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Histogram tools: NEST and HistoFit Oleksandr Volynets Histogram tools: NEST and HistoFit NEST Motivation Implementation Results Oleksandr Volynets HistoFit Motivation Implementation Dummy data Max-Planck-Institute for Physics Results

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Histogram tools: NEST and HistoFit

Oleksandr Volynets

Max-Planck-Institute for Physics

MaGe Workshop 2010, Munich

January 19, 2010

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Outline

  • Introduction
  • NEST(New Energy Spectrum Toolkit):
  • Motivation
  • Implementation
  • Results
  • HistoFit
  • Motivation
  • Implementation, method
  • Creating dummy data for check
  • Results of decomposing spectras

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Introduction

  • MaGe/Geant4 is a powerful tool to get the expected

energy spectrum of the experiment.

  • However, all we get is a set of files with spectras from

each holder, cable, detector etc.

  • But the Data only contains one single part which is

naturally a sum of all contributions.

  • We have to do offline histogram analysis to get all those

files together to see how good we understand our detector.

  • In this presentation two histogram tools for spectra

analysis will be shown

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

NEST(New Energy Spectrum Toolkit)

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation

  • The detector has many parts, we simulate (dominant)

radioactive sources in separate parts;

  • In order to plot MC spectrum we have to add all

background contributions with its’ weights according to activities/masses/time;

  • To deal with all these histograms a tool with simple

control of masses, activity etc. of all sources is needed;

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Implementation

The tool called NEST(New Energy Spectrum Toolkit) was created by Jens Schubert. It has the following features:

  • Draw separetely Total energy in all crystals/Total energy

in every crystal/Energy in the individual segment;

  • Draw separately All/Single-crystal/Single-segment events;
  • All parameters of the sources are read from a single text

file; all the parameters of the geometry are read from a single XML-file;

  • Flexible control of output (counts in energy window,

expected counts of every single background contribution etc.);

  • Tag the contributions and get numbers (e.g. background

index) for only needed tags;

  • ...

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Implementation

Example list of parameters:

# +--------------------------------------------------------------------------------+ # | +----------------------------------------------------------------------------+ | # | | LIFE TIMES | | # | +----------------------------------------------------------------------------+ | # +--------------------------------------------------------------------------------+ #HALFlifetime___Agm108 418 years "the HALFlifetime of Agm108" lifetime___Agm108 1.9032785e10 s "the lifetime of Agm108" #HALFlifetime___Agm110 249.9 days "the HALFlifetime of Agm110" lifetime___Agm110 3.11497e7 s "the lifetime of Agm110" # +--------------------------------------------------------------------------------+ # | CONTAMINATION LEVELS

  • - in Phase-1-Crystals

| # +--------------------------------------------------------------------------------+ contamination_Th232___Xtal_ANGx 5.5e-8 Bq/kg "The contamination of contamination_Th232_MeasurementDate___Xtal_ANGx/date 2008-01-01 none "The contamination of Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Implementation

Example geometry description (PhaseIIideal.xml):

<ListOfElBaCos> <Replacer> <ReplaceExpressionName> <RM>ProcBaseName</RM><RM>Nnu</RM> </ReplaceExpressionName> <ReplaceExpressionValue> <RM>DBD_2nu2beta</RM><RM>2 </RM> </ReplaceExpressionValue> <ReplaceExpressionValue> <RM>DBD_0nu2beta</RM><RM>0 </RM> </ReplaceExpressionValue> </Replacer> <!-- loop over all phase-1 crystals --> <ListOfElBaCos switch="on"> <Replacer> <ReplaceExpressionName> <RM>XtalName</RM><RM>GeXXFrac</RM><RM>PhysVolIndex </R <ReplaceExpressionValue switch="on"> <RM>ANG1 </RM><RM>ANG1 </RM><RM>6 </R <ReplaceExpressionValue switch="on"> <RM>ANG2 </RM><RM>ANG2 </RM><RM>12 </R <ReplaceExpressionValue switch="on"> <RM>ANG3 </RM><RM>ANG3 </RM><RM>13 </R <ReplaceExpressionValue switch="on"> <RM>ANG4 </RM><RM>ANG4 </RM><RM>7 </R <ReplaceExpressionValue switch="on"> <RM>ANG5 </RM><RM>ANG5 </RM><RM>11 </R <ReplaceExpressionValue switch="on"> <RM>GTF1 </RM><RM>GTFx </RM><RM>5 </R <ReplaceExpressionValue switch="on"> <RM>GTF2 </RM><RM>GTFx </RM><RM>3 </R <ReplaceExpressionValue switch="on"> <RM>GTF3 </RM><RM>GTFx </RM><RM>2 </R <ReplaceExpressionValue switch="on"> <RM>GTF4 </RM><RM>GTFx </RM><RM>1 </R <ReplaceExpressionValue switch="on"> <RM>GTF5 </RM><RM>GTFx </RM><RM>4 </R <ReplaceExpressionValue switch="on"> <RM>GTF6 </RM><RM>GTFx </RM><RM>0 </R <ReplaceExpressionValue switch="on"> <RM>RG1 </RM><RM>RG1 </RM><RM>9 </R <ReplaceExpressionValue switch="on"> <RM>RG2 </RM><RM>RG2 </RM><RM>10 </R <ReplaceExpressionValue switch="on"> <RM>RG3 </RM><RM>RG3 </RM><RM>8 </R </Replacer> .... Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Results

