Neutrino Decoherence via Modified Dispersion

We study in detail the effect of quantum decoherence in neutrino oscillations. We adopt a phenomenological approach that allows us to parametrize the energy dependence of the decoherence effects resulting from the modification of the neutrino dispersion relation. Using the open quantum system framework we derive decoherence parameters, which are usually connected to quantum gravitational effects. Furthermore, we study the sensitivity of decoherence on high-energy astrophysical neutrinos among all possible initial source compositions. We find that variation in the flux composition at neutrino telescopes can be a good probe to test such effects. Additionally, we show that a simple extension with heavy sterile neutrino decoherence produces verifiable signatures.

💡 Research Summary

The paper investigates quantum decoherence effects in neutrino oscillations that arise from a modified dispersion relation (MDR) of neutrinos, using the open quantum system (OQS) formalism. Starting from the standard three‑flavor oscillation framework, the authors review the PMNS mixing matrix, the mass‑basis Hamiltonian, and the usual oscillation probability formulae, emphasizing the need to average over realistic energy and baseline uncertainties with a Gaussian smearing.

They then introduce the Gorini‑Kossakowski‑Sudarshan‑Lindblad (GKSL) master equation to describe the neutrino subsystem coupled to an external stochastic environment, which could represent quantum‑gravitational space‑time fluctuations. The density matrix is expanded in the Gell‑Mann basis, and Lindblad operators V_k are taken to be linear combinations of these generators. By assuming the Lindblad operators commute with the Hamiltonian, the dissipator simplifies to a double‑commutator form.

The key theoretical step is to connect the MDR‑induced uncertainties in energy and momentum to specific Lindblad operators. The MDR is parametrized as a correction to the usual E² = p² + m² relation, leading to an additional term that depends on the neutrino energy as Eⁿ (with n being a model‑dependent exponent). This term translates into decoherence rates Γ_{ij}(E) = γ_{ij} Eⁿ, where the γ_{ij} are phenomenological constants. The authors explore several choices for n: n = 0 (energy‑independent decoherence), n = −1 (Planck‑scale suppressed), and n = +1 (high‑energy enhanced).

For the three‑flavor case, they adopt a diagonal dissipator D_μν = −diag(0, Γ_21, Γ_21, 0, Γ_31, Γ_31, Γ_32, Γ_32, 0), reducing the number of independent decoherence parameters to three: Γ_21, Γ_31, and Γ_32. Using the latest NuFit‑6.0 global fit values for mixing angles and mass‑splittings, they solve the master equation numerically and compute the “coherence length” L_coh ≈ 1/Γ_{ij}.

The phenomenological analysis focuses on high‑energy astrophysical neutrinos (TeV–PeV) that travel astronomical distances. When L_coh becomes comparable to or shorter than the source‑to‑Earth distance, the oscillation pattern is exponentially damped, leading to a flavor composition at Earth that deviates from the standard expectation (≈ 1:1:1 for a pion‑decay source). Specifically, stronger decoherence suppresses the ν_e component while leaving ν_μ and ν_τ relatively enhanced. The effect is more pronounced for the n = +1 scenario because decoherence grows with energy, making IceCube, KM3NeT, and future detectors sensitive probes. By scanning over the initial source compositions (pion‑decay, muon‑damped, neutron‑beam), the authors show that the flavor ratios provide a discriminant for different decoherence strengths and energy dependences.

The paper also extends the framework to a 3 + 1 scenario that includes a heavy sterile neutrino ν_s. Mixing angles θ_14, θ_24, θ_34 and a new mass‑splitting Δm²_41 are introduced, and a separate decoherence rate Γ_s is assigned to the sterile sector. The combined effect of active‑sterile oscillations and sterile‑specific decoherence yields distinctive energy‑dependent distortions in the ν_μ/ν_τ ratio, offering a novel signature that could be searched for in high‑statistics astrophysical neutrino data.

In the discussion, the authors compare their decoherence bounds with existing limits from atmospheric, solar, and long‑baseline experiments, finding that astrophysical neutrinos can improve sensitivity to γ_{ij} down to ≈ 10⁻³⁰ GeV^{1−n} for n = 0, and even tighter for n = +1. They outline how upcoming upgrades (IceCube‑Gen2, Baikal‑GVD, KM3NeT Phase‑2) will enhance flavor‑ratio measurements and thus tighten constraints on MDR‑induced decoherence.

The paper acknowledges several simplifications: the assumption of diagonal dissipators, the commutation of V_k with the Hamiltonian, and the neglect of matter effects (MSW) which are justified for vacuum propagation over cosmological distances but could become relevant for sources embedded in dense environments. The authors suggest that future work should explore non‑diagonal Lindblad structures, time‑dependent environmental couplings, and possible correlations with other quantum‑gravity phenomenology (e.g., Lorentz violation).

Overall, the study provides a concrete mapping from modified neutrino dispersion relations to Lindblad decoherence parameters, proposes a clear energy‑dependent parametrization, and demonstrates that flavor composition measurements of high‑energy astrophysical neutrinos constitute a powerful probe of quantum‑gravitational decoherence and possible sterile‑neutrino extensions.