1. Prospects for the detection of sterile neutrinos with KATRIN-like experiments Anna Sejersen Riis, Steen Hannestad “Detecting sterile neutrinos with KATRIN like experiments” JCAP02(2011)011

2. KATRIN

3. 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 Δm 2 ~ 1eV 2. This can NOT be explained by the standard oscillation scheme!

4. Sterile Neutrinos Recent support:

5. The current cosmological bounds From Hamann, Hannestad, Lesgourges, Rampf & Wong: Cosmological parameters from large scale structure - geometric versus shape information (JCAP07 2010 No 22) Using the minimal Cosmological Model

6. Active Neutrinos Three known active neutrino species with 2 mass squared differences: Cannot be detected with KATRIN’s sensitivity of 0.2 eV

7. Sterile Neutrinos Toy Model One active massless neutrino One sterile massive neutrino What is KATRINs detection potential for the sterile neutrino [= m s 2 /σ(m s 2 )]? Parameters

8. Sterile Neutrinos Toy Model One active massless neutrino One sterile massive neutrino What is KATRINs detection potential for the sterile neutrino [= m s 2 /σ(m s 2 )]? Parameters

9. 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..

10. 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..

11. Bayesian statistics A ’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

12. Bayesian statistics The 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

13. 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 larger Otherwise accept with probability r, reject with probability 1-r

14. 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.

15. 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

16. Graphical output

17. KATRIN Standard Setup

19. Degeneracy for m s 2 = {0.08,0.16, 0.32, 0.64, 1.3} eV 2 For |U es | 2 = 0.18

20. KATRIN Standard Setup Degeneracy for m s 2 = {0.08,0.16, 0.32, 0.64, 1.3} eV 2 For |U es | 2 = 0.18

21. SuperKATRIN? We investigate what happens when tuning the KATRIN parameters in our code

22. 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)

23. Effect of Enhanced Amplitude

25. Effect of Reduced Background

26. Effect of Better Energy Resolution

27. 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

28. Summary 2 KATRIN will definetely be able to see sterile neutrinos if they have high enough mass or mixing weight: 3 σ detection for m s ≥ 3.2 eV Or |U es | 2 ≥ 0.055 1 σ detection for m s ≥ 0.8 eV Or |U es | 2 ≥ 0.018 The latest result suggest these particles may actually exist!

29. The End Thank you for your attention!

30. Oscillation experiments

31. Active Neutrinos Three known active neutrino species Where c ik =cos(θ ik ), s ik =sin(θ ik ) are the mixing angles and δ,α & β are the Majorana phase and the two Dirac phases

32. 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)