First observation of a tau neutrino charged current interaction with charm production in the Opera experiment

An event topology with two secondary vertices compatible with the decay of short-lived particles was found in the analysis of neutrino interactions in the Opera target. The observed topology is compatible with tau neutrino charged current (CC) interactions with charm production and neutrino neutral current (NC) interactions with $c\overline{c}$ pair production. However, other processes can mimic this topology. A dedicated analysis was implemented to identify the underlying process. A Monte Carlo simulation was developed and complementary procedures were introduced in the kinematic reconstruction. A multivariate analysis technique was used to achieve an optimal separation of signal from background. Most likely, this event is a $\nu_{\tau}$ CC interaction with charm production, the tau and charm particle decaying into 1 prong and 2 prongs, respectively. The significance of this observation is evaluated.


Introduction
Charmed hadron production in neutrino interactions has been studied in two ways: dilepton searches in calorimeter detectors [1] and identification of charm decay topologies in nuclear emulsions [2][3][4][5][6][7][8]. Emulsion-based experiments allow a highly detailed reconstruction of the event topology, such that background can be reduced by a factor 10 4 [7]. Background arises from pions and kaons decaying in flight or hadron interactions without any visible nuclear break-up.
The OPERA experiment [9] was designed to observe ν µ → ν τ oscillations in the CERN to Gran Sasso (CNGS) ν µ beam [10] by the detection of tau leptons produced in ν τ CC interactions. The experiment has been searching for neutrino interactions with one secondary short-lived particle as a signature of the τ lepton. OPERA reported in 2015 the discovery of ν τ appearance in a muon neutrino beam [11], later extended to a significance of 6.1 σ with its final data sample [12].
An interesting muon-less event with two secondary vertices was observed in the target of the OPERA detector. Both vertices can be interpreted as short-lived heavy particle decays. Such an event can originate, at the CNGS energy, either from a ν τ CC interaction with charm production or from a ν NC interaction with cc production. The first process has never been directly observed, while the CHORUS experiment observed three events with cc production in ν NC interactions [7]. The expected number of such events is smaller than one.
In this paper the analysis and interpretation of this event is reported. After a brief description of the apparatus (section 2), the event measurement and analysis are reported in sections 3 and 4, respectively. The statistical significance of the observation is discussed in section 5.

The OPERA experiment
The detector was located at the LNGS underground laboratory and was exposed to the CNGS beam. The experiment profited from a 730 km long baseline and the average neutrino energy was 17 GeV. The beam exposure started in 2008 and ended in 2012, 1.8 × 10 20 protons on target were collected. 19 505 neutrino interactions were recorded in the fiducial volume of the detector target.

The detector
In order to observe and fully reconstruct decay topologies of short-lived particles, a spatial resolution at the micrometer scale is required. The target consisted of lead plates interspaced with nuclear emulsion films acting as high accuracy tracking devices, a configuration also known as Emulsion Cloud Chamber (ECC). The target was segmented into 150 000 units (bricks), each consisting of 57 nuclear emulsion films alternating with 56 1 mm thick lead plates. Emulsion films were made of 2 emulsion layers, each 44 µm thick coated on both sides of a 205 µm transparent plastic base. The brick cross section was 103 mm × 128 mm; its thickness was 7.5 cm corresponding to about 10 radiation lengths. The brick mass was 8.3 kg. The achieved spatial resolution was ∼ 1 µm and the angular resolution was ∼ 2 mrad [9]. Charged particle momentum is measured by Multiple Coulomb Scattering (MCS) in the lead plates [13]. A changeable sheet (CS) doublet consisting of a pair of emulsion films is attached on the brick downstream face [14] as an interface between bricks and electronic detectors.
The active mass of the target amounted to 1.25 kton. Bricks were housed in a modular detector structure made of two identical Super Modules (SM) [9]. Each SM was composed of a target section and a muon spectrometer, as shown in Figure 1. In each SM, the bricks were arranged in 29 vertical walls orthogonal to the beam direction and alternated with electronic detectors [15] consisting of two orthogonal planes of plastic scintillators for each wall, called Target Tracker system (TT). TT planes were made up of scintillator strips 2.6 cm wide and 1 cm thick. The TT was used to select the brick in which the neutrino interaction occurred. It also provided muon identification and an estimation of the energy deposited by hadronic and electromagnetic cascades. The spectrometers were designed to measure the charge and the momentum of muons [9].

