A plethora of long-range neutrino interactions probed by DUNE and T2HK

Neutrino flavor transitions offer a powerful tool in the search for physics beyond the Standard Model (SM). Many proposed models introduce new flavor-dependent neutrino interactions – interactions beyond the standard weak interactions that, by affecting νe, νμ, and ντ differently, can alter transitions between them. Detecting these interactions is challenging due to their anticipated feebleness. However, if the interaction's range is long, vast reservoirs of matter far from the neutrino source can create a significant matter potential, influencing flavor transitions even with weak interactions. Currently, there's no evidence for such long-range neutrino interactions (LRIs), but existing data from atmospheric, solar, accelerator, and astrophysical neutrinos, along with other constraints (gravitational fifth-force searches, tests of the equivalence principle, black-hole superradiance, etc.), provide stringent limits. Long-baseline neutrino oscillation experiments, with their long baselines (hundreds of kilometers), high-precision detectors, and well-characterized neutrino beams, are ideally suited for detecting these subtle deviations from standard expectations. They have already placed stringent limits on LRIs. The next generation of long-baseline experiments—DUNE and T2HK—promise significant advancements with larger detectors, advanced detection techniques, and more intense neutrino beams. This paper forecasts the potential of DUNE and T2HK to constrain, discover, and characterize new flavor-dependent neutrino interactions, focusing on LRIs. We introduce new neutrino interactions by considering accidental global U(1) symmetries of the SM involving combinations of lepton numbers (Le, Lμ, Lτ) and baryon number (B). Gauging these symmetries introduces a new neutral vector gauge boson (Z′) with unknown mass (mZ′) and coupling strength (gZ′), creating a Yukawa potential sourced by electrons, protons, or neutrons, depending on the symmetry. The symmetry also dictates how the interaction affects νe, νμ, and ντ, and modifies flavor transitions accordingly. We focus on ultra-light mediators (10⁻¹⁰ eV to 10⁻³⁵ eV), corresponding to interaction ranges from meters to gigaparsecs. Our analysis leverages three key ingredients: (1) a long-range matter potential sourced by matter in the Earth, Moon, Sun, Milky Way, and cosmological matter distribution; (2) detailed simulations of DUNE and T2HK; and (3) exploration of a wide range of candidate U(1)′ symmetries, each inducing unique effects on neutrino oscillations. This builds upon previous work but extends the analysis by incorporating protons in the potential calculation and exploring a broader range of U(1)′ symmetries than previously considered.

Previous research has explored the possibility of long-range neutrino interactions, primarily focusing on specific U(1) symmetries. Studies have investigated the constraints on such interactions using data from atmospheric neutrinos [7], solar and reactor neutrinos [8], accelerator experiments [20, 21], and high-energy astrophysical neutrinos [12, 22]. Global oscillation fits [6, 13, 15, 23–25] have also been used to constrain these interactions. Several works have explored the potential of long-baseline neutrino oscillation experiments, such as DUNE and T2HK, to probe for such effects. A significant prior work [30] has investigated three candidate symmetries and demonstrated their potential to constrain and discover LRIs, however, this work used older oscillation parameter values. The present study expands on this by including a much more extensive set of potential U(1) symmetries and uses updated oscillation parameters from the most recent NuFIT global analysis. Furthermore, unlike earlier calculations of long-range matter potentials that considered only electrons and neutrons, the current study incorporates the contribution of protons, leading to a more comprehensive assessment. Indirect limits have been derived from observations of black-hole superradiance [14], the early universe [15], compact binaries [16], and the weak gravity conjecture [17], providing a broader context for evaluating the significance of any future results from DUNE and T2HK.

