Transcript Detecting sterile neutrinos with KATRIN

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
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)
 m  0.6 eV @ 95 C.L.
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(ms2)]?
Parameters
Sterile Neutrinos Toy Model
• One active massless neutrino
• One sterile massive neutrino
• What is KATRINs detection potential for the
sterile neutrino [= ms2/σ(ms2)]?
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.
2
• 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..

2
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.
2
• 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..

2
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
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
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 MetroplisHastings 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
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  -2
function
• Analyse with
COSMOMC
Graphical output
KATRIN Standard Setup
KATRIN Standard Setup
KATRIN Standard Setup
• Degeneracy for ms2 = {0.08,0.16, 0.32, 0.64, 1.3} eV2
• For |Ues|2 = 0.18
KATRIN Standard Setup
• Degeneracy for ms2 = {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: MiniBoone results and
neuutrino schemes
with two sterile
neutrinos: possible
mass orderings and
observables related
to neutrino masses
(JHEP10 2007 No
73)