Beyond $\Delta m^2$: Absolute Mass Sensitivity in Neutrino Oscillations

Technical Summary: Beyond $\Delta m^2$: Absolute Mass Sensitivity in Neutrino Oscillations

Problem Statement
Conventional wisdom in neutrino physics holds that oscillation experiments are strictly sensitive only to neutrino mass-squared differences ($\Delta m^2_{ij}$) and are blind to the absolute neutrino mass scale. This conclusion relies on the leading-order (LO) approximation of the oscillation phase, where the phase difference is proportional to $\Delta m^2_{ij}L/2E$. However, this approximation neglects higher-order terms in the expansion of the neutrino mass $m_i$ relative to its energy $E$ ($m_i/E$). The authors posit that at next-to-leading order (NLO), the oscillation phase acquires terms proportional to $m^4_i - m^4_j$, which depend on the sum of the squared masses ($m^2_i + m^2_j$). Consequently, neutrino oscillations are, in principle, sensitive to the absolute mass scale. The challenge lies in the fact that deriving these NLO corrections requires a rigorous treatment that avoids the inconsistent assumptions (such as equal energy or equal momentum prescriptions) often used in LO derivations, which fail to yield unique or correct results at higher orders.

Methodology
The authors employ a wave-packet formalism to derive the NLO corrections to the neutrino oscillation phase. This approach is necessary to unambiguously relate propagation time to detection position and to account for the kinematics of the neutrino production process.

1. Wave-Packet Treatment: Neutrinos are modeled as coherent superpositions of Gaussian wave packets in momentum space. The time-evolved wave function is calculated by expanding the energy $E_i(p)$ around the mean momentum $P_i$ to linear order in $(p-P_i)$.
2. Production Kinematics: To fix the mean energy and momentum of the mass eigenstates, the authors analyze the kinematics of reactor antineutrino production via nuclear beta decay. They utilize an effective two-body description where the daughter nucleus and the emitted lepton are treated as a single recoiling object with invariant mass $m_{\text{eff}}$.
3. Expansion and Phase Derivation: Using the kinematic constraints from the production process, the authors expand the oscillation phase in powers of $m_i/E_0$ (where $E_0$ is the energy of a massless neutrino). They demonstrate that the NLO correction to the oscillation phase is proportional to $(m^4_i - m^4_j)L/E^3_0$.
4. Experimental Application: The derived NLO probability is applied to the Jiangmen Underground Neutrino Observatory (JUNO). The analysis involves simulating the inverse beta decay (IBD) event spectrum, incorporating JUNO's energy resolution, reactor flux models (Huber-Mueller), and systematic uncertainties. A $\chi^2$ fit is performed to determine the sensitivity to the lightest neutrino mass $m_1$.

Key Contributions

• Derivation of NLO Phase: The paper provides a rigorous derivation of the NLO correction to the oscillation phase, showing it scales as $(m^4_i - m^4_j)L/E^3_0$. This term introduces a dependence on the absolute mass scale ($m^2_i + m^2_j$) distinct from the standard $\Delta m^2_{ij}$ dependence.
• Resolution of Ambiguities: The authors demonstrate that plane-wave approaches (using equal-energy or equal-momentum prescriptions) fail at NLO, yielding ambiguous or incorrect results depending on how the propagation time $t$ is related to the baseline $L$. The wave-packet treatment combined with production kinematics resolves these ambiguities.
• JUNO Sensitivity Analysis: The paper quantifies the sensitivity of the JUNO experiment to the absolute neutrino mass. It identifies that the NLO effect manifests as an energy-dependent shift in the oscillation frequency, distinct from amplitude-suppressing effects like decoherence or matter effects.

Results

• Sensitivity Limits: Applying the NLO model to JUNO data (assuming 6 years of operation), the authors find that JUNO can constrain the lightest neutrino mass $m_1$ to be less than 305 keV at $1\sigma$ and 434 keV at $2\sigma$ (without external priors on oscillation parameters).
• Degeneracy: The sensitivity is limited by a parameter degeneracy where the NLO correction mimics a rescaling of $\Delta m^2_{21}$. This degeneracy is broken only by the specific $1/E^2_0$ energy dependence of the NLO term.
• Channel Contribution: Both the "solar" ($\Delta m^2_{21}$) and "atmospheric" ($\Delta m^2_{31}, \Delta m^2_{32}$) oscillation channels contribute to the sensitivity. While the atmospheric shift is larger in absolute magnitude due to the larger $\Delta m^2$, the solar channel provides a slight edge in sensitivity because the solar oscillation dip falls within JUNO's high-statistics energy band and is less smeared by the detector's energy resolution than the rapid atmospheric oscillations.
• Comparison to Other Probes: The derived bounds ($m_1 \lesssim 300$ keV) are significantly weaker than current limits from beta decay (KATRIN: $< 0.45$ eV), electron capture, and cosmology ($\sum m_i < 0.053$ eV).

Significance and Claims
The authors explicitly state that while the JUNO sensitivity to the absolute mass scale is not competitive with existing bounds from beta decay, electron capture, or cosmology, the significance of this work is conceptual and complementary.

• Novel Probe: Neutrino oscillations provide a "novel, complementary probe" of the neutrino mass scale. Unlike kinematic methods that measure weighted sums of masses ($m^2_{\nu_\alpha} = \sum |U_{\alpha i}|^2 m^2_i$) or cosmological bounds on the sum of masses, oscillation experiments probe a different combination of masses ($m^2_i + m^2_j$) via the propagation phase.
• Independence: This approach relies on fundamentally different physical mechanisms and assumptions. Agreement across these diverse methods would strengthen the robustness of neutrino mass measurements, while tensions could indicate new physics.
• Applicability: The derived NLO corrections may be practically useful for other systems, such as hypothetical quasi-degenerate heavy neutrinos or very-low-energy neutrinos (e.g., tritium beta decay endpoints), where the $m^2/E^2$ suppression is less severe.

The paper concludes that while the effect is small due to the ultrarelativistic nature of neutrinos ($m^2/E^2 \sim 10^{-14}$), the theoretical framework established allows for a consistent treatment of absolute mass sensitivity in oscillation experiments, establishing a new, albeit currently weak, avenue for probing the absolute neutrino mass scale.