The study employs a comprehensive methodology to forecast the sensitivity of DUNE and T2HK to new flavor-dependent neutrino interactions mediated by a light Z' boson. The approach begins by introducing new neutrino-matter interactions through the gauging of accidental global U(1) symmetries of the Standard Model, which involves combinations of lepton numbers (Le, Lμ, Lτ) and baryon number (B). A total of fourteen candidate symmetries are considered, each leading to a unique effective interaction Lagrangian. The Lagrangian incorporates the interaction mediated by the Z' boson and the mixing between Z and Z' bosons, which introduces a four-fermion interaction. The Yukawa potential experienced by a neutrino due to these interactions is calculated, accounting for the contributions from electrons, protons, and neutrons in various celestial objects (Earth, Moon, Sun, Milky Way, and cosmological matter distribution). The calculation of the matter potential includes a detailed treatment of the spatial distribution of these particles. The long-range matter potential is then incorporated into the neutrino oscillation probability calculations. The authors use GLOBES, a simulation toolkit for long-baseline neutrino oscillation experiments, along with a modified version of the SNU matrix-diagonalization library to compute the oscillation probabilities numerically for the four relevant oscillation channels: νμ → νe, ν̅μ → ν̅e, νμ → νμ, and ν̅μ → ν̅μ. These probabilities are used to simulate event rates in DUNE and T2HK, taking into account detailed experimental configurations (detector types, fiducial volumes, beam properties, running times, and systematic uncertainties). Statistical methods are employed to determine the sensitivities to the new neutrino-matter interactions. Constraints on the new matter potential are derived by comparing true event spectra (with no new interactions) to test spectra (with varying amounts of the new interaction). A Poisson χ² function is used, with profiling over relevant oscillation parameters (θ23, δCP, Δm³₁²) and systematic uncertainties. Discovery prospects are assessed by comparing the minimum χ² values for the true (with new interaction) and test (no new interaction) spectra. The distinguishability between different U(1)′ symmetries is evaluated by comparing the minimum χ² values for event distributions generated assuming different true symmetries.

The analysis yields several key findings. First, DUNE and T2HK, individually and in combination, exhibit remarkable sensitivity to long-range neutrino interactions, regardless of the underlying U(1)′ symmetry. The strongest limits and discovery potential are achieved when the new matter potential primarily affects the μ-τ sector, leading to stronger constraints on the new interaction's coupling strength (G'). The results show that DUNE and T2HK can independently constrain the new matter potential to values comparable to the standard oscillation terms in the Hamiltonian, triggering resonant effects in the oscillation probabilities. The combined analysis of DUNE and T2HK significantly enhances the sensitivity, particularly for high values of the new matter potential, where degeneracies between the potential and other oscillation parameters are lifted. The combination of DUNE and T2HK allows for a substantial improvement in the limits on the effective coupling strength of the Z' mediator, G', especially for mediator masses lighter than 10⁻¹⁸ eV. These results significantly improve upon existing constraints from atmospheric, solar, reactor, and astrophysical neutrinos and are projected to establish the most stringent constraints to date. In addition to constraints, the paper also forecasts discovery prospects. The combination of DUNE and T2HK significantly improves the potential to discover the new interactions. The study shows that the experiments can discover long-range interactions across various U(1)' symmetries, provided the new matter potential is roughly comparable to the standard oscillation terms. The analysis also examines the possibility of distinguishing between different U(1)' symmetries in the event that a new interaction is discovered. The results suggest that distinguishing between symmetries is more feasible for higher values of the new matter potential and when the symmetries have different textures in their matter potential matrices. The capability of DUNE and T2HK to identify or narrow down the potential U(1)' symmetry responsible for the observed interaction is significant, further emphasizing the power of these experiments in exploring physics beyond the Standard Model.

The findings address the research question by demonstrating the exceptional sensitivity of DUNE and T2HK to a wide range of long-range neutrino interactions, irrespective of the underlying U(1)′ symmetry. The results highlight the complementary nature of the two experiments, with DUNE providing stronger constraints at lower potential values due to its higher energy reach, and T2HK improving the significance of the results and breaking parameter degeneracies. The significance of the results is that they significantly extend the reach of current searches for physics beyond the Standard Model, potentially revealing new fundamental interactions of neutrinos. The relevance to the field lies in the potential for groundbreaking discoveries, furthering our understanding of neutrino physics and the fundamental forces of nature. The study's comprehensive approach, considering multiple symmetries and a realistic simulation of the experiments, enhances the reliability of the predictions and provides a robust framework for future research in this area.

This study demonstrates that DUNE and T2HK offer a powerful combined capability to constrain, discover, and potentially identify the underlying symmetry responsible for new flavor-dependent neutrino interactions, particularly those with a long range. The findings significantly advance our ability to probe physics beyond the Standard Model. Future work could include incorporating more sophisticated models of the cosmological matter distribution or investigating the effects of the relic neutrino background on the long-range potential. Further refinement of the experimental simulations, including more detailed systematic uncertainties, is also warranted.

The analysis relies on several approximations and assumptions. The calculation of the long-range matter potential approximates the Earth, Moon, Sun, Milky Way, and cosmological matter distribution as continuous or point-like sources. The effect of neutrino propagation through the Earth's varying density profile is not explicitly modeled but instead is approximated by using an average matter density. The systematic uncertainties used in the event rate calculations are based on current estimations, which might be refined with better understanding of the detectors and beams. Finally, the analysis assumes that the new interactions do not significantly affect the charged leptons. These approximations, while providing a robust framework for the analysis, might introduce minor uncertainties in the final predictions. Further investigations into relaxing these assumptions are recommended in the future.