Analysis strategies and treatment of systematic effects in the KATRIN experiment Martin Sle zák for the KATRIN Collaboration Max Planck Institute for Physics Munich, Germany TAUP 2019 Toyama, Japan
Outline • first KATRIN neutrino mass measurement campaign • fit model and data combination • analysis procedure • treatment of systematic effects • conclusion & outlook 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 2
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) 2h live time fit range 117 detector pixels combined zoom into fit range 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 3
KATRIN integral β -spectrum differential rate 𝐸 : • Fermi theory with final states distribution (FSD) of T 2 isotopologues response function 𝑆 : magnetic adiabatic collimation with electrostatic filter (MAC-E filter) • integral rate 𝑂 : • Free parameters 𝜾 2 𝑛 𝜉 effective electron anti-neutrino mass 𝐹 0,eff effective endpoint of the β -spectrum 𝐵 𝐵 signal amplitude (normalization) 2 𝑛 𝜉 𝐹 0,eff 𝑂 bkg constant background rate 𝑂 bkg 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 4
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 scan-wise spectra sum counts over pixels sum counts over scans average response function average slow control readings 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 5
Data analysis procedure Fake data analysis Model blinding • • 𝟑 fake data to mimic actual measurement fake molecular final states distribution 𝒏 𝝃 • • „Asimov data set“ : no statistical fluctuations to hide value of neutrino mass • to implement and freeze analysis before but not other parameters 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) 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 6
Likelihood function • Profile likelihood pdf to describe data points d : Poisson distribution • statistics-only: model m with unconstrained 2 , 𝐹 0,eff , 𝐵 , 𝑂 bkg parameters 𝑛 𝜉 • 𝟑 Treatment of negative 𝒏 𝝃 Asimov dataset statistics only asymmetric Diff. spectrum (w/o FSD) likelihood function no modification of phase 2 < 0 space factor for 𝑛 𝜉 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 7
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 sample systematic parameters initialize model fit with 4 free parameters only ? 𝟑 𝒏 𝝃 ... and repeat References: • R. D. Cousins and V. L. Highland, NIM A 320, 331 (1992) • G. Cowan et al., EPJ C 71, 1554 (2011) • P. M. Harris and M. G. Cox, Metrologia 51, S176 (2014) • S. D. Biller and S. M. Oser, NIM A 774, 103 (2015) Analysis strategies and treatment of systematic effects in the KATRIN experiment 12.09.2019 8
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 true data set model best-fit values fit 2 result 𝑛 𝜉 fake data set (stat. randomized) 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 9
Monte Carlo propagation (systematics only) 2 fit Asimov spectrum with randomized model to retrieve 𝑛 𝜉 • propagation: learn from data: fit actual data to retrieve likelihood value ℒ • distribution of fit results weighted by the likelihood value gives syst-only uncertainties true data set model 10 % uncertainty on ρ d σ likelihood ℒ (exaggerated 10 × !) (randomized) fit best-fit values fit ρ d σ 2 result 𝑛 𝜉 fake data set (Asimov) calibration (PDF for ρ d σ ) ρdσ : gas column density × inelastic cross section 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 10
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 10 % uncertainty on ρ d σ (exaggerated 10 × !) true data set model likelihood ℒ (randomized) fit best-fit values fit ρ d σ 2 result 𝑛 𝜉 fake data set (stat. randomized) calibration (PDF for ρ d σ ) 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 11
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 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 12
Application of MC propagation on fake data • statistical + all identified systematic effects 2 (1 σ ): 0.79 eV 2 (stat) / 0.26 eV 2 (syst) / 0.84 eV 2 (total) sensitivity to 𝑛 𝜉 • first ν -mass campaign: dominated by statistical uncertainty 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 13
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 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 14
𝟑 observable to 𝒏 𝝃 From 𝒏 𝝃 Feldman-Cousins 1 and Lokhov-Tkachov 2 belts constructed at 90 % CL • sensitivity to 𝒏 𝝃 : 1.1 eV @ 90 % C.L. • • compatible with analysis by independent team (see previous talk by T. Lasserre) 1 G. J. Feldman, R.D. Cousins, Phys. Rev. D 57, 3873 (1998) 2 A. V. Lokhov, F. V. Thachov, Phys. Part. Nuclei 46, 347 (2015) 12.09.2019 Analysis strategies and treatment of systematic effects in the KATRIN experiment 15
Conclusion • successful first physics run of KATRIN • developed independent analysis methods ensuring robust and bias-free result • outlook: 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!
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