KATRIN Experimental Setup

• Goal: Measure the β-decay electron energy spectrum of tritium near the endpoint (18.6 keV) to search for neutrino masses and sterile neutrinos.
• Setup includes:
  • Gaseous tritium source (WGTS) with high isotopic purity (~99%).
  • Magnetic guidance of electrons (2.5 T field in WGTS), differential and cryogenic pumping to reduce tritium flow, chicanes to reduce residual tritium.
  • Two spectrometers: a pre-spectrometer (low resolution) and main spectrometer (high resolution ~1 eV).
  • Silicon p-i-n segmented detector with about 148 pixels.
• Backgrounds: Arise from cosmic muons, Rn decays, ions/electrons trapped magnetically, and sputtered 210Pb decays; mitigated by magnetic shielding, wire electrodes, cryogenic baffles, and optimized electromagnetic fields (SAP setting).
• Background rate improved over campaigns—from ~0.29 cps (KNM1) to 0.12 cps (KNM3-SAP).

Data Collections (Campaigns KNM1–KNM5)

• Each campaign (KNM) collects β-decay spectra over many retarding potential scans.
• Source conditions improved over time (density approaching design value, temperature adjustments).
• Later campaigns deployed SAP settings to reduce backgrounds.
• Data divided into sets grouped by different detector configurations and operational modes (NAP vs SAP).
• Total data contain ~36 million counts from 68,237 scan steps across all campaigns.
• KNM4 campaign was split into two sub-campaigns due to changes in measurement time distribution and pre-spectrometer configurations (KNM4-NOM and KNM4-OPT).

Analysis Frameworks

• Two independent analysis toolkits used:
  • KaFit: C++ based, uses numerical integrals and caching techniques for spectrum calculation and χ² minimization with MINUIT.
  • Netrium: Neural-network-based model approximation trained on simulated spectra, providing ~1000x speed-up.
• Both frameworks cross-validate and agree well (e.g., exclusion contours and best-fit parameters).
• Blinding strategy is employed using blind Asimov datasets to avoid bias and validate analysis before unblinding real data.
• Anomalies in intermediate analyses (like KNM4 closed contour) triggered technical investigations and corrections.

Statistical Model and Likelihood

• Likelihood modeled as a product of Poisson or Gaussian pdfs, depending on count size per pixel or patch.
• Joint χ² function combines contributions from all campaigns, accounting for nuisance parameters and correlations via covariance matrices.
• Systematic uncertainties included as Gaussian penalty terms.
• Raster scans performed to evaluate individual and combined systematics impact; result: statistics dominate overall uncertainties.
• Main systematics impacting sensitivity are related to source gas density, energy-loss function, source potential, and backgrounds.

Final-State Distribution Systematics

• Ro-vibrational and electronic excited states in tritium decay affect β energy spectrum shape.
• Evaluated via variations in theoretical models; impact found to be negligible for sterile neutrino sensitivity.
• Nominal final-state distribution models are sufficient for current analysis precision.

Statistical Validations and Wilks’ Theorem

• Use Δχ² test statistic: (\Delta \chi^{2} = \chi^{2}(H{0}) – \chi^{2}(H{1})) for hypotheses testing.
• Wilks’ theorem states Δχ² follows a chi-square distribution with degrees of freedom equal to the number of tested parameters (here 2).
• Monte Carlo simulations (~1000 pseudo-experiments) validated Wilks’ theorem applicability for:
  1. Null hypothesis (no sterile neutrinos).
  2. Best-fit sterile neutrino parameters.
• Empirical cumulative distribution functions match the theoretical chi-square distribution well.
• Critical values (95% CL) match expected Δχ² ~5.99.
• This enables use of Wilks’ theorem to efficiently set exclusion limits and confidence intervals without extensive simulations.

Results and Sensitivity

• Individual campaigns provide exclusion regions in sterile neutrino parameter space; combined data sets improve limits significantly.
• Exclusion contours from measured data mostly lie within expected sensitivity bands but show some deviations attributed to statistical fluctuations or systematic effects.
• Sensitivity increases with more data and lower backgrounds, validating KATRIN’s approach for sterile neutrino searches.

If you want, I can help you generate:

• Specific plots or interpret existing data
• Mathematical expressions or code snippets related to likelihood or fit procedures
• More detailed explanations of certain experimental or analysis components

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