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CP Violation and Mass Hierarchy with a Combined Sensitivity of T2K-II

CP violation and mass hierarchy with a combined sensitivity of T2K-II, NOνA and JUNO Nath Ankur1, Cao Son2, Ngoc Tran Van3, Van Nguyen Th4, Quyen Phan To3, Francis Ng K1 1Tezpur University, Assam, India; 2High Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan; 3Institute For Interdisciplinary Research in Science and Education, Quy Nhon, Vietnam; 4Institute of (IOP), VAST, Hanoi, Vietnam

Abstract Result Recent T2K data indicates a CP violation in the and mildly favours the normal neutrino mass hierarchy. This work explores Unless mentioned, the following values (mostly from global analysis [6]) ues, δCP = 0, π, is calculated assuming either the MH is known or not the physics potentials with a combined sensitivity of T2K-II, NOνA, and JUNO experiments. T2K-II, a proposed run extension up to 2026 by are taken as the truth for sensitivity studies: known. Although the result below is tagged as with “unknown” MH, it T2K collaboration, is sensitive to CP violation at a level of 3σ or higher if δCP ∼ −π/2. NOνA, proposed to run until 2024, provides a significant should be closely equivalent to “known” MH when all experiments are 2 2 2  sensitivity to both mass hierarchy and CP violation. JUNO, expected to take data for six years starting from 2021, has 3σ or higher sensitivity sin θ12, sin θ13, sin θ23, δCP = (0.310, 0.02241, 0.5, −π/2) combined since MH is solved definitely in this case. to the mass hierarchy and 1% or better precision measurement of solar parameters and atmospheric mass splitting. It is shown that the joint 2 2  −5 2 −3 2 ∆m21, ∆m31 = 7.39 × 10 eV , 2.523 × 10 eV analysis can determine definitely the neutrino mass hierarchy. Also it provides > 4σ to exclude CP conserving values if δCP ∼ −π/2 and > 50% Preliminary fractional region of δCP can be explored at ≥ 3σ significance. 9 Mass Hierarchy (MH) Sensitivity Assume neutrino MH is nor- True: NH, sinθ2 =0.5 2 23 mal, statistical significance χ to exclude the inverted MH is calculated 8 T2K-2 only Objectives at each possible true value of δ . =0 CP CP 7 + short-baseline reactor δ Neutrino oscillations establish that have mass and the are mixed. mixing matrix, which connects the mass 6 + NOvA (extend to 2024) eigenstates and flavor eigenstates of neutrinos, is presumed to be unitary 3 × 3 matrix, which are commonly parameterized by three mixing Preliminary 5 + JUNO a 10 angles θ12, θ13, θ23, one Dirac CP-violation phase δCP . The probability for a α-flavor to oscillate into β-flavor,P(να→νβ ), depends on these four 2 2 9 4 parameters, two mass square splitting ∆m , ∆m , its energy, Eν , propagation distance L, and amount of it passing through, ρ: 21 31 8 3 2 2  7 2 P(να→νβ ) = f θ12, θ13, θ23, δCP ; ∆m21, ∆m31; Eν , L, ρ (1) 6 Sigma to exclude sin 1 • Experiments basically measures the probabilities to extract parameters, e.g T2K, NOvA measure P ( ν disappearance), (νµ→νµ) µ 5 0 −3 −2 −1 0 1 2 3 P(νµ→νe) ( νe appearance), and corresponding processes with νµ; JUNO will measure P(νe→νe) (IH assumed)

2 4 δ NOvA only True values of CP [rad] χ 3 2  ∆ JUNO only π • Each experiment is sensitive to a specific set of parameters, e.g T2K, NOvA are sensitive to θ13, θ23, δCP , ∆m31 ; JUNO (a) For θ23 = 4 , MH is not known 2 2  2 NOvA + JUNO θ12, θ13, ∆m21, ∆m31 . Also there are degeneracy among parameters, challenging the precision measurements from single experiment. Preliminary 1 Joint analysis 9 Joint analysis It is essential to combine data from multiple experiments to attain a precision measurement. Main objectives of T2K-2, NOvA 0 0 1 2 3 4 5 6 8 2θ sin 23 = 0.50 and JUNO joint analysis are to (i) determine the neutrino mass hierarchy (MH), (ii) enhance sensitivity to CP violation, (iii) δ =0 CP [rad.] (True, MH) 2

CP 7 θ sin 23 = 0.60 precision measurement of other oscillation parameters, and (iv) to test the unitary of the lepton mixing matrix. 2 δ (a) Individual and combined sensitivity to MH at sin θ23 = 0.5 2θ 6 sin 23 = 0.43 aIf neutrino is Majorana particle, two additional Majorana-CP-violation phases are included but these are irrelevant for Preliminary 10 5 9 4 Experimental and Simulation Details 8 3 GLoBES [1] is used for simulating the experiments and calculating the Parameters T2K-II NOνA JUNO 7 2 statistical significance. We describe the experiments closely as Exposure (POT) 20 × 1021 7.2 × 1021 6 yrs. @ 36 GW-th 6 Sigma to exclude sin 1 much as possible by using the updated information of flux, sig- Baseline (km) 295 810 52.5 5 0 −3 −2 −1 0 1 2 3 (IH assumed) nal/background efficiency, and systematic error. Each experi- 2 4 δ Energy peak/range ∼0.6 GeV ∼2.0 GeV 1-8 MeV Joint analysis True values of CP [rad] χ 3 2θ mental setup is validated at the event rate level and sensitivity (Far) Det. Type WC LS LS ∆ sin = 0.50 23 (b) For different values of θ23, MH is not known level. An overview of experimental specification is shown in Table 1 and 2θ (Far) Det. Mass 50 kt 14kt 20kt 2 sin 23 = 0.60 details are described below: 2θ 1 sin 23 = 0.43 Figure 3: Sensitivity to CP violation Table 1: Experimental Specifications 0 0 1 2 3 4 5 6 21 δ T2K-II An exposure of 20 × 10 -on-target (POT) equally di- CP [rad.] (True, MH) Appearance ν mode Disappearance ν mode Fig. 3(a) shows the sensitivity to the leptonic CP violation for

