Reconstruction algorithms are used in order to estimate the direction and energy of the incoming neutrino. Depending on the event topology, diferent reconstructions are used. Some of the output parameters of these algorithms are used in the analyses described in this thesis in order to select events with the best reconstruction quality. hey will be presented.
2.6.1 crak atronstrurtion
A detailed description of the track reconstruction algorithm can be found inα[56]. he recon-struction is divided into two algorithms, one for the direction of the event and an other one for the energy.
Evtnt Dirtrtion
he event direction relies on a hit pre-selection, which selects only the hits that are causally related by|��− �max| ≤ ( ⃗�− ⃗max)/� � ��� ns, with��and �⃗ the time and position of the hit i and�maxand max⃗ the time and position of the hit with the largest amplitude. he parameter� is the group velocity of light in water.
In order to estimate the event direction, the position of the track at a time�0 should also be determined. herefore, there are ive free parameters to estimate. A iting procedure in multiple steps is used, each step being the starting point of the following one. he inal step account for all L0-hits and is the maximization of a likelihood function to obtain this set of hits with their time and amplitude, accounting for the optical background and the light scatering.
he ited value of the logarithm of the likelihood per degrees of freedomΛTr is used as an estimator of the it quality, indeed lower is the likelihood less likely is the ited value. his is combined with the information of the number of times the same value has been obtained from its with diferent starting points. An estimation of the angular error of the reconstruction
Tr is also computed from the second derivative of the likelihood function at the ited point, which corresponds to the standard deviation of the minimum of the likelihood in the Gaussian approximation.
Evtnt Entrgy
A simple estimator of the event energy is the number of hits ⁸�hits⁹ selected for the direction reconstruction, as an estimation of the number of hits produced by the track. But this is not
Figurt 2.14–Muon tntrgy losstsfor propagation in water. Figure taken fromα[44].
accurate. Several algorithms have been developed to beter estimate the energy of the events, I describe here thedEdX algorithm which is used in chapterα6.
Track events detected by A are not contained in the detector. herefore, most of the energy of the particles is not deposited in the detector and the neutrino energy is not easy to estimate. he dEdX algorithm uses the fact that the energy losses of muons increase with energy as can be seen in igureα2.14. However, dEdX is not eicient at energies lower than 100 GeV as the energy losses are dominated by ionisation which is constant with energy.
2.6.2 bhowtr atronstrurtion
A detailed description of the shower reconstruction algorithm can be found inα[13]. he recon-struction is divided into two algorithms, one for the position of the event, the vertex, and an other one for the direction and energy.
Position atronstrurtion
As for the tracks, the algorithm start by selecting the hits causally correlated. Every pair of hits has to fulil the criterion �⃗ − ⃗�≥ � · |��− ��|with��and �⃗ the time and position of a hit i and
� is the group velocity of light in water.
he estimation of the shower position is done making the assumption that all the light is emited by a point-like source at an instant�Sh. In this hypothesis, all hits should follow the
cablt 2.2–Evtnt prt-stltrtion.
Event Type Criterion Condition Track Upward-going cos(�Tr) �0.2
uality ΛTr �-6 Error Estimate Tr�1.5°
Shower Upward-going cosor (�Sh) �0.2
relation( ⃗�− ⃗Sh)2 = �2· (��− �Sh)2. his system of equation is linearised and solved using the linear least square it methodα[57].
his is used as a starting point for the M-estimator ⁸�Estin chapterα6⁹ it which is a modiied χl minimizing the residual time and accounting for the amplitude of the hitsα[13]. he residual time is deined as�res � = ��− �Sh− | ⃗�− ⃗Sh|/� for a hit�.
Dirtrtion ans Entrgy atronstrurtion
he direction and energy reconstruction is performed with a likelihood function which accounts for the probability of each hit to come from the shower or the optical background. he proba-bility that an unhit optical module does not see light is also used. hese probabilities depend on the shower characteristics, therefore the likelihood is maximized by iting the energy and di-rection. his estimated energy will be used is the following of this work, it will be called T in chapterα6.
An estimator of the angular error is also computed. Ater the direction has been ited, the likelihood landscape around the it is scanned by increasing the angular distance to the best it direction by steps of one degree. he angular distance which decreases the log-likelihood value of more than one in respect to the best it value is taken as angular error.
As for tracks, the number of hits selected for the reconstruction ⁸�hits⁹ can also be used as an energy estimator.
2.6.3 Prt-stltrtion
Both reconstructions are applied on each event, then a pre-selection is applied before writing events to the data iles used in the upward-going analyses as the one presented in partαII. he pre-selection conditions are given in tableα2.2. he zenith�is deined in igureα2.15,�Trand�Sh
being the reconstructed zenith from the track and shower algorithms respectively.
Figurt 2.15–Dtinition ou tht ztnith�. he green arrow is the direction of the neutrino and the black line the vertical axis of the detector.
ν
ANTARES
θ