Search for sterile neutrino mixing in the νμ → ντ appearance channel with the OPERA detector
EPJ Web of Conferences
Search for sterile neutrino mixing in the νμ → ντ appearance channel with the OPERA detector
N. Mauri 0
on behalf of the OPERA Collaboration
0 INFN - Sezione di Bologna , Viale Berti Pichat 6/2, I-40127 Bologna , Italy
The OPERA experiment has observed muon neutrino to tau neutrino oscillations in the atmospheric sector in appearance mode. Five ντ candidate events have been detected, a number consistent with the expectation from the “standard” 3ν framework. Based on this result new limits on the mixing parameters of a massive sterile neutrino have been set. The analysis is performed in the 3+1 neutrino model.
The discovery of neutrino oscillations established the fact that neutrinos have a non-zero mass,
pointing to physics beyond the Standard Model. Since the first observation of the disappearance of
atmospheric muon neutrinos in 1998, many experiments contributed to draw a coherent picture of the
new “standard” 3ν framework. The oscillations are formalized by the PMNS unitary matrix UPMNS
through which three flavour eigenstates are mixed with three mass eigenstates [
]. After less than
20 years, the three mixing angles θ12, θ13, θ23 parameterized in UPMNS are measured as well as the two
squared mass differences Δm221, Δm232 determining the oscillation frequencies .
However, a certain number of so-called neutrino “anomalies” show tensions with this well
established 3ν framework [
]. Different kinds of experiments, both in appearance and disappearance [
point towards a new parameter region Δm2 ∼ 1 eV2. Since the number of flavour-active neutrinos
is bound to 3 by the coupling with the Z0, the new squared mass difference could be accounted for
by the existence of a sterile neutrino. A sterile neutrino is a neutral lepton which does not couple
to W±/Z0 bosons. It is not an exotic particle, e.g. right-handed neutrinos are singlets under S U(2)L
gauge. Sterile neutrinos can mix with the active ones and the mass scale of additional states has no
strong a priori. The experimental “anomalies” hint to the existence of light O(1) eV steriles.
The OPERA experiment was designed to observe νμ → ντ oscillations in appearance mode, in
order to unambiguously prove the νμ → ντ transition at the atmospheric scale in the 3ν framework.
OPERA recently assessed the discovery of ντ appearance in the CNGS νμ beam with a significance of
]. The number of ντ events detected by OPERA is compatible with the expectations from the
standard 3ν framework. We can therefore set limits on the oscillations induced by a sterile neutrino,
here formalized by the 3 + 1 neutrino model.
2 The 3+1 neutrino model
The new 3+1 model should include the well established 3ν framework. The additional sterile
eigenstate can be represented through an extended 4 × 4 mixing matrix U which slightly perturbs the inner
3 × 3 UPMNS and extends the mixing to a 4th neutrino. In this 3+1 neutrino model, the first three mass
eigenstates are mostly composed by flavour-active states with the well known mixing, while the forth
mass eigenstate is almost exclusively composed by the sterile state. The 4th mass term is supposed to
be heavier than the other three ones, since the experimental anomalies suggest a Δm2 ∼ eV2 and the
cosmological limits on the sum of neutrino masses favour a positive Δm241 [
]. In the 3+1 model,
defining Δi j = 1.27 Δmi2j L/E (where Δmi2j is expressed in eV2, L in km and E in GeV), the probability
for νμ → ντ transitions in given by
4|Uμ3|2|Uτ3|2 sin2 Δ31 + 4|Uμ4|2|Uτ4|2 sin2 Δ41
2R[Uμ3Uτ∗3Uμ∗4Uτ4] sin 2Δ31 sin 2Δ41
4I[Uμ3Uτ∗3Uμ∗4Uτ4] sin2 Δ31 sin 2Δ41
8R[Uμ3Uτ∗3Uμ∗4Uτ4] sin2 Δ31 sin2 Δ41
4I[Uμ3Uτ∗3Uμ∗4Uτ4] sin 2Δ31 sin2 Δ41
In the above formula, the solar-driven term is neglected due to the CNGS baseline and neutrino energy
(Δ21 ≈ 4 × 10−3). In the first row of Eq. 1, the first term corresponds to the standard oscillation
probability for ντ appearance. The second term corresponds to the oscillation purely induced by the
mixing with the sterile state, with an effective mixing parameter sin 2θμτ = 2|Uμ4||Uτ4|. The remaining
four terms correspond to the interference between active and sterile neutrinos, and depending on the
extra terms in the extended U matrix they can lead to an enhancement or a suppression of the expected
ντ. These interference terms depend on the possible CP−violating phase φμτ = Arg(Uμ∗4Uτ4Uμ3Uτ∗3)
and on the mass hierarchy of standard neutrinos (Normal Hierarchy, NH, Δm231 > 0, or Inverted
Hierarchy, IH, Δm231 < 0).