Event reconstruction
The emulsion data taking is performed by fast automatic scanning systems, based on microscopes equipped with a computer-controlled motorised stage and a digital camera mounted on top of a dedicated optical system. Track recognition in emulsion films is performed on 16 tomographic images, grabbed at equally spaced depth levels through the 44 µm sensitive layer [16][17][18][19]. The first step of the event reconstruction is the location of the primary neutrino interaction inside the brick [9]. The vertex location procedure in a brick starts from a set of predictions provided by the electronic detectors that are confirmed in the CS films. Then, the tracks of secondary particles produced in the neutrino interaction are followed back in the brick, film by film, from the most downstream one to the interaction point from where they originate. Whenever a track is not found in three consecutive films, a 1 cm 2 surface is scanned in each of the 5 films upstream and 10 films downstream of the last observed track segment in order to fully reconstruct the event.
In the decay search procedure [6], secondary vertices are searched for and all the selected tracks are double checked by manual measurements. The hint of a decay topology is the observation of a significant impact parameter (IP) with respect to the primary vertex.
The precision obtained in the vertex position is affected by particle scattering in lead plates that was evaluated by Monte Carlo (MC) simulations. Figure 2 shows the impact parameters of reconstructed primary tracks as a function of the primary vertex depth in lead (∆z). If secondary vertices are found, a full kinematical analysis is performed combining the measurements in nuclear emulsions with data from the electronic detectors.
The appearance of the τ lepton is identified by the detection of its characteristic decay topologies, either in one prong (electron, muon or hadron) or three prongs. Kinematical selection criteria are applied according to the decay channel [20,21].
The detection and reconstruction efficiencies are evaluated by MC simulations [6].

Description of the tau neutrino candidate event with charm production
The event was recorded on May 23 rd , 2011 in the most upstream SM. The event display is shown in Figure 3: the number of fired TT planes is 9. No muon track is reconstructed by the electronic detectors, thus the event is tagged as 0-muon. It is worth mentioning here that a track is tagged as a muon either if the product of its length and the density along its path is larger than 660 g/cm 2 or if the total number of electronic detector planes crossed is larger than 19. The energy reconstructed by the TT is equivalent to 20 ± 6 GeV [15].

