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

The study investigates whether new, flavor-dependent neutrino interactions with matter—beyond the standard weak interactions—could modify neutrino flavor transitions and be detected at next-generation long-baseline experiments. If mediated by an ultralight boson, these interactions may have long range and be sourced by large reservoirs of matter (Earth, Moon, Sun, Milky Way, cosmological matter), inducing sizable potentials despite feeble couplings. The research aims to forecast the sensitivity of DUNE and T2HK to such long-range neutrino interactions (LRI), constructed from gauged, anomaly-free U(1)′ combinations of lepton and baryon numbers. It addresses whether these experiments can constrain or discover LRIs across many candidate symmetries and, if detected, whether they can identify the underlying symmetry. The work is motivated by stringent, yet model-dependent and channel-specific, existing constraints and by the imminent high-precision capabilities of DUNE and T2HK.

Prior constraints on long-range neutrino interactions arise from atmospheric, solar, reactor, accelerator, and high-energy astrophysical neutrino data, as well as global oscillation fits that encompass U(1)′ models. Additional limits come from non-neutrino probes such as fifth-force searches, equivalence-principle tests, black-hole superradiance, compact-binary dynamics, and planetary perihelion precession. Earlier forecasts for DUNE and T2HK considered only a subset of symmetries (e.g., Le−Lμ, Le−Lτ, Lμ−Lτ). Recent works also quantified the long-range potentials sourced by astrophysical bodies and explored screening effects from the relic neutrino background. This paper extends these by treating a broad set of fourteen anomaly-free, flavor-dependent U(1)′ symmetries built from lepton and baryon numbers, incorporating sourcing by electrons, protons, and neutrons, and employing detailed experimental simulations.

- Model framework: Gauge accidental global U(1)′ symmetries that are anomaly-free (with or without right-handed neutrinos). Consider 14 flavor-dependent candidates involving combinations of Le, Lμ, Lτ, and B. Each symmetry introduces a new neutral vector boson Z′ with unknown mass mZ′ and coupling gZ′. - Interaction and potentials: Compute flavor-diagonal, long-range matter potentials from Yukawa interactions mediated by Z′, sourced by electrons, protons, and neutrons in the Earth, Moon, Sun, Milky Way, and cosmological matter. For Lμ−Lτ, include Z–Z′ mixing leading to neutron-sourced potentials. Treat mediator masses mZ′ = 10−35–10−10 eV (ranges from Gpc to hundreds of meters). Assume charge neutrality (Ne = Np) and isoscalarity (Np ≈ Nn) except for the Sun and cosmological matter; use approximate particle counts and spatial treatments (Sun and Moon as point sources; Earth, Milky Way, cosmological matter as continuous distributions). Sum contributions to obtain VLRI,α = bα Σf κf Vf(mZ′,G′). - Oscillations and event generation: Use Hamiltonian H = Hvac + Vmat + VLRI. Adopt NuFIT 5.1 best fits as true values; keep θ13 and θ12 fixed in fits; profile over sin2θ23, δCP, Δm2 31 within 3σ. Compute oscillation probabilities and event rates with GLoBES and a modified SNU diagonalization library, including appearance and disappearance channels for ν and ν̄. Implement realistic detector configurations, fluxes, energy binning, systematic uncertainties, and running times for DUNE (10 years, 5ν+5ν̄) and T2HK (10 years, 2.5ν+7.5ν̄). - Statistics: Build Poisson χ2 across energy bins and channels, with pulls for signal/background systematics. Forecast (i) constraints by comparing VLRI=0 truth to VLRI>0 tests; (ii) discovery by comparing VLRI>0 truth to VLRI=0 test; (iii) distinguishability via pairwise confusion-matrix tests between symmetry-induced VLRI textures. Convert constraints/discovery intervals on VLRI to effective coupling G′ versus mZ′ using symmetry-specific charge assignments and the sourced-body composition.

