Short description of the algorithms that we use.

Track reconstruction

Track-like event signatures, e.g. of muons passing the detector volume, are reconstructed from the PMT hits in triggered events. Several different methods have been developed and are in use. In the following two of them are highlighted.

The method with the best accuracy uses a multi-step algorithm (see Heijboer, 2004 and The Astrophysical Journal 760:53(2012) for a more detailed description). The initial steps provide a starting point for the final maximization of the track likelihood. The likelihood is defined as the probability density of the observed hit time residuals, r, given the track parameters (position at some arbitrary time and direction). The time residual r is defined as the difference between the observed and expected hit time for the assumed track parameters. It was found that the likelihood function has many local maxima and that the maximization procedure needs to be started with track parameters close to the optimal values. The initial steps in the algorithm provide this near-optimal solution, estimating the track parameters using increasingly refined score functions. Each fit uses increasingly more inclusive hit selections based on the preceding stage. This sequence is started at nine different starting points to further increase the probability of finding the global optimum. Using more than nine starting points was found to have only marginal impact on the reconstruction quality and was not deemed worth the additional processing time. The final likelihood function uses parameterizations for the probability density function (pdf) of the signal hit time residual, derived from simulations. The pdfs also include hits arriving late due to Cherenkov emission by secondary particles or light scattering. Furthermore, the probability of a hit being due to background is accounted for. The score of the final likelihood fit is used to reject badly reconstructed events, in particular atmospheric muons that are misreconstructed as upgoing. In addition, assuming that the likelihood function near the fitted maximum follows a multivariate Gaussian distribution, the error on the zenith and azimuth angles are estimated from the covariance matrix. The angular uncertainty on the muon track direction is obtained from these errors and is used to further reject misreconstructed atmospheric muons.

A simpler and more generic, fast track fit algorithm is used to reliably distinguish upward-going neutrinos from the overwhelming background of downward-going muons (for details see Astropart. Phys. 34, 9 (2011) 652). The method has been used in ANTARES for different real-time applications such as an online event display, a neutrino monitor and an alert sending program to trigger optical follow-ups of selected neutrino events.

A classification method based on Random Forests has been devised to determine the best reconstruction solution for a given event. For details see Astropart. Phys. Vol. 114 (2020) 35-47.

Deep learning reconstruction methods using deep convolutional networks have recently been introduced, details of first results can be found in JINST 16 C09018 (2021).

Shower reconstruction

Shower-like event signatures in a neutrino telescope are mostly the result of neutral-current neutrino interactions or of charged-current electron or, partly, of tau neutrino interactions on nucleons. These events constitute an important channel for astrophysical neutrino searches and for studies of the atmospheric neutrino background. Two similar maximum-likelihood algorithms h ave been devised. These are described in Astron. J. 154, 275 (2017) and Eur. Phys. J. C 77 (2017) 419.

Energy reconstruction

The energy is one of the prime parameters to discriminate between atmospheric and astrophysical neutrinos. It is expected that the astrophysical neutrino flux follows a harder spectrum (typically described by an E^(-2) energy dependence), whereas the atmospheric flux is falling more rapidly with increasing energy (E^(−3.7) in the energy range accessible with theANTARES detector). Several algorithms have been developed within the ANTARES collaboration to estimate the energy of a recorded event. All of them exploit that at energies above the critical energy, at which energy losses due to Bremsstrahlung and ionisation losses are equal, a clear correlation between the particle energy and the energy deposited within the traversed medium is expected. This energy deposit can be estimated using several means:

  • Nhits: The most basic estimator is the number of optical modules that have seen a signal associated to the reconstructed track. The higher the energy deposit within the instrumented volume, the more light is being produced and the more modules record a signal.
  • dE/dX:  Using the detection efficiency of the light produced along the reconstructed track we can reconstruct the deposited energy dE. With the length X of the track within a fiducial volume, the energy deposit dE/dX can be reconstructed. Details can be found in ICRC 2011 and ICRC 2013.
  • ANN: Using a dedicated neural network, an extensive set of event parameters is used to estimate the energy of the recorded event.

Exploiting the mentioned linear correlation, the estimated energy deposit is converted into an estimation of the particle energy using detailed Monte Carlo simulations.