1. Monte Carlo Simulation of Neutrino Mass Measurements
Amy Lowitz
4 May 2011

2. Neutrino Mass Believed to be very small, but non-zero
Small deviations from zero are difficult to measure with statistical significance
Current best estimates:
From cosmology, hard limit of 50 eV avg per neutrino to prevent universe collapse
Analysis of CMB and galactic survey data lead us to believe the sum of the neutrino masses must be less than .3eV
More stringent limits have come out of a number of recent experiments

3. Project
Generate simulated neutrino mass measurements for 2 different instrumental resolutions
Investigate the effect of instrumental resolution on ability to reject mass = 0

4. Methodology Monte Carlo-based simulation technique
Underlying distribution
σ = .2 eV or .05 eV
μ = .2 eV
Upper bound of 2.5 eV
Lower bound of 0 eV
Training Data Set
10 Million samples total, at 500 different means
For numerical maximum likelihood estimation
Testing Data Set
2000 pseudo-random samples from the underlying distribution

5. Hypothesis testing Significance level: α = .01 Ho : mass = 0
Ha : mass > 0

6. Mean .2eV, Standard Deviation .05 eV
Estimated μ: eV
Test Statistic:
Z = 183.3
counts
Sample value [eV]
For α = .01, rejection region corresponds to Z ≥ 2.58
Therefore we can reject Ho.
Indeed, even with a single data point of .205, we could have rejected Ho.

7. Likelihoods vs estimated mean

8. Mean .2eV, Standard Deviation .2 eV
Estimated μ: .185eV
Test statistic:
Z = 41.3
For α = .01, rejection region corresponds to Z ≥ 2.58
Therefore we can reject Ho.
Even with just 500 runs, Ho still rejected

9. 500 runs Estimated μ: .195eV Test statistic: Z = 21.8
For α = .05, rejection region corresponds to Z ≥ 2.58
Therefore we can again reject Ho.
If you get a mean of .2, you only need 7 data points to reject

10. Likelihoods, 500 runs
σ = .2
σ = .05

11. Important Assumptions and Limitations
Underlying distribution: Clipped Gaussian
Other option: use convolution of Gamma with Gaussian
This method still captures the issue of resolution in statistical significance
Resolution of Training Data and Number of Trials
Limited by memory capability of Octave and processor speed

12. Conclusions
Even relatively low resolution can rule out massless neutrinos without very many data points
However, this simulation doesn’t take into account the realities of real measurement devices
Random errors from multiple instrumental elements
systematics