- Sensitivity scale: DUNE and T2HK are most sensitive when the new potential is comparable to standard oscillation terms in the Hamiltonian. Typical sensitivity ranges for VLRI are ~10−14–10−13 eV (DUNE driven by higher energies; T2HK complements at higher VLRI and lifts degeneracies). For DUNE, standard terms are ~10−13–10−12 eV; for T2HK, ~10−12–10−11 eV. - Constraints on VLRI: Across all fourteen symmetries, combined DUNE+T2HK can constrain VLRI to near the standard-oscillation scale, typically O(10−14–10−13 eV). Strongest limits occur for textures primarily affecting the μ–τ sector (VLRI = diag(0, VLRI, −VLRI)); weakest when only the electron sector is affected (VLRI = diag(VLRI,0,0)). - Discovery reach: Combined experiments can achieve 3σ–5σ discovery for VLRI in similar ranges (∼10−14–10−13 eV), with discovery prospects mirroring constraint strengths. Disappearance channels (higher statistics) drive the reach. - Effective coupling G′ vs mZ′: Converting VLRI limits to G′ shows projected bounds stronger than existing limits across many symmetries, especially for ultralight mediators mZ′ ≲ 10−18 eV. Curves exhibit step-like transitions as the interaction range reaches successive source distances (Earth, Moon, Sun, Milky Way, cosmological matter). - Degeneracy breaking: T2HK helps resolve θ23–δCP degeneracies that weaken individual-experiment constraints at higher VLRI, while DUNE constrains the mass ordering and extends reach to lower VLRI. Combination is necessary to stabilize limits across the full parameter space. - Symmetry identification: For sufficiently large VLRI, differences in potential textures allow distinguishing among candidate symmetries. Separation is strong when textures differ markedly; indistinguishable when textures are identical or very similar.

The study demonstrates that next-generation long-baseline experiments can probe an extensive class of long-range neutrino interactions, independent of which U(1)′ symmetry generates them. By leveraging realistic detector simulations and comprehensive sourcing of long-range potentials from astronomical bodies, the forecasts establish that DUNE and T2HK can set unprecedented constraints on the effective coupling of an ultralight mediator and, in favorable cases, discover the interaction. Sensitivity peaks when VLRI matches standard Hamiltonian terms, yielding resonant modifications of probabilities. The complementary energy coverages and systematics of DUNE and T2HK enable degeneracy breaking in oscillation parameter fits, which is essential both for robust constraints and for discovery significance. Furthermore, the experiments can, in some scenarios, identify or narrow down the responsible U(1)′ symmetry based on the induced VLRI texture. These results advance the field by moving beyond single-symmetry forecasts and by quantifying reach against a broad, realistic model set, thus informing both theoretical model building and experimental strategy.

DUNE and T2HK can broadly and deeply probe flavor-dependent long-range neutrino interactions mediated by ultralight Z′ bosons, sourced by electrons, protons, and neutrons in nearby and distant matter. Across fourteen anomaly-free, flavor-dependent U(1)′ symmetries, the combined experiments can constrain VLRI to O(10−14–10−13 eV), discover it at 3σ–5σ if present at similar levels, and, in favorable cases, distinguish the underlying symmetry via differences in VLRI textures. Converting to effective coupling G′ versus mediator mass mZ′, the projected limits surpass existing constraints over wide mass ranges, notably for mZ′ ≲ 10−18 eV. The results underscore the necessity of combining DUNE and T2HK to lift parameter degeneracies. Future work could incorporate detailed Earth matter profiles along paths, potential screening by the cosmic neutrino background, correlations among oscillation parameters, and information from near detectors and complementary experiments, to refine and extend sensitivity and discrimination power.

- Earth potential treatment uses an average along the baseline and does not follow the changing potential during propagation; approximation is valid primarily for mZ′ ≲ 10−14 eV where the interaction range exceeds Earth’s radius. - Screening of long-range potentials by the cosmic neutrino background is not included; potential impact at very small couplings (G′ ≲ 10−29) could reduce sensitivity. - θ13 and θ12 are fixed to current best-fit values; profiling assumes no correlations among sin2θ23, δCP, and Δm2 31 within 3σ ranges. - Only far detectors are modeled; near-detector capabilities are not included in the sensitivity forecasts. - Sun and cosmological matter are treated with simplified source models and particle-number estimates; Moon and Sun as point sources, Earth/Milky Way/cosmological matter as continuous distributions. - Constraints on charged-lepton couplings are acknowledged; viability of sizable neutrino interactions may require specific model-building to evade bounds. - The main-text results assume normal mass ordering; inverted ordering results shown in appendices indicate similar conclusions but with some differences in degeneracy behavior.