Analysis strategies and treatment of systematic effects in the - - PowerPoint PPT Presentation

Analysis strategies and treatment of systematic effects in the KATRIN experiment

Martin Slezák for the KATRIN Collaboration Max Planck Institute for Physics Munich, Germany TAUP 2019 Toyama, Japan

12.09.2019 2

Outline

• first KATRIN neutrino mass measurement campaign
• fit model and data combination
• analysis procedure
• treatment of systematic effects
• conclusion & outlook

Analysis strategies and treatment of systematic effects in the KATRIN experiment

12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 3

First neutrino mass campaign @ KATRIN (KNM1)

• 22 % of nominal tritium activity ↔ gas density in tritium source
• 2 million electrons in ν mass fit range (> 40 eV below endpoint)
• about 5 day equivalent of nominal KATRIN time (out of 1000 days)

single spectrum (out of 274 golden scans)

fit range zoom into

2h live time 117 detector pixels combined

fit range

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KATRIN integral β-spectrum

• differential rate 𝐸:

Fermi theory with final states distribution (FSD) of T2 isotopologues

• response function 𝑆: magnetic adiabatic collimation with electrostatic filter (MAC-E filter)
• integral rate 𝑂:

Free parameters 𝜾

𝑛𝜉

2

effective electron anti-neutrino mass 𝐹0,eff effective endpoint of the β-spectrum 𝐵 signal amplitude (normalization) 𝑂bkg constant background rate 𝐵 𝑂bkg 𝐹0,eff 𝑛𝜉

2

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Data combination

• each pixel of focal plane detector measures statistically independent spectrum
• multiple scans (stepping of retarding potential) of the β-spectrum
• first campaign approach: combine all into single spectrum

pixel-wise spectra sum counts over pixels average response function scan-wise spectra sum counts over scans average slow control readings

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Data analysis procedure

𝒏𝝃

𝟑 Model blinding

• fake molecular final states distribution
• to hide value of neutrino mass

but not other parameters Fake data analysis

• fake data to mimic actual measurement
• „Asimov data set“: no statistical fluctuations
• to implement and freeze analysis before

using on real data Complementarity

• two independent approaches to assess, include, and propagate systematic uncertainties
• covariance matrix (see previous talk by T. Lasserre), Monte Carlo propagation of uncertainty (this talk)

Asimov dataset statistics only 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 7

Likelihood function

• pdf to describe data points d: Poisson distribution
• statistics-only: model m with unconstrained

parameters 𝑛𝜉

2, 𝐹0,eff, 𝐵, 𝑂bkg

• Profile likelihood
• Diff. spectrum (w/o FSD)

no modification of phase space factor for 𝑛𝜉

2 < 0

asymmetric likelihood function

Treatment of negative 𝒏𝝃

𝟑

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Monte Carlo propagation of uncertainty

• fits to obtain maximum likelihood infeasible if too many additional free parameters
• general idea: propagate systematics by fitting many times

with randomized but fixed values of systematic parameters

• propagation of distributions by random sampling, adapted for KATRIN

References:

• G. Cowan et al., EPJ C 71, 1554 (2011)
• S. D. Biller and S. M. Oser, NIM A 774, 103 (2015)
• R. D. Cousins and V. L. Highland, NIM A 320, 331 (1992)
• P. M. Harris and M. G. Cox, Metrologia 51, S176 (2014)

?

sample systematic parameters initialize model fit with 4 free parameters only

𝒏𝝃

𝟑 ... and repeat

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Monte Carlo propagation (statistics only)

• sample MC integral spectrum counts from Poisson distribution and fit it
• Poisson mean centered at the model value given from the best fit of the data
• distribution of fit results gives stat-only uncertainties

best-fit values

fake data set

(stat. randomized)

true data set

fit result 𝑛𝜉

2

model

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Monte Carlo propagation (systematics only)

• propagation:

fit Asimov spectrum with randomized model to retrieve 𝑛𝜉

2

• learn from data: fit actual data to retrieve likelihood value ℒ
• distribution of fit results weighted by the likelihood value gives syst-only uncertainties

10 % uncertainty on ρdσ (exaggerated 10× !)

best-fit values

fake data set

(Asimov)

true data set

fit result 𝑛𝜉

2

model

(randomized) fit likelihood ℒ ρdσ

calibration

(PDF for ρdσ)

ρdσ: gas column density × inelastic cross section

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MC propagation (statistics + systematics)

• randomize fake data set statistically and model systematically at the same time
• retrieves both statistical and systematic uncertainty combined
• no need for adding uncertainties in squares

best-fit values

fake data set

(stat. randomized)

true data set

fit result 𝑛𝜉

2

model

(randomized) fit likelihood ℒ ρdσ

calibration

(PDF for ρdσ)

10 % uncertainty on ρdσ (exaggerated 10× !)

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Selling points for MC propagation

 feasible fits as systematic effects are fixed at the start of a fit

× free nuisance parameters × full Bayesian sampling

 no assumption of Gaussian-distributed integral spectrum rates

× covariance matrix

 no special algorithm for sampling (requires minimizer though)

× full Bayesian sampling (e.g. Metropolis-Hastings algorithm)

• need to perform thousands of fits

 but embarrassingly parallel → run on computing cluster www.mpcdf.mpg.de

Acknowledgement:

• S. Ohlmann et al., Max Planck Computing and Data Facility

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Application of MC propagation on fake data

• statistical + all identified systematic effects
• sensitivity to 𝑛𝜉

2 (1σ): 0.79 eV2 (stat) / 0.26 eV2 (syst) / 0.84 eV2 (total)

• first ν-mass campaign: dominated by statistical uncertainty

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Systematics breakdown on fake data

• background, gas density × inelastic cross section, magnetic fields
• activity fluctuations and high-voltage reproducibility
• final state distribution

0.013 0.002

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From 𝒏𝝃

𝟑 observable to 𝒏𝝃

• Feldman-Cousins1 and Lokhov-Tkachov2 belts constructed at 90 % CL
• sensitivity to 𝒏𝝃: 1.1 eV @ 90 % C.L.
• compatible with analysis by independent team (see previous talk by T. Lasserre)
• 1G. J. Feldman, R.D. Cousins, Phys. Rev. D 57, 3873 (1998)
• 2A. V. Lokhov, F. V. Thachov, Phys. Part. Nuclei 46, 347 (2015)

Conclusion

• successful first physics run of KATRIN
• developed independent analysis methods ensuring robust and bias-free result
• utlook: utilize full information of pixelated detector → multi-pixel fit

– normalization and background per pixel, common endpoint and neutrino mass – low counts per pixel, cannot use covariance matrix

• MC propagation as promising tool for future analysis
• see talk tomorrow by G. Drexlin for measurement result

Thank you for your attention!