Energy / MeV 0.5 1 1.5 2 2.5 3 y keV)

enr Ge

counts / (kg

−4

10

−3

10

−2

10

−1

10 1 0.5 1 1.5 2 2.5 3

−4

10

−3

10

−2

10

−1

10 1

Total Energy Spectrum

Energy / MeV 0.5 1 1.5 2 2.5 3 y keV)

enr Ge

counts / (kg

−4

10

−3

10

−2

10

−1

10 1 holders 0.5 1 1.5 2 2.5 3

−4

10

−3

10

−2

10

−1

10 1 Energy / MeV 0.5 1 1.5 2 2.5 3 y keV)

enr Ge

counts / (kg

−4

10

−3

10

−2

10

−1

10 1 holders

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

HistoFit

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation

Let’s imagine the situation:

  • Monte Carlo energy spectras calculated

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation

Let’s imagine the situation:

  • Monte Carlo energy spectras calculated
  • Data energy spectrum obtained

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation

Let’s imagine the situation:

  • Monte Carlo energy spectras calculated
  • Data energy spectrum obtained
  • Monte Carlo describes the shape, but not the numbers

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation

Let’s imagine the situation:

  • Monte Carlo energy spectras calculated
  • Data energy spectrum obtained
  • Monte Carlo describes the shape, but not the numbers

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

DummyData.root Sum of all MC-s

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation

Let’s imagine the situation:

  • Monte Carlo energy spectras calculated
  • Data energy spectrum obtained
  • Monte Carlo describes the shape, but not the numbers
  • Background or Signal contribution estimated wrong?

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

DummyData.root Sum of all MC-s

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation

Tool developed for:

  • Fitting several main MC contributions to data spectrum
  • Getting correct estimates of the contribution

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Motivation, implementation

Tool developed for:

  • Fitting several main MC contributions to data spectrum
  • Getting correct estimates of the contribution

Method: χ2 =

i,bins

(Di−α0MC0

i −α1MC1 i −...)

  • σ2

Di+α2 0σ2 MC0 i

+α2

1σMC1 i +...

  • Use MINUIT to minimize and get αi parameters

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Creating dummy data spectrum

To check whether it works a dummy data was created:

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Cs137.root Cs137.root Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Th232.root Th232.root Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 U238.root U238.root

×2 ×1 ⇒ ×5

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

DummyData.root DummyData.root

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Self-check: Decomposing spectrum

Using the same 3 histograms to fit to “Dummy Data”:

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

DummyData.root Cs137.root Th232.root U238.root Sum of all MC-s

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Self-check: Decomposing spectrum

Using the same 3 histograms to fit to “Dummy Data”:

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

DummyData.root Cs137.root Th232.root U238.root Sum of all MC-s

Parameter 0 = 2 ± 0.00679609 Parameter 1 = 0.999997 ± 0.00316915 χ2 ≈ 10−5 Parameter 2 = 4.99999 ± 0.00722358

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Self-check 2: Decomposing wrong spectrum

Same procedure, but now Dummy Data contains deposits from 3 sources: 137Cs, 232Th and 238U, but set of MC-spectras contains only 2 of them. And it converges but with wrong results (using given spectras):

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Self-check 2: Decomposing wrong spectrum

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 DummyData.root Th232.root U238.root Sum of all MC-s

Parameter 0 = not used Parameter 1 = 1.029 ± 0.003 χ2 = 150000 Parameter 2 = 5.638 ± 0.008

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Self-check 2: Decomposing wrong spectrum

Energy [MeV] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Entries per primary 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 DummyData.root Cs137.root Th232.root Sum of all MC-s

Parameter 0 = 2.266 ± 0.009 Parameter 1 = 4.794 ± 0.008 χ2 = 530000 Parameter 2 = not used

Oleksandr Volynets Histogram tools: NEST and HistoFit

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Histogram tools: NEST and HistoFit Oleksandr Volynets NEST

Motivation Implementation Results

HistoFit

Motivation Implementation Dummy data Results

Conclusions and discussion

Next steps:

  • Wait for the data at GERDA, or
  • Find some data with measuring several sources

simultaneously Is the following needed:

  • Fitting MC-s within different regions

(e.g. Sp1=0..1.5 MeV; Sp2=1..2.3 MeV) - complicated but possible

  • Else?

Oleksandr Volynets Histogram tools: NEST and HistoFit