OPERA Neutrino Oscillation Experiment

• OPERA is a long-baseline neutrino experiment designed to directly observe ντ appearance via τ-lepton decay using a hybrid lead-emulsion detector.
• The experiment utilized an almost pure νμ beam from CERN to LNGS over a 730 km baseline, achieving up to 6.1σ significance in ντ appearance through precise event reconstruction.
• Advanced emulsion scanning and electronic detectors enabled OPERA to perform detailed momentum measurements and investigate νe appearance as well as sterile neutrino scenarios.

OPERA, the Oscillation Project with Emulsion tRacking Apparatus, was a long-baseline neutrino experiment at the Laboratori Nazionali del Gran Sasso (LNGS) designed to establish the oscillation channel $\nu_\mu \rightarrow \nu_\tau$ in appearance mode by directly observing $\tau$-lepton production and decay in the CERN Neutrinos to Gran Sasso (CNGS) beam. Located $730$ km from CERN and exposed from 2008 to 2012 to an almost pure $\nu_\mu$ beam, OPERA combined a $1.25$ kton lead-emulsion target with electronic detectors to resolve sub-millimetric $\tau$-decay topologies on an event-by-event basis. Over its full run it accumulated $17.97\times 10^{19}$ protons on target and ultimately provided a conclusive direct observation of $\nu_\tau$ appearance, while also performing $\nu_e$ appearance searches and $3+1$ sterile-neutrino tests (Galati, 2015, Collaboration et al., 2019).

1. Scientific aim and beam configuration

OPERA was conceived to test the dominant atmospheric-sector oscillation mechanism through appearance, rather than through a disappearance deficit. In operational terms, the experiment sought the charged-current interaction of an oscillated $\tau$0, followed by direct reconstruction of the produced $\tau$1 lepton. This design distinguished OPERA from earlier atmospheric and accelerator measurements that had established $\tau$2 disappearance without directly imaging the daughter flavor (Galati, 2015).

The experiment used the CNGS beam from CERN to LNGS over a baseline of $\tau$3 km. The beam had an average energy of about $\tau$4 GeV, chosen to remain above the $\tau$5-production threshold while retaining sensitivity to atmospheric-scale oscillations. In the standard long-baseline approximation, the relevant appearance probability takes the familiar form

$\tau$6

with $\tau$7 in km and $\tau$8 in GeV (Galati, 2015).

Beam purity was central to the physics case. The CNGS beam was described as an “almost pure” $\tau$9 beam; the $730$0 contamination was $730$1 in terms of interactions, the total $730$2 contamination was below $730$3, and prompt $730$4 contamination was negligible (Galati, 2015). Data taking from 2008 to 2012 yielded a total exposure of $730$5 protons on target, about $730$6 of the originally foreseen exposure (Fukuda, 2016).

The central experimental challenge was imposed by the $730$7 lifetime. With

$730$8

the decay occurs within sub-millimetric distances in dense material. OPERA therefore required both large target mass and micrometric tracking, a combination that strongly shaped the detector architecture (Galati, 2015).

2. Detector architecture and event reconstruction

OPERA was a hybrid detector composed of nuclear emulsions and electronic detectors, arranged in two identical super-modules. Its core target consisted of about $730$9 Emulsion Cloud Chamber bricks for a total target mass of about $\nu_\mu$0 kton (Pupilli, 2014). Each brick contained 56 lead plates, each $\nu_\mu$1 mm thick, interleaved with 57 nuclear emulsion films; in one description the brick dimensions were $\nu_\mu$2 with mass $\nu_\mu$3 kg (Galati, 2015). Each emulsion film had two $\nu_\mu$4 emulsion layers on a $\nu_\mu$5 plastic base (Fukuda, 2016).

Lead supplied target mass for neutrino interactions, while emulsions supplied sub-micron spatial resolution. Bricks were arranged in walls transverse to the beam, each followed by two planes of plastic scintillator strips forming the Target Tracker. On the downstream face of each brick, a pair of removable emulsion films called Changeable Sheets acted as an interface between the emulsions and the electronic detectors. Downstream spectrometers based on dipole magnets, Resistive Plate Chambers, Drift Tubes, and precision trackers identified muons and measured their momentum and charge (Pupilli, 2014, Fukuda, 2016).

A major technical component of OPERA was large-scale emulsion analysis. Compared with earlier systems used in DONUT at about $\nu_\mu$6hour, OPERA deployed S-UTS scanners at up to $\nu_\mu$7hour and ESS scanners at $\nu_\mu$8hour. A Compton alignment technique improved alignment precision from $\nu_\mu$9–$1.25$0 to about $1.25$1 and reduced background by a factor of $1.25$2, while a likelihood-based track-ranking method improved Changeable Sheet signal-to-noise by about $1.25$3 with only $1.25$4 efficiency loss (Fukuda, 2016).

