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

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

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

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

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

Mean .2eV, Standard Deviation .05 eV Estimated μ: 0.205 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.

Likelihoods vs estimated mean

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

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

Likelihoods, 500 runs σ = .2 σ = .05

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

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