Event topology
The neutrino interaction occurred in brick 77152 which was selected exploiting TT data using the procedure described in [15]. The analysis of the CS doublet reveals a converging pattern of 27 tracks. Out of them, 11 are found also in the most downstream film of the brick (plate 57). These tracks are clustered in a region of a few hundreds of micrometers, indicating an electromagnetic activity possibly related to the neutrino interaction. All tracks are followed upstream in the brick: most of them are just few emulsion films long. By visual inspection these are confirmed as being part of an electromagnetic shower.
In the location and decay search procedures (see section 2.2), a primary convergence point of 5 tracks is found in film 32.
The reconstructed slopes are reported for each track in Table 1. The neutrino interaction point is located in the lead plate between emulsion films 31 and 32. As the impact parameter (IP) of track 4 w.r.t. the primary vertex is larger than the 10 µm threshold, a 5-prong primary vertex topology (V 5p ) is discarded. The most probable topology, taking into account also particle scattering [6], is a double vertex event with the primary neutrino vertex (V I ) formed by tracks 2, 4 and 5, and a secondary vertex (V II ) formed by tracks 1 and 3 (see Figure 4). Other configurations have negligible probabilities. Table 1: Track slopes p x /p z and p y /p z at film 32 and their impact parameters (IPs), evaluated assuming a single vertex topology (V 5p ) and a double vertex one. Errors on IP values are evaluated to be of the order of 0.6 µm. The interaction is located well inside the brick. The coordinates of vertices V I and V II are reported in Table 2. Two additional measurements are performed, both yielding a better resolution than the standard one: i) manual measurement with a higher magnification objective and ii) highresolution automatic image acquisition and analysis. In the first case, the tracks are measured in plate 32 and 33 under a 100 times magnification objective mounted on the micro- scope; thus achieving a 0.3 µm resolution on the film transverse coordinates (X,Y) [17]. In the second case an improved scanning procedure based on emulsion images acquired with 1 µm pitch tomography, detailed in [22], is applied. By this precise 3D tomographic technique it is possible to achieve a spatial resolution of 0.1 µm and an angular resolution of 1 mrad. Such accuracy allowed reducing random coincidences to less than 5 % while keeping track reconstruction efficiency close to 100 %.
The primary vertex is reconstructed (581.8 ± 0.4) µm upstream with respect to the downstream surface of film 32.
A particle fully contained in the lead (non-visible), emitted at the primary vertex with angles (0.086, 0.077) rad and joining the secondary vertex V II has a flight length of (103.2 ± 0.4) µm.
Track 4 (labelled as kink parent in Figure 4) exhibits a kink topology (V III ) between films 32 and 33. The minimum distance between track 4 and track 6 (daughter ) emerging from the kink, is (0.9 ± 0.4) µm. The kink angle is (95 ± 2) mrad; the parent flight length is (1174 ± 5) µm. A scheme of the full event is shown in Figure 5.
All tracks reconstructed at films 32 and 33 are followed down in the brick in order to estimate their momenta.
Track 2 stops at film 34; track 3 undergoes a re-interaction at film 53, while tracks 1, 5 and 6 reach the CS films. The coordinates of the three vertices are listed in Table 2.
Two e + e − pairs are identified in films 35 (γ 1 ) and 41 (γ 2 ). An image based procedure is applied to identify and reconstruct the electromagnetic showers [22]. An additional image data taking with 1 micron Z pitch is performed in a cone of 400 mrad aperture around the slope of the primary photon (e + e − mean slope), starting from film 31 down to film 57 in the brick. All tracks in the volume are reconstructed using the 3D clustering algorithm. The main features of the reconstructed showers are listed in Table 3 and shown in Figure 6.
The most downstream shower tracks are reconstructed in the CS films. Given the accuracy of the reconstruction, γ 1 is most probably attached to V III , while γ 2 may emerge from any vertex (V I , V II or V III ), see IPs in Table 3. In the next step of the analysis the photons origin vertex is not taken into account since the classifier procedure relies only on the total visible electromagnetic energy. In order to reduce hadron interaction background, a dedicated scanning system with high efficiency at large angles is also used [23] to search for nuclear fragments around each vertex, within a | tan θ| < 3 acceptance window. No nuclear fragments are detected. Independent analyses were performed in three different scanning laboratories confirming all the results.

Event kinematics
Momenta of tracks 1, 3, 5, 6 are estimated using the MCS method. The alignment uncertainties are evaluated from angular and position residuals of a sample of tracks penetrating the entire scanned volume. All measurements are performed using high-resolution images taken with the acquisition system described in section 3.1. The angular and position resolutions are 2.4 mrad and 0.6 µm, respectively. Results are shown in Table 4.
Track 2 is observed only in three emulsion films and it is identified as a Minimum Ionizing Particle (MIP) by counting the grains along the track. The momentum estimation by range [24] discards the proton hypothesis. The particle is most likely a pion with an   energy of 0.2 GeV. An additional estimation is performed considering absorption processes. Pion absorption cross-section has a resonance at a kinetic energy of about 0.2 GeV in any material [25,26]. In this region, especially for heavy nuclei, this cross section is up to ∼ 40 % of the total cross section. Under these assumptions, the momentum estimation for track 2 is (0.31 ± 0.08) GeV/c. This is the initial momentum of a pion which is absorbed after crossing 3 mm of lead and that has a kinetic energy of about 0.2 GeV when absorbed. The uncertainty is evaluated assuming a uniform kinetic energy distribution: the minimum is the kinetic energy such that β > 0.7; while the maximum is 0.3 GeV, which is the endpoint of the absorption peak. β = 0.7 is the minimum for a MIP according to the emulsion grain density [27]. The energy of the electromagnetic showers, γ 1 and γ 2 , are estimated by counting the tracks belonging to each shower. The procedure is calibrated with MC simulations,  taking also into account background tracks [22]. The result is E γ 1 = (7.2 ± 1.7) GeV and E γ 2 = (5.3 ± 2.2) GeV. Considering the absence of hard scattering of track 6, γ 1 and γ 2 are not bremsstrahlung photons therefore track 6 can not be a positron nor an electron.
In conclusion, the event is identified as a neutrino interaction with two secondary vertices: V II has a 2-prong topology while V III is a kink originated by a primary charged particle.