Reconstruction began with the electronic detectors. Events time-correlated with the CNGS beam were classified as contained in the target or external; only contained events entered oscillation analyses. They were also divided into CC-like ($1.25$5) and NC-like ($1.25$6) classes according to whether at least one three-dimensional track was identified as a muon. A brick-finding algorithm selected the most probable interaction brick, which was then extracted if its Changeable Sheets contained compatible tracks (Pupilli, 2014).

Within the selected brick, tracks found in the Changeable Sheets were extrapolated into the most downstream emulsion film and followed backward film by film until they disappeared in three consecutive films. That stopping point indicated either a primary or a secondary vertex. A surrounding volume was then scanned, and a dedicated decay search looked for $1.25$7-like topologies or secondary interactions. The main observables were a sizable kink angle or a daughter track with large impact parameter relative to the primary vertex; for genuine primary tracks the impact parameter usually does not exceed $1.25$8 (Pupilli, 2014). Kinematic reconstruction used Multiple Coulomb Scattering in lead, with momentum resolution about $1.25$9, and calorimetric reconstruction of electromagnetic showers in a brick corresponding to about $\tau$0 (Pupilli, 2014).

The principal analyzed $\tau$1 decay channels were $\tau$2, $\tau$3, $\tau$4, and $\tau$5 (Pupilli, 2014).

3. Direct observation of $\tau$6 appearance

OPERA’s core result emerged incrementally as the analyzed sample grew and background estimates improved.

Stage	Observed $\tau$7 candidates	Significance / background
Status report	3	$\tau$8 against null hypothesis (Pupilli, 2014)
Extended analysis	4	$\tau$9; expected background $17.97\times 10^{19}$0 (Galati, 2015)
Discovery result	5	$17.97\times 10^{19}$1; expected background $17.97\times 10^{19}$2 (Collaboration et al., 2015)
Final full-dataset analysis	10	$17.97\times 10^{19}$3; expected background $17.97\times 10^{19}$4 (Collaboration et al., 2019)

At the stage reported in early 2014, OPERA had observed three $17.97\times 10^{19}$5 candidates with channel-dependent expected backgrounds of 0.027 events in $17.97\times 10^{19}$6, 0.116 in $17.97\times 10^{19}$7, 0.021 in $17.97\times 10^{19}$8, and 0.020 in $17.97\times 10^{19}$9, corresponding to $\nu_\tau$0 significance (Pupilli, 2014). By the end of 2014, four candidates satisfied all kinematic criteria, giving $\nu_\tau$1 against the background-only hypothesis (Galati, 2015). After inclusion of a fifth candidate in an enlarged sample and a reduced estimate of the large-angle muon-scattering background, OPERA reported discovery of $\nu_\tau$2 appearance with $\nu_\tau$3 significance (Collaboration et al., 2015). The final full-dataset analysis identified 10 $\nu_\tau$4 candidates over an expected background of $\nu_\tau$5, leading to a final $\nu_\tau$6-appearance significance of $\nu_\tau$7 (Collaboration et al., 2019).

Candidate-event topology was central to the claim. The first candidate was compatible with $\nu_\tau$8; the invariant mass of two $\nu_\tau$9 rays was $\nu_e$0, compatible with a $\nu_e$1, and the $\nu_e$2 invariant mass was $\nu_e$3, consistent with $\nu_e$4 (Pupilli, 2014). The third candidate, in the $\nu_e$5 channel, had a daughter muon with negative charge determined at $\nu_e$6, strongly suppressing the charm-background hypothesis with an unseen primary muon (Pupilli, 2014). The fifth candidate, reported in the discovery paper, was a $\nu_e$7 event with kink angle $\nu_e$8 mrad and flight length $\nu_e$9 (Collaboration et al., 2015).

Backgrounds were dominated by charm decays when the primary muon was missed, hadronic re-interactions, and large-angle muon scattering. Charm also served as a control sample: in 2008–2010 data, 50 charm events were observed in good agreement with a Monte Carlo expectation of $3+1$0 (Pupilli, 2014). In a later control sample, 49 charm decays were found against $3+1$1 expected (Kose, 2013).

Beyond the discovery claim, OPERA extracted an appearance-based oscillation parameter constraint. Assuming full mixing, the best-fit atmospheric mass-squared difference was

$3+1$2

with a $3+1$3 C.L. interval

$3+1$4

(Fukuda, 2016).

4. $3+1$5 appearance and sterile-neutrino searches

OPERA also exploited its electron-identification capability to search for $3+1$6 appearance. In the 2008–2009 sample, corresponding to $3+1$7 p.o.t., the collaboration examined 505 $3+1$8 events and found 19 $3+1$9 candidates, consistent with the expected beam contamination plus backgrounds, $\tau$00 (Pupilli, 2014). After imposing a reconstructed-energy cut of $\tau$01 GeV, 4.6 events were expected in the standard three-flavor scenario and 4 were observed, leading to

$\tau$02

at $\tau$03 confidence level (Pupilli, 2014).

