Quantifying the sensitivity of oscillation experiments to the neutrino mass ordering
Mattias Blennow
3
Pilar Coloma
1
Patrick Huber
1
Thomas Schwetz
0
2
0
Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University
, SE-10691 Stockholm,
Sweden
1
Center for Neutrino Physics
, Virginia Tech, Blacksburg,
VA 24061, U.S.A
2
Max-Planck-Institut fur Kernphysik
, Saupfercheckweg 1,
69117 Heidelberg, Germany
3
Department of Theoretical Physics, School of Engineering Sciences, KTH Royal Institute of Technology, AlbaNova University Center
,
106 91 Stockholm, Sweden
Determining the type of the neutrino mass ordering (normal versus inverted) is one of the most important open questions in neutrino physics. In this paper we clarify the statistical interpretation of sensitivity calculations for this measurement. We employ standard frequentist methods of hypothesis testing in order to precisely define terms like the median sensitivity of an experiment. We consider a test statistic T which in a certain limit will be normal distributed. We show that the median sensitivity in this limit is very close to standard sensitivities based on 2 values from a data set without statistical fluctuations, such as widely used in the literature. Furthermore, we perform an explicit Monte Carlo simulation of the INO, JUNO, LBNE, NOA, and PINGU experiments in order to verify the validity of the Gaussian limit, and provide a comparison of the expected sensitivities for those experiments.
1 Introduction 2 3 4
Terminology and statistical methods
2.1 Frequentist hypothesis testing
2.2 Application to the neutrino mass ordering
2.3 Median sensitivity or the sensitivity of an average experiment
3.1 Simple hypotheses
3.2 Composite hypotheses
Monte Carlo simulations of experimental setups
4.1 Medium-baseline reactor experiment: JUNO
4.2 Atmospheric neutrinos: PINGU and INO
4.3 Long-baseline appearance experiments: NOA and LBNE
Comparison between facilities: future prospects
Discussion and summary
A The distribution of T
B Simulation details
B.1 Medium baseline reactor experiment: JUNO
B.2 Atmospheric neutrino experiments: PINGU and INO
B.3 Long baseline beam experiments: NOA, LBNE-10 kt, LBNE-34 kt
Introduction
The ordering of neutrinos masses constitutes one of the major open issues in particle
physics. The mass ordering is called normal (inverted) if m231 m23 m21 is
positive (negative). Here and in the following we use the standard parameterization for the
neutrino mass states and PMNS lepton mixing matrix [1]. Finding out which of these
two possibilities is realized in Nature has profound implications for the flavor puzzle, as
well as phenomenological consequences for cosmology, searches for neutrino mass, and for
neutrinoless double-beta decay. Therefore, the determination of the mass ordering is one
of the experimental priorities in the field. In particular, with the discovery of a large value
of 13 [25] an answer within a decade or so is certainly possible and first hints may be
obtained even sooner in global fits to the worlds neutrino data.
New information is expected to come from long-baseline experiments, like T2K [6] and
NOA [7, 8], which look for the appearance of e(e) in a beam of (). Proposals for
a more long-term time frame include LBNE [911], LBNO [12], a superbeam based on
the ESS [13], and eventually a neutrino factory [14]. Matter effects [1517] will induce
characteristic differences between the neutrino and antineutrino channels, which in turn
will allow inference of the mass ordering, see e.g., refs. [18, 19] for early references. The
fact that a comparison of neutrino and antineutrino channels is performed also implies that
the leptonic CP phase cannot be ignored and has to be included in the analysis as well.
A selective set of recent sensitivity studies for present and future proposed long baseline
oscillation experiments can be found in refs. [2031].
Another possibility to determine the mass ordering arises from observing the energy
and zenith angle dependence of atmospheric neutrinos in the GeV range, which will also
have the mass ordering information imprinted by matter effects [3237]. The flux of
atmospheric neutrinos follows a steep power law with energy and thus the flux in the GeV range
is quite small and requires very large detectors. IceCube technology can be adapted to
neutrino energies in the GeV range by reducing the spacing of optical modules, eventually
leading to the PINGU extension [38] and a similar low-energy modification can also be
implemented for neutrino telescopes in the open ocean, called ORCA [39]. Another way
to overcome the small neutrino flux is to separate neutrino and antineutrino events using
a magnetic field like in the ICal@INO experiment [40, 41] (INO for short in the following).
Mass ordering sensitivity calculations have been performed for instance in refs. [4250] for
PINGU/ORCA and in refs. [5159] for INO or similar setups.
Finally, the interference effects between the oscillations driven by m221 and m231
in the disappearance (...truncated)