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In this work we study the potential of the future experiments INO, JUNO and T2HK to determine the neutrino mass ordering. When these three experiments are combined, one can achieve mass ordering sensitivity at a significant confidence level irrespective of the energy resolution of JUNO or the value of $\delta_{\rm CP}$. The main synergy between the reactor experiment and the accelerator/atmospheric experiment come from its sensitivity to the parameter $\Delta m^2_{31}$. In addition we will also explore

(i) effect of varying energy resolution of JUNO, (ii) the effect of longer run-time of INO, (iii) effect of octant degeneracy in the determination of neutrino mass ordering.

For INO, we use the GEANT4 based geometry of the ICAL detector with specifications given in the INO white paper. ICAL is a 50 kt iron calorimeter with 1.5-tesla magnetic field which make it the world's unique detector which can distinguish atmospheric neutrino and anti-neutrino using a magnetic field. The atmospheric flux used in our analysis is Honda fluxes calculated for the Theni site (INDIA). We use the GENIE event generator to generate 1000 years of data for the analysis and then normalize it to 10 years to reduce Monte Carlo fluctuations. Neutrino oscillations are incorporated via the re-weighting algorithm and the detector efficiency and resolutions are included.

The experiments T2HK and JUNO are simulated using GLoBES. For T2HK, We consider two water-Cerenkov detector tanks having a fiducial volume of 187~kt each located at Kamioka which is 295 km from the neutrino source at J-PARC having a beam power of 1.3 MW with a total exposure of $27 \times 10^{21}$ protons on target, corresponding to 10~years of running. We have divided the total run-time into 5 years in neutrino mode and 5 years in anti-neutrino mode. For systematic errors, we have considered an overall normalization error of 4.71% (4.13%) for the appearance (disappearance) channel in neutrino mode and 4.47% (4.15%) for the appearance (disappearance) channel in anti-neutrino mode. The systematic error is the same for both signal and background.

For JUNO, we consider the same configuration as given in JUNO white paper. We consider a liquid scintillator detector having a 20 kton fiducial mass located at a distance of around 53 km from Yangjiang and Taishan nuclear power plants. We have considered the energy resolution of $3%/E$ unless otherwise mentioned. In this analysis, we consider all the reactor cores are located at the same distance from the detector. We use 200 same-size bins within the energy window of 1.8 MeV and 8.0 MeV. We have taken the backgrounds and systematic uncertainties as presented in. We consider the run-time to be 6 years.

It is known that T2HK is capable of neutrino mass ordering only for the favourable values of $\delta_{\rm CP}$ whereas to measure ordering, the energy resolution of JUNO has to be very precise. On the other hand, the sensitivity of INO is independent of the values of $\delta_{\rm CP}$. Taking the true values of $\delta_{\rm CP}$ as $0^\circ$ and $-90^\circ$, we have shown that the combination of INO, JUNO and T2HK can determine mass ordering at $\chi^2 = 100$ and 126 respectively considering 3\% energy resolution of JUNO and 10 years running of INO corresponding to the analysis of muon energy and muon angle. Note that for $\delta_{\rm CP} = 0^\circ$, the mass ordering sensitivity of T2HK is negligible, however with the combination of JUNO, the sensitivity becomes 9.3 $\sigma$. Further, when the energy resolution of JUNO is 5\%, the mass ordering sensitivity becomes very negligible, however, when combined with T2HK the sensitivity goes to 6.2 $\sigma$. The main reason of this excellent synergy is due to the parameter $\Delta m^2_{31}$. As the mass ordering sensitivity comes from different oscillation channels in the accelerator, atmospheric and reactor neutrino experiments, the parameter $\Delta m^2_{31}$ depends differently on these channels.For this reason, a same true value of $\Delta m^2_{31}$ leads to different values of $\Delta m^2_{31}$ (test) in the $\chi^2$ minimum. Therefore when different experiments are added, the $\chi^2$ minimum of the added $\chi^2$ occurs at a different value of $\Delta m^2_{31}$ leading to an enhanced mass ordering sensitivity. Among INO, JUNO and T2HK, the $\chi^2$ minimum of INO are very shallow, therefore, the synergistic effect in the combination of INO+JUNO and INO+T2HK is less as compared to the synergistic effects in T2HK+JUNO. As atmospheric experiments can have the opportunity of running for a longer period, we have shown that if INO run-time is increases to 30 years, then the combined $\chi^2$ reaches to 122 (147) for $\delta_{\rm CP} = 0^\circ (-90^\circ)$. While studying the effect of true $\theta_{23}$ we find that except T2HK+JUNO for both the values of $\delta_{\rm CP}$ and INO+JUNO+T2HK for $\delta_{\rm CP} = 0^\circ$, sensitivity increases as $\theta_{23}$ increases. In the case of T2HK+JUNO for both the values of $\delta_{\rm CP}$ and INO+JUNO+T2HK for $\delta_{\rm CP} = 0^\circ$, mass ordering sensitivity decreases as $\theta_{23}$ increases from $45^\circ$. This is because, as $\theta_{23}$ increases, the $\chi^2$ minimum of T2HK shift towards left in the $\chi^2$ vs $\Delta m^2_{31}$ plane. This leads to a reduction of the combined $\chi^2$. As this effect is more prominent for $\delta_{\rm CP} = 0^\circ$, this effect remains visible for the combination of INO+JUNO+T2HK.In summary, INO+JUNO+T2HK is a powerful combination of experiments that can establish the true nature of the mass ordering within a significant confidence level irrespective of true values of $\delta_{\rm CP}$ and energy resolution of JUNO.

Collaboration | Indian Neutrino Observatory (INO) |
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