The same dataset was interpreted in a non-standard appearance scenario motivated by LSND and MiniBooNE, with effective probability

$\tau$04

Using a $\tau$05 GeV reconstructed-energy cut, OPERA expected $\tau$06 background events and observed 6; a Bayesian analysis then set

$\tau$07

at $\tau$08 C.L. (Pupilli, 2014).

OPERA’s $\tau$09 appearance sample was also used to test a $\tau$10 scenario with one additional sterile state $\tau$11. In that framework the effective $\tau$12 mixing parameter is

$\tau$13

At high $\tau$14, OPERA reported the $\tau$15 C.L. upper limit

$\tau$16

and extended exclusion down to $\tau$17 for large mixing (Galati, 2015).

The final oscillation analysis used, for the first time, the full $\tau$18 and $\tau$19 appearance samples jointly. It identified 10 $\tau$20 candidates and 35 $\tau$21 candidates, with the $\tau$22 sample remaining consistent with the standard three-flavor expectation rather than showing an anomalous excess (Collaboration et al., 2019). In the $\tau$23 framework, for $\tau$24, OPERA derived

$\tau$25

at $\tau$26 C.L., and excluded the MiniBooNE combined best-fit point at $\tau$27 (Collaboration et al., 2019).

5. The 2011 timing anomaly and its re-evaluation

A major historical episode associated with OPERA was the 2011 report of an apparent neutrino early arrival of about $\tau$28 ns over the $\tau$29 km baseline, corresponding in contemporaneous discussions to $\tau$30. That provisional result triggered a large theoretical literature exploring possible interpretations, including energy-dependent phenomenology, Lorentz-invariance-violation constraints, bimetric relativity, universal-limiting-speed models, and tunneling-time or postselection analogies (Amelino-Camelia et al., 2011, Bi et al., 2011, Moffat, 2011, Oda, 2011, Amelino-Camelia, 2012).

A later internal LNGS cross-calibration provided a detector-based check independent of the CERN-to-LNGS neutrino time of flight. Using 306 high-energy horizontal cosmic muons crossing OPERA and LVD over about 1200 live days, the study found a negative timing shift in the OPERA setup,

$\tau$31

between the periods August 2007–August 2008 plus January–March 2012 and August 2008–December 2011 (Agafonova et al., 2012). The paper stated that this was a systematic effect in the OPERA timing system from August 2008 until December 2011 and that its size was comparable with the earlier neutrino-velocity excess (Agafonova et al., 2012).

That cross-check also connected the timing discrepancy to instrumental issues discussed in the OPERA timing chain, including a mismatch in the frequency of the internal Master Clock oscillator and a problem in the optical-fiber connection carrying the GPS timing signal (Agafonova et al., 2012). Historically, the episode became part of OPERA’s record, but it was separate from the experiment’s oscillation result, which rested on direct topological identification of $\tau$32-lepton decays.

6. Auxiliary measurements and broader legacy

Although OPERA was built for long-baseline oscillation physics, its detector also supported non-beam measurements. Because the apparatus was located under about $\tau$33, it functioned as a deep-underground TeV muon observatory. Using about $\tau$34 selected single-muon events from January 2008 to March 2013, OPERA measured a yearly underground muon-flux modulation with relative amplitude

$\tau$35

peaking at

$\tau$36

corresponding to July 5, and found an effective atmospheric-temperature coefficient

$\tau$37

(Agafonova et al., 2018). This established OPERA as an atmospheric monitor complementary to other LNGS experiments.

OPERA also produced detector- and interaction-physics measurements that were directly relevant to its oscillation program. A study of charged-current $\tau$38-lead interactions selected 795 $\tau$39 CC events with identified muons and measured a mean charged hadron multiplicity

$\tau$40

The average multiplicity was parameterized as

$\tau$41

with

$\tau$42

and the data were found to be consistent with approximate KNO scaling after introduction of the modified variable $\tau$43 (Collaboration, 2017). These results provided a lead-specific benchmark for tuning neutrino-interaction generators.

An earlier electronic-detector study of the 2008–2009 CNGS runs, corresponding to $\tau$44 p.o.t., validated event classification, muon momentum reconstruction, calorimetry, and the NC/CC ratio. The measured ratio,

$\tau$45

was statistically consistent with the Monte Carlo expectation $\tau$46 (Collaboration, 2011). This detector understanding was integral to the brick-finding, muon-tagging, and background-control chain on which the emulsion analyses depended.

OPERA’s long-term significance lies in having turned the atmospheric-sector oscillation picture into a direct appearance observation. By combining a kiloton-scale lead target with micrometric emulsion tracking and a large electronic detector system, it established $\tau$47 appearance event by event, constrained subleading appearance channels, and extended sterile-neutrino exclusions with joint $\tau$48 and $\tau$49 data (Collaboration et al., 2019). A plausible implication is that OPERA’s enduring methodological legacy is not only its discovery result, but also its demonstration that hybrid emulsion-electronic instrumentation can perform rare-topology neutrino physics at kiloton scale.