The number of ντ events observed by OPERA is compared to the number of events expected from
the 3+1 model as a function of the new mixing angles and squared mass difference. In Sect. 4 these
numbers are used to constrain the parameters appearing in Eq. 1.
3 The OPERA experiment
OPERA is a long baseline experiment located in the underground Gran Sasso laboratory and exposed
to the CNGS νμ beam from 2008 to 2012. The experiment was designed to perform a direct
observation of ντ charged-current interactions on event-by-event basis, with a signal to background ratio of
The topological observation of the short-lived τ decay requires an exceptional granularity
integrated in a large mass. This is achieved in OPERA using Emulsion Cloud Chambers (ECC) and
real-time electronic detectors with a modular structure [
]. The ECC basic unit is a “brick”
composed of 57 nuclear emulsion films, providing the necessary micrometric accuracy, interleaved with
56 lead plates, providing the necessary mass. The target is a hybrid modular structure in which the
bricks are arranged in vertical “walls”, transverse to the beam direction, alternated with planes of
plastic scintillator strips. The detector is made of two identical Super Modules, each consisting of
a target section and a muon spectrometer. The latter is a dipolar iron magnet instrumented with
Resistive Plate Chambers (RPC) and high precision drift tube detectors (PT). The electronic detectors
trigger the read-out and allow identifying the brick containing the neutrino interaction. If a muon
track crosses the spectrometers, the RPCs and PTs are used to measure the muon charge and
]. The neutrino interaction vertex and its full topology are reconstructed in the brick with a
sub-μm spatial resolution.
3.1 νμ → ντ search
In five years of data taking, from 2008 to 2012, OPERA integrated a CNGS beam luminosity
corresponding to 17.97 × 1019 protons on target (p.o.t.), the 80% of the nominal design value. A total
of 19505 CNGS events have been registered correspondingly. Only interactions inside the OPERA
target volume are analysed for oscillation studies. These internal events are further classified by an
automatic algorithm into 0μ and 1μ through the identification of a muon track [
] or the total number
of fired scintillator or RPC planes.
The data set used for the νμ → ντ search is composed by internal 0μ events and 1μ events with
a muon momentum below 15 GeV/c, for a total of 5408 fully analysed events in the ECCs. In this
sample, after the whole scanning and decay search procedure [
], 5 ντ candidate events are observed.
The total expected background is 0.25 ± 0.05 events. The background fluctuation probability is
evaluated with two test statistics, one based on the Fisher’s method and the other on the profile likelihood
ratio. The background-only hypothesis is excluded with a 5.1σ significance by both methods [
The expected signal from the standard 3ν model, assuming Δm232 = 2.44 × 10−3 eV2 [
] and a
maximal mixing, considering all the τ decay channels, amounts to 2.64 ± 0.53 events, compatible
with the observed ντ candidates [
4 Constraints on the mixing with a sterile neutrino
In this paper we interpret the OPERA results in the context of the 3+1 neutrino model, deriving limits
on the oscillations induced by a massive sterile neutrino. Limits on the sterile neutrino mixing based
on the observation of 4 ντ candidate events have been recently published by the OPERA
]. Here we report on the preliminary updated analysis considering the current number of 5 ντ
The results of this analysis are given in terms of the effective mixing parameter sin 2θμτ =
2|Uμ4||Uτ4| (see Sect. 2), which is the leading mixing term at short baseline experiments, allowing
a direct comparison with their results.
