Study of neutrino oscillation parameters at the INO-ICAL detector using event-by-event reconstruction

We present the reach of the proposed INO-ICAL in measuring the atmospheric-neutrinooscillation parameters θ23 and ∆m 2 32 using full event-by-event reconstruction for the first time. We also study the fluctuations in the data and their effect on the precision measurements and mass-hierarchy analysis for a five-year exposure of the 50 kton ICAL detector. We find a mean resolution of ∆χ2 ≈ 2.9, which rules out the wrong mass hierarchy of the neutrinos with a significance of approximately 1.7σ. These results are similar to those to presented earlier studies that approximated the performance of the ICAL detector. ∗Electronic address: rebin@physics.iitm.ac.in †Electronic address: libby@iitm.ac.in ‡Electronic address: indu@imsc.res.in §Electronic address: lakshmilsm9@gmail.com 1 ar X iv :1 80 4. 02 13 8v 1 [ he pex ] 6 A pr 2 01 8


Neutrino oscillations
Neutrinos are massive and undergo oscillations (ν e ν µ ν τ ). Three flavors : mixing is governed by 3 × 3 unitary matrix. Absolute masses are yet to be determined.
Measure the MH by observing matter effects separately in νµ andνµ.

Motivation
Devise a method, which can be used on real ICAL data.
Study the reach of ICAL for the run of 5 years.
To account for the tails of resolution functions, which have been approximated by single Gaussians and Vavilov functions in the previous studies.  Our analysis : 1000 years NUANCE [1] unoscillated CC νµ events (0.4 GeV to 500 GeV).

Analysis procedure
Separate data sets were generated for 5 and 995 years after simulating in GEANT4 [2].
5 year data : the experimental data set. 995 year data : the probability distribution function (PDF). Hence data is: uncorrelated with fluctuations.
To see the effect of fluctuations: chose sixty different combinations of data and PDF.
To reconstruct: INO-ICAL code (E rec µ and cos θz ). Event selection is applied in different regions [3].  Applying oscillations and binning scheme

Event selection
The fraction of νe in the sample is very low, hence only νµ flux is used in the analysis.

Fnue
The data is subjected to three flavor matter oscillations, assuming PREM density profile of Earth [4].

Osc
Binning: Two variables : the reconstructed muon zenith angle (cos θz ) and the muon energies, tagged positive for µ + and negative for µ − (QµEµ). Bins νµ andνµ are binned in separate bins in QµEµ according to charge ID.
The pull approach [5] is used in defining the Poisson χ 2 incorporating systematic uncertainties.
Tν ij and T ν ij areν µ and ν µ PDFs respectively. f is a free parameter describing the fraction ofν µ in the sample. The systematic errors are parametrized in terms of variables {ξ k } called pulls, and π k corresponds to the resulting uncertainty. Considered two systematic uncertainties : 5% uncertainty on the zenith angle dependence of the flux. 5% on the energy dependent tilt error.
The normalization uncertainty is excluded from systematics and instead the free parameter R fixes the overall normalization. The significance of the fit: Relatively worse precision, as we loose 40% of events after selection cuts.
Hence choose not to apply any cuts.
Conclusion: loose selection cut gives better results.
Adding prior constrains on sin 2 θ13 and ∆m 2 12 , was observed not to make any difference in the fit.  The analysis was repeated for sixty different data sets. Roughly the fit converges : 68% of times with in 1σ 95% of times with in 2σ Mass hierarchy determination  Fit to sixty different data sets: mean ∆χ 2 MH = 2.9 (≈ 1.7σ). 15% probability of identifying wrong MH. 13 year run of ICAL will give a 3σ separation to differentiate the MH.

Conclusion
Event-by-event reconstruction is used for the first time.
The effect of event selection is studied for the first time.
For the first time we study the effect of low event statistics on the precision and MH measurements, by introducing fluctuations in the data.
We also find a mean resolution of ∆χ 2 MH = 2.9 from an ensemble of sixty experiments, which rules out the wrong hierarchy with a significance of ≈ 1.7σ.