Prospects for the detection of sterile neutrinos with KATRIN-like

experimentsAnna Sejersen Riis, Steen Hannestad

“Detecting sterile neutrinos with KATRIN like experiments”JCAP02(2011)011

KATRIN

Sterile Neutrinos

• Could there be more than three neutrino species?• The suggestion is: sterile neutrinos. They mix with

the active species via a larger mixing matrix, but otherwise do not interact in the Standard Model.

• The LSND experiment observed an excess appearance of electron antineutrinos in muon antineutrino beam from an accelerator. At Δm2 ~ 1eV2.

• This can NOT be explained by the standard oscillation scheme!

Sterile Neutrinos• Recent support:

The current cosmological bounds

From Hamann, Hannestad, Lesgourges, Rampf & Wong:Cosmological parameters from large scale structure - geometric versus shape information (JCAP07 2010 No 22)

C.L. 95 @ eV 6.0m Using the minimal Cosmological Model

Active Neutrinos

• Three known active neutrino species with 2 mass squared differences:

• Cannot be detected with KATRIN’s sensitivity of 0.2 eV

Sterile Neutrinos Toy Model

• One active massless neutrino• One sterile massive neutrino• What is KATRINs detection potential for the

sterile neutrino [= ms2/σ(ms

2)]?

Parameters

Sterile Neutrinos Toy Model

• One active massless neutrino• One sterile massive neutrino• What is KATRINs detection potential for the

sterile neutrino [= ms2/σ(ms

2)]?

Parameters

Original features of KATRIN simulation and analysis code

• Monte Carlo and analysis code from the KATRIN collaboration

• Minimization using Minuit. Now a part of the ROOT package

• This is a search for minima in -parameterspace. To be performed for x spectra.

• CombinedMinimizer uses Migrad (covariance matrix evaluation) and Simplex (simplex minimum search)

• The minimization approach is NOT well suited for multi-parameter spaces with e.g. shallow minima, more than one minimum, correlated parameters..

22

Original features of KATRIN simulation and analysis code

• Monte Carlo and analysis code from the KATRIN collaboration

• Minimization using Minuit. Now a part of the ROOT package

• This is a search for minima in -parameterspace. To be performed for x spectra.

• CombinedMinimizer uses Migrad (covariance matrix evaluation) and Simplex (simplex minimum search)

• The minimization approach is NOT well suited for multi-parameter spaces with e.g. shallow minima, more than one minimum, correlated parameters..

22

Bayesian statisticsA ’subjective’ probability analysis

• We ask: What is the most probable value of our parameters – given data and model?

• Combined with the question: What is the probability of the data given parameters and model?

• ..and Bayes theorem:

• We get the posterior

Bayesian statisticsThe ingredients:

The Likelihood function is the probability of the dataset

The Prior (which has no dependence on the data) is our subjective, or theoretical knowledge before taking any data into account

The evidence (which has no dependece on the parameters) is in effect a normalisation factor

The Posterior is the probability of the parameters given the data and our chosen theoretical model

Markov Chain Monte Carlo and Metropolis-Hastings Algorithm

We use a random walk, and a bayesian probability analysis to probe the parameter space

We then use the Metroplis-Hastings algorithm: - Choose starting point - Propose a step in a random direction - Decide whether to take step:Yes, if P is largerOtherwise accept with probability r, reject with probability 1-r

Advantages• Markov Chain Monte Carlo probes also outside the

extrema. This makes it more suitable for discovering multiple minima.

• The parameter space is better charted near minima.• With multiple chains that start at random initial points

one gets very good picture of the parameter space.

Input data • Use the KATRIN

standard analysis code to generate one theoretical data-set with added sterile mass-state.

• Keep error-bars from original Monte Carlo

• Use the same code as -function

• Analyse with COSMOMC

2

Graphical output

KATRIN Standard Setup

KATRIN Standard Setup

KATRIN Standard Setup• Degeneracy for ms

2 = {0.08,0.16, 0.32, 0.64, 1.3} eV2

• For |Ues|2 = 0.18

KATRIN Standard Setup• Degeneracy for ms

2 = {0.08,0.16, 0.32, 0.64, 1.3} eV2

• For |Ues|2 = 0.18

SuperKATRIN?• We investigate what

happens when tuning the KATRIN parameters in our code

SuperKATRIN!• We investigate what happens

when tuning the KATRIN parameters in our code:

Increase the countrate near the endpoint (current amplitude 477.5 Hz)

Lower the background rate (currently 0.01Hz)

Improve the energy resolution (currently 0.93eV)

Effect of Enhanced Amplitude

Effect of Enhanced Amplitude

Effect of Reduced Background

Effect of Better Energy Resolution

Summary 1• Better results can be achieved

with higher signal countrate or lower background.

• KATRIN’s current source is optimized for the size of the spectrometer

• It is unclear if the background can be lowered in KATRIN

• Maybe Future experiments such as MARE and Project 8 can be more easily improved

Summary 2• KATRIN will definetely be able

to see sterile neutrinos if they have high enough mass or mixing weight:

3 σ detection for ms≥ 3.2 eV

Or |Ues|2 ≥ 0.055

1 σ detection for ms≥ 0.8 eV

Or |Ues|2 ≥ 0.018

• The latest result suggest these particles may actually exist!

The End

Thank you for your attention!

Oscillation experiments

Active Neutrinos• Three known active neutrino species

• Where cik=cos(θik), sik=sin(θik) are the mixing angles and δ,α & β are the Majorana phase and the two Dirac phases

Example: 3+2 scenario

Goswami & Rodejohann: Mini-Boone results and neuutrino schemes with two sterile neutrinos: possible mass orderings and observables related to neutrino masses (JHEP10 2007 No 73)