Event analysis
The event described in this paper was one of the 10 events selected as ν τ candidates in the OPERA final analysis on ν µ → ν τ oscillation [12]. Nevertheless, given the presence of two short-lived particle decay candidates (the kink topology and the additional vertex) a further dedicated analysis was performed for the event classification. Two short-lived particle decays can be produced by the following processes: • ν τ CC interaction with charm production; • ν NC interaction with cc pair production.
Other processes mimicking this topology are: • ν µ CC interaction with a mis-identified muon and two secondary interactions.
• ν µ CC interaction with single charm production, a mis-identified muon and one secondary interaction; • ν NC interaction with two secondary interactions; • ν τ CC interaction with one secondary interaction; As secondary interaction, is meant either i) a hadronic interaction of a final state particle, ii) a decay of pions or kaons, or iii) a large-angle Coulomb scattering of hadrons or mis-identified muons.
The analysis is intended to establish the likelihood of the event with respect to different physics hypotheses. It is based on the distributions of kinematical variables obtained through a dedicated MC production. Neutrino interactions are generated using GENIE [28], except for charm pair production, simulated using HERWIG [29]. The ν τ CC interaction cross sections used are in agreement with [30]. Due to the high multiplicity of MIP tracks associated to the primary vertex for the event, only DIS interactions are taken into account. In total, about 300 million events are generated.
Particles from neutrino interactions are propagated in a 17 cm 3 volume of the brick using the Geant4 framework [31,32], generating the primary vertex always at the same depth in lead as the one estimated for the event. The MCS is taken into account using a parameterisation based on the standard OPERA MC. The hadron interaction simulations are validated using dedicated test beam data [27].
For each process, the number of expected events is normalised to the 12 352 observed ν µ CC events with a primary vertex in the target section of the detector. This strategy is applied in order to maximise the sample under analysis. The shape of the CNGS neutrino flux [10], the oscillation probabilities and the cross sections are considered. The vertex location efficiency is determined according to a data-driven parameterisation. The efficiencies related to the electronic detectors (brick selection, muon identification, muon momentum estimation) are evaluated using the standard MC with a parameterisation based on hadronic energy and muon momentum. Simulated events are selected regardless of the multiplicity at the primary vertex by requiring: • no muon identified by the electronic detectors; • a one prong-like secondary vertex (1pr-like) with charged parent; • a two prong-like secondary vertex (2pr-like); • no nuclear fragments at any vertex.
• daughter particles should not be electrons nor positrons.
Requiring a charged parent for the 1pr-like secondary vertex implies that the parent track has to be measured in at least one emulsion film. No kinematic cuts are applied. The total number of expected events matching this topology is ∼ 0.1 as shown in Table 5. Table 5: Expected number of events with a two secondary vertices as selected by the analysis. Parameters used to obtain the oscillated ν τ flux are: sin 2 2θ 13 = 9.3 × 10 −2 , sin 2 2θ 23 = 1.0, ∆m 2 32 = 2.44 × 10 −3 eV 2 , ∆m 2 21 = 7.5 × 10 −5 eV 2 [33].

Samples
Expected number of events (10 −3 ) ν τ CC + charm 44.5 ν NC + cc pair 12.6 ν µ CC + two 2ry 4.0 ν µ CC + charm + 2ry 20.5 ν NC + two 2ry 3.8 ν τ CC +2ry 9.0 Total 94.4 A multivariate analysis is applied to the selected events and the signal to background discrimination is based on 12 kinematic variables as follows.  Table 5 is shown with a different color. The vertical black line represents the ANN output for the event.
• for the entire event: i) total EM energy, i.e. the sum of any reconstructed photon energy, regardless of the photon origin vertex; ii) the angle ϕ between the parents of the 1pr-like and 2pr-like vertices in the transverse plane; iii) the projection in the transverse plane of the momentum at primary vertex; iv) the hadronic momentum, i.e. the sum of the primary track momenta excluding the two parents; • for the 1pr-like vertex: v) the daughter momentum; vi) the daughter transverse momentum with respect to the parent direction; vii) the flight length; viii) the kink angle between parent and daughter; • for the 2pr-like vertex: ix) the total daughters' momentum; x) the total daughters' transverse momentum with respect to the parent direction; xi) the flight length; xii) the invariant mass of the charged daughters.
In order to find the best method for the discrimination of the ν τ CC interaction with charm production, several algorithms have been tested: an Artificial Neural Networks (ANN) method [34], two kinds of Boost Decision Trees [35] and the Fisher Discriminant [36]. The best one turns out to be the ANN, whose output variable distribution is shown in Figure 7. According to this multivariate analysis the event can be classified as ν τ CC interaction with charm production with rather high probability.