9 2 π vided among ν and ν running modes. The signal/background efficiency 22 (b) Combined sensitivity for three values of sin θ ν →ν 23 the case when θ23 = and the MH is assumed to be “not µ e ν ν 4 20 ν →ν 8 µ + µ µ e and spectral information for T2K-II is obtained by scaling the 2017 anal- ν 18 µ CC 7 NC + Cosmic known” by adding up experiments starting from T2K-2. Fig. 3(b) ν CC 16 µ Figure 2: Mass hierarchy resolving as a function of true δ ysis [2] to same exposure as T2K proposal [3]. Four data samples are NC + Cosmic 6 SIG, 2019 CP 14 ν ν shows the combined sensitivity to CP violation at different val- Beam e+ e 5 12 SIG, 2019 2 used: νµ disappearance, νe appearance in both ν-mode and ν-mode. A Beam BKG, 2019 ues of sin θ . Table 2 shows the fractional region of δ in 10 4 23 CP 3% systematic error for all samples and 3% energy resolution are used. 8 3 Fig.2(a) shows sensitivity to mass hierarchy from different experiment which CP violation can be explored with 3σ or higher significance. Number of events/0.5GeV 6 Number of events/0.1GeV 2 2 2 4 and combination at sin θ23 = 0.5. The combined sensitivity for different sin θ23 0.43 0.50 0.60 1 2 2 21 0 0 values of sin θ is shown in Fig.2(b). 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 23 Fraction of δ 61.6% 54.6% 53.3% NOνA w/ run extension A total exposure of 7.2×10 POT equally rec rec CP Reconstructed Neutrino Energy, Eν (GeV) Reconstructed Neutrino Energy, Eν (GeV) divided among ν and ν modes; We closely followed [4] to obtain the flux (a) Appearance (neutrino) (b) Disappearance (neutrino) 2 Table 2: Fractional region of δCP , depending on sin θ23, can be explored information and [5] to obtain the signal, background efficiency and spec- Appearance ν mode Disappearance ν mode CP Violation Sensitivity Considering δCP can be varied between 6 with 3σ or higher significance 9 ν →ν (−π, +π), the statistical significance of excluding the CP-conserving val- tral information. A 5% systematic error for all samples and energy reso- µ e ν ν ν →ν µ + µ µ e 5 8 ν lution from 8 − 10% are assigned. Fig. 1 shows an example of comparing µ CC NC + Cosmic 7 νµ CC NC + Cosmic 4 SIG, 2019 6 Beam ν +ν event rate obtained by our setup and real NOvA simulation. e e Summary and Discussion 5 SIG, 2019 Beam BKG, 2019 3 4

3 2 • Mass hierarchy will be determined with this joint analysis provement in solving the θ23 octant degeneracy, more precise

235 238 Number of events/0.5GeV Number of events/0.1GeV JUNO Neutrinos flux is simulated with four isotopes of U, U, 2 1 measurements on other oscillation parameters and provide a great 239 241 P u and P u with an efficiency of 73%, predicting 60 IBD events 1 • CP violation can be explored > 4σ if δCP ∼ −π/2 (T2K data 0 0 test to the standard neutrino oscillation paradigm. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Reconstructed Anti-Neutrino Energy, Erec (GeV) Reconstructed AntiNeutrino Energy, Erec (GeV) per day. Detector setup is simplified with a single reactor core of 36 ν ν indication) and > 50% fractional region of δCP with ≥ 3σ signifi- cance. GW-th and no simulation of background. This simplification affects the (c) Appearance (antineutrino) (d) Disappearance (antineutrino) • Further consideration: background simulation for JUNO; sys- solar parameter precision, but less on the MH sensitivity. A 3% energy • (Not shown in the poster), a joint analysis provides a great im- tematic modeling; correlation among experiments) resolution and 1% error for flux and detector uncertainties are used. Figure 1: NOνA FD event spectra: our setup w/ GLoBES compared to [5] References

[1] P. Huber et. al. Comput. Phys. Commun., 177(432), 2007. [3] K. Abe et.al. T2K Collaboration, arXiv, 1607.08004(hep-ex), 2016. [5] M. A. Acero et. al. Phys. Rev. Lett., 123(151803), 2019. -[2] K. Abe et.al. Phys Rev D, 96, 092006(98, 019902(E)), 2017 (2018E). [4] M. Sanchez. https://doi.org/10.5281/zenodo.1286757, 2018. [6] I. Esteban et. al. Journal of High Energy Physics, (106), 2019.

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