The number μ of expected ντ events in the 3+1 model is evaluated as:
μ = A
φνμ (E) Pμτ(E) σντ (E) ντ (E) dE + nb
where A is a normalization factor taking into account the delivered p.o.t. and the target mass, φνμ is the
CNGS neutrino flux, Pμτ is the oscillation probability given by Eq. 1, σντ is the ντ CC cross section,
ντ is the ντ identification efficiency, and nb is the number of expected background events.
A gaussian prior is assumed for the atmospheric squared mass difference Δm231 with parameters
determined from global fits, i.e. (2.47 ± 0.06) × 10−3 eV2 for normal hierarchy and (−2.34 ± 0.06) ×
10−3 eV2 for inverted hierarchy [
In order to derive limits on the sterile neutrino mixing, the test statistics −2 ln λp is used, where
λp is the profile likelihood ratio. In this counting analysis, the likelihood is given by a poissonian
depending on the number of expected events μ (Eq. 2) and on the number of observed events nντ = 5.
Two independent implementations of the method give similar results. Details on the statistical
treatment of both analyses can be found in [
The limits on the sterile neutrino parameters are derived minimizing −2 ln λp and are shown in
Fig. 1. The 90% C.L. exclusion regions in the (Δm241, sin2 2θμτ) parameter space are obtained for
both normal (NH) and inverted (IH) mass hierarchies. The OPERA results in this parameter space
can be directly compared to the limits given by the CHORUS and NOMAD short baseline νμ → ντ
The OPERA sensitivity extends the limits on Δm241 to 10−2 eV2 for a relatively large mixing, i.e.
sin2 2θμτ > 0.5, for both hierarchies. In case of normal hierarchy, a small region at Δm241 ∼ 10−3 eV2 is
also excluded, since the number of expected ντ events in this model is lower than the number expected
from the 3ν framework. The suppression is due to the interference terms in Eq. 1. As said in Sect. 2,
cosmological limits on the sum of neutrino masses favour Δm241 > 0, which is the assumption of the
analysis here presented. For negative values of Δm241 the exclusion plots are similar but with NH and
IH regions exchanged.
At large values of Δm241 (> 1 eV2), there is almost no correlation between Δm241 and the
effective mixing parameter, and the dependence of the oscillation probability Pνμ→ντ on Δm241 vanishes.
In this context, which is in fact the phenomenological 3+1 model, the limits are expressed in the
(φμτ, sin2 2θμτ) space. In Fig. 2 the 90% C.L. exclusion regions are shown for NH and IH hierarchies.
Marginalizing over the phase φμτ, values of sin2 2θμτ > 0.119 are excluded at 90% C.L. Given the
definition of the effective mixing parameter sin 2θμτ = 2|Uμ4||Uτ4|, the upper limit sin2 2θμτ < 0.119
can be translated into an exclusion curve in the (|Uμ4|2, |Uτ4|2) space, as shown in Fig. 3 together with
the unitarity bound |Uμ4|2 + |Uτ4|2 ≤ 1.
2 | 4 1
The OPERA experiment has observed νμ → ντ oscillations in the atmospheric sector in appearance
mode detecting 5 ντ event candidates with an expected background of 0.25 events. The 5.1σ discovery
of ντ appearance is compatible with the standar 3ν oscillation framework.
In this paper, OPERA results have been used to derive limits on the oscillations induced by a sterile
neutrino, obtaining 90% C.L. exclusion regions for three different parameter spaces. The effective
mixing parameter of the 3 + 1 neutrino model, for Δm241 > 1 eV2, is constrained at 90% C.L. at
sin2 2θμτ < 0.119. Based on this upper limit, constraints on |Uτ4|2 and |Uμ4|2 have also been set.
The OPERA sterile mixing search in appearance mode provides complementary information with
respect to disappearance experiments, and the long baseline search further complements the short
baseline one, providing stringent limits in the effective mixing angle.
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