1 [MeV]

Mea

n2 [M

eV]

[MeV] [MeV]

[MeV]

[MeV]

Summary 2[About 12

ΛB(1-,2-) separation]• What we can say from this study

• We could not reproduce paper values….(E01-011 data could be reproduced though)(I would like to see Hampton’s side study)

• What we thought from this study• In the case of simple Gaussian

• Difficult to find the answer with this method…• In the real case (peaks are not simple Gaussian distributions)

• If this method works well after some analysis improvements, we need to confirm whether the method works or not for peaks which affected by energy straggling, production point displacement from matrix origin, detector resolutions, spectrometer acceptance, beam raster and so on. Can be checked by blind analyses.

• Is there any good cut (selection) condition to find the answer ? need further study.

English ver.