T versus CP effects in DUNE and T2HK

TL;DR

This work investigates time-reversal violation in neutrino oscillations within the standard three-flavour framework by exploiting an $L$-odd component in the appearance probability $P_{\nu_\mu\to\nu_e}$ and combining data from DUNE and T2HK. By decomposing the probability into $P_{\rm even}$ and $P_{\rm odd}$ and focusing on the energy window $E_\nu\in[0.68,0.92]$ GeV, the authors show that T violation can be detected with up to $\sim 4\sigma$ significance, with the second oscillation maximum in DUNE playing a pivotal role. A comparison with CP violation reveals that DUNE neutrino-mode data is particularly powerful for T-violation while T2HK excels in CP-violation tests that compare neutrino and antineutrino data; together they provide complementary, cross-validated constraints on the phase $\delta_{\rm CP}$. The analysis also introduces the model-independent $X_T$ observable, offering an additional consistency check across baselines. Overall, the study demonstrates a strong, complementary strategy for probing the PMNS phase and potential fundamental T violation using realistic, planned experimental configurations.

Abstract

Time reversal (T) symmetry violations in neutrino oscillations imply the presence of an $L$-odd component in the transition probability at fixed neutrino energy, with $L$ denoting the distance between neutrino source and detector. Within the standard three-flavour framework, we show that the combination of the transition probabilities determined at the DUNE and T2HK experiments can establish the presence of an $L$-odd component, and therefore provide sensitivity to T violation, up to $4σ$ significance. The optimal neutrino energy window is from 0.68 to 0.92 GeV, and therefore a crucial role is played by the low-energy part of the DUNE event spectrum covering the second oscillation maximum. We compare the sensitivity to T violation based on this energy range using neutrino data only with the more traditional search for charge-parity (CP) violation based on the comparison of neutrino versus anti-neutrino beam data. We show that for DUNE it is advantageous to run in neutrino mode only, i.e., searching for T violating effects, whereas T2HK is more sensitive to CP violation, comparing neutrino and anti-neutrino data. Hence, the two experiments offer complementary methods to determine the complex phase in the PMNS mixing matrix.

Figures (12)

• Figure 1: Sensitivity to T violation for DUNE+T2HK as a function of the true value of $\delta_{\rm CP}$ for two energy bins between 0.68 and 0.92 GeV. Left and middle panels show the bins separately and the right panel corresponds to the combination. Different curves correspond to different assumptions on prior knowledge on the mixing angles $\theta_{ij}$, namely no prior knowledge (green), uncertainties corresponding to current global fit uncertainties (blue), and mixing angles fixed to their best fit points (red).
• Figure 2: Bi-probability plot for $P_{\nu_\mu\to\nu_e}$ for DUNE and T2HK for three energies where there is overlap between the two experiments. Oscillation parameters are chosen according to \ref{['tab:osc-params']} and the symbols indicate values of $\delta_{\rm CP}$. We indicate the $\pm1\sigma$ error bands for the T-conserving cases, using the expected number of events in a bin with width 0.12 GeV centred at the energies of each panel, for our default assumptions about exposure.
• Figure 3: Dependence of the sensitivity to T violation on prior knowledge on mixing angles. The left panel assumes a prior corresponding to current global fit uncertainties for two mixing angles and no prior for the third one. The right panel shows the dependence on the $\theta_{23}$ octant: for the solid (dashed) curves we assume a true value of $\theta_{23}$ in the 1st (2nd) octant, namely $\sin^2\theta_{23} = 0.435\, (0.565)$; for the red (blue) curves we adopt a prior on $\sin^2\theta_{23}$ ($\sin^22\theta_{23}$), with an uncertainty of $\sigma_{\sin^2\theta_{23}} = 0.015$ ($\sigma_{\sin^22\theta_{23}} = 0.01$).
• Figure 4: Sensitivity to T violation as a function of the DUNE exposure in the neutrino beam mode for $\delta_{\rm CP}^{\rm true} = 90^\circ \, (270^\circ)$ for the left (right) panel. The T2HK exposure is kept fixed at 608 kt MW yr. For reference, our default DUNE exposure of 336 kt MW yr is obtained roughly after 7 years of operation. We show sensitivities from combining the two energy bins $[0.68,0.8]$ and $[0.8,0.92]$ GeV. Different curves correspond to re-scaling the energy resolution of DUNE by factors of 2, 1, 0.5, 0.3 compared to the default assumption stated in \ref{['sec:simulation']} which corresponds to the blue curves.
• Figure 5: Sensitivity to $\delta_{\rm CP} \neq 0,\pi$ from full spectral analysis for DUNE (left) and T2HK (right), for total exposures of 336 kt MW yr and 1824 kt MW yr, respectively. We compare the sensitivity obtained from using the full exposure in neutrino mode only (red) to the one when the exposure is divided into neutrino and anti-neutrino running with ratio 1:2 (blue). For T2HK we show for comparison also the neutrino-only sensitivity using 608 kt MW yr.