Results
The significance of the ν τ CC interaction with charm production (signal ) observation is based on a frequentist hypothesis test using a likelihood ratio as a test statistic [37,38].
The ANN response x plays the role of observable and its distribution, normalised to the expected number of events, is shown in Figure 7. The shape of the distribution of x is obtained by the sum of the contributions of each process listed in Table 5 and is described by where index i ranges over the background processes; b i (x) and s(x) are the probability densities for background and signal, respectively; n i and n s are the expected number of events. The parameter µ (signal strength) is introduced as a scale factor on the number of signal events: µ = 0 corresponds to the background-only hypothesis and µ = 1 corresponds to the ν τ CC interaction with charm production as predicted by Table 5.
The effect of uncertainties on the expected number of events are introduced as scale factors f i for each background process and f s for the signal. They depend on 5 nuisance parameters: i) a 20 % normalisation factor, dominated by the CNGS flux uncertainty [10]; ii) a 20 % uncertainty on the cross section of ν NC interactions with charm pair production; iii) a 20% uncertainty on the cross section of ν τ CC interactions with single charm; iv) a 6 % uncertainty on ν τ CC interactions cross section (without charm), for ν τ energies in the range of few tens of GeV [39]; v) a 30 % uncertainty on the hadronic re-interaction rate, based on test beam results [27]. These nuisance parameters σ k are constrained by some uniform or Gaussian probability densities g k .
Including systematic these terms and considering that the probability to observe N events follows a Poisson distribution, the likelihood function is: where σ σ denotes the whole set of nuisance parameters, and ν(µ, σ σ) is the number of expected events.
In order to test which values of the signal strength µ are consistent with data, the profile likelihood ratio λ(µ) = L(µ,σ σ)/L(μ,σ σ) is used [33], where L(μ,σ σ) is the value of the likelihood at its maximum andσ σ indicates the profiled values of the nuisance parameter β c , maximizing L for the given µ. The distribution for the profile likelihood ratio λ(µ) is obtained with a sample of Monte Carlo pseudo-experiments generated according to the background-only hypothesis using RooFit RooStats libraries [40] and the ROOT framework [41]. For each pseudo-experiment, nuisance parameters σ k are randomly generated according to their PDFs g k .
The probability that the background-only would produce events less likely compatible with the observed one is (1.3 ± 0.3) × 10 −5 .
This result refers to the observed topology, i.e. to the search for a single prong tau decay and a neutral charmed hadron decaying into 2 prongs. It provides evidence for the first observation of a ν τ CC interaction with a charmed hadron. The significance of this observation is 4.0 σ.
Under the condition that the number of events is regarded as fixed, i.e. the Poissonian term is excluded from the likelihood, the p-value is (6.6 ± 0.1) × 10 −3 , corresponding to 2.5 σ. This estimate only relies on the event features and it is independent on fluctuations of the total number of observed events.
The most likely interpretation is that V II is a charmed particle decay and V III is a tau lepton decay into a hadron.

Conclusions
A neutrino interaction was observed in the target of the OPERA detector having a rare topology: two secondary vertices within about 1 mm from the primary one were reconstructed. High-accuracy scanning procedures were applied and a dedicated analysis has been set up. Monte Carlo simulations were developed and additional procedures were introduced in the kinematic reconstruction. Multivariate analysis techniques were used to achieve an optimal separation between signal and background.
The event reported in this paper is the first observation of a ν τ CC interaction with charm production candidate, tau and charm particles decaying into 1 prong and 2 prongs, respectively. The significance of this observation is 4.0 σ.
Under the condition that the number of events is regarded as fixed, i.e. the Poissonian term is not included in the likelihood, the significance of the observation is 2.5 σ.