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to study the sensitivity to atmospheric neutrino oscillation
parameters θ
23
and Δm
2
32
at INO-ICAL and resolving the
MH. Including hadron information is beyond the scope of
this paper.
3 Analysis procedure
The first step in the procedure is event generation. The gen-
erated events are reconstructed in the GEANT4-simulated
ICAL and oscillations applied event-by-event after event
selection. The oscillated events are binned and used in the
χ
2
analysis to determine the oscillation parameters. Each of
these procedures are described in detail in the subsections
below.
3.1 Event generation
In this analysis, NUANCE data for an exposure of 50 kton
× 1000 years is generated, out of which sub-samples corre-
sponding to 5 years of data are used as the experimentally
simulated sample and the remaining 995 years of data are
used to construct probability distribution functions (PDF)
that are used in the χ
2
fit. Hence the data are uncorrelated
with the PDFs that are used to fit the data. This paper is
based only on the CC neutrino events with energies less than
50 GeV which corresponds to 98.6% of the sample. The ide-
alized case, where the NUANCE data is folded with detector
efficiencies and smeared by the resolution functions obtained
from GEANT-based studies of single muons with fixed direc-
tion and energy, has been presented previously [38]. In the
earlier analysis, although the data was analysed for an expo-
sure of 5 or 10 years, it was scaled down from the 1000 year
sample. Hence, the reconstructed central value was always
practically the same as the input value. Here we examine in
detail the more realistic case, where the data size and central
value are both subject to fluctuations.
3.2 Event reconstruction
The generated NUANCE data is simulated in GEANT4-
based detector environment. The energy deposited due to
the energy loss of the charged particle in the RPCs are con-
verted to signals, where they are detected by the mutually
orthogonal copper strips (along x and y directions parallel to
the global detector coordinates described in Sect. 3.3)onthe
RPCs. Hence the measured data is digitized to form (x, z)
or (y, z) and time t of the signal, referred to as hits. Here
the z position is given by the layer number of the RPC. A
recursive optimal state estimator – the Kalman Filter [39,40],
uses the local geometry and magnetic field information to fit
the muon hits, where the muons passing through a minimum
of three layers are fit to form the track. The direction and
θcos
1−−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
events / bin
μ
ν
&
μ
ν
0
200
400
600
800
1000
True
Reconstructed
z
Fig. 1 Comparison of true (dashed black) and reconstructed (solid
orange) zenith angle (cos θ
z
) distribution for muons, averaged over
energy and azimuthal angle for an exposure of 50 kton × 5 years of
ICAL.
the momentum of the muon is obtained from the best fit val-
ues of the track. Also the timing information from the RPCs,
with a resolution of approximately 1 ns enables the distinc-
tion between upward and downward going particles. More
details can be found in Ref. [40].
Hence for the first time we have done this analysis per-
forming event-by-event reconstruction, where each event is
simulated through the detector and reconstructed to obtain
the observables. Therefore the tails of the resolution func-
tions, which have been approximated by single Gaussians
and Vavilov [41] functions in the previous studies [33], are
also taken in to account in this analysis.
The μ
±
leave one or two hits per layer on average, form-
ing a well-defined track, whereas the hadrons leave several
hits per layer forming a shower of hits. Rarely (less than 1%
of the time) a pion may also leave a well-defined track in the
ICAL and may be misidentified as a muon. In this case the
longest track is identified as the muon. The iron plates will
be magnetised to produce a field upto 1.5 T and this will be
used in the ICAL to probe the charge and momentum of the
muon. The direction and the curvature of the muon trajec-
tory, as it propagates through the magnetized detector, gives
its charge and momentum, respectively. Figure 1 shows the
zenith angle (θ
z
) distribution before (true) and after recon-
struction. Note that in the current analysis cos θ
z
=+1isthe
up-going direction.
The energy of hadrons is obtained by calibrating the num-
ber of hits not associated with the muon track, in the event
[42]. The incident neutrino energy (E
ν
) can be reconstructed
from the energies of the muons and hadrons produced in the
detector. The poor energy resolution of hadrons [42] affects
the reconstruction of the incident neutrino. Hence for ICAL
physics analysis hadron and muon energies are used sepa-
rately, without losing the good energy and angular resolution
of muons [33,38,43,44].
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