Understanding gravitationally induced decoherence parameters in neutrino oscillations using a microscopic quantum mechanical model

TL;DR

This work builds a microscopic quantum mechanical model for gravitationally induced decoherence in neutrino oscillations, grounded in linearised gravity and a bath of environmental oscillators. By deriving a TCL master equation with renormalisation, the authors connect the resulting decoherence parameters to those used in phenomenological models, showing exact vacuum correspondence with a subclass exhibiting inverse-energy-squared scaling, and reveal density-dependent decoherence in matter that cannot be captured by constant parameters. The analysis clarifies how the choice of Lindblad operators affects the connection to phenomenology and identifies KamLAND and future neutrino telescopes as viable avenues to constrain the model's coupling η and environmental temperature T. The work also demonstrates the importance of renormalisation to obtain regulator-independent predictions and outlines several path forward, including field-theoretic projections and extensions to wave-packet formalisms and more sophisticated gravitational environments. This provides a concrete framework to interpret potential decoherence signals in neutrino experiments within a microscopically motivated gravitational open quantum-system setting.

Abstract

In this work, a microscopic quantum mechanical model for gravitationally induced decoherence introduced by Blencowe and Xu is investigated in the context of neutrino oscillations. The focus is on the comparison with existing phenomenological models and the physical interpretation of the decoherence parameters in such models. The results show that for neutrino oscillations in vacuum gravitationally induced decoherence can be matched with phenomenological models with decoherence parameters of the form $Γ_{ij}\sim Δm^4_{ij}E^{-2}$. When matter effects are included, the decoherence parameters exhibit a dependence on the varying matter density across the Earth layers. This behavior can be explained by the nature of the coupling between neutrinos and the gravitational wave environment, as suggested by linearised gravity. On a theoretical level, these different models can be characterised by a different choice of Lindblad operators, with the model with decoherence parameters that do not include matter effects being less suitable from the point of view of linearised gravity. Consequently, in the case of neutrino oscillations in matter, the microscopic model does not agree with many existing phenomenological models that assume constant decoherence parameters in matter. Nonetheless, we identify the KamLAND experimental setup as particularly well-suited to establish the first experimental constraints on the model parameters, namely the neutrino coupling to the gravitational wave environment and its temperature, based on a prior analysis using the phenomenological model.

Figures (9)

• Figure 1: Integrands $I_\Lambda(\tau)$ (first row) and $I_\Gamma(\tau)$ (second row) defined in \ref{['eq:DefintLam']} and \ref{['eq:DefintGam']} for the different cutoff functions and with parameter values $\eta = 10^{-8}\,\mathrm{s}$, $T=0.9\,\mathrm{K}$ and $\Omega=1\,\mathrm{Hz}$ (first column), $\Omega=100 \,\mathrm{GHz}$ (second column, first row), and $\Omega=10\,\mathrm{kHz}$ (second column, second row).
• Figure 2: Neutrino oscillation probabilities in matter for a $4\,\mathrm{GeV}$ neutrino as a function of the travelled baseline in Earth. The plots compare standard oscillations without decoherence (Std.) with the model in this work (GQD) and a phenomenological model with $n=-2$ (PQD). The GQD model parameters are set to $\eta=10^{-8}\,\mathrm{s}$ and $T=0.9\,\mathrm{K}$ which implies for the PQD model in vacuum $\gamma_{21} = 1.00694\cdot 10^{-25}, \gamma_{31} = 1.08067\cdot 10^{-22}$ and $\gamma_{32} = 1.0157\cdot 10^{-22}$. The Earth matter effects are accounted for via the PREM model prem: the clear discontinuity for neutrino trajectories passing inside of the Earth core is due to the net change in density between mantle and core. The plots have been created with OscProboscprob.
• Figure 3: Neutrino oscillation probabilities in matter for a baseline of $12000\,\mathrm{km}$, corresponding to $\cos\theta_{Zenith} = -0.94$, which is a trajectory passing through the Earth core. The plots compare standard oscillations without decoherence (Std.) with the model in this work (GQD) and a phenomenological model with $n=-2$ (PQD). For the GQD model $\eta=10^{-8}\,\mathrm{s}$ and $T=0.9\,\mathrm{K}$ are assumed which implies for the PQD model in vacuum $\gamma_{21} = 1.00694\cdot 10^{-25}, \gamma_{31} = 1.08067\cdot 10^{-22}$, and $\gamma_{32} = 1.0157\cdot 10^{-22}$. The Earth matter effects are accounted for via the PREM model prem. The difference between constant decoherence parameters independent of the Earth matter density (PQD) and a parameter depending on the Earth matter density (GQD) is evident. The plots have been made with OscProboscprob.
• Figure 4: Difference of neutrino oscillation probabilities in matter for model in this work (GQD) and a phenomenological model for $n=-2$ (PQD). For the GQD model $\eta=10^{-8}$ s and $T=0.9\,\mathrm{K}$ are assumed which implies for the PQD model in vacuum $\gamma_{21} = 1.00694\cdot 10^{-25}, \gamma_{31} = 1.08067\cdot 10^{-22}$, and $\gamma_{32} = 1.0157\cdot 10^{-22}$. The Earth matter effects are accounted for via the PREM model prem. The difference between constant decoherence parameters independent of the Earth matter density (PQD) and a parameter depending on the Earth matter density (GQD) is evident. The plots have been made with OscProboscprob.
• Figure 5: Upper limits at $90\%$ C.L. for neutrino coupling $\eta$ (s) as a function of the temperature $T$ (K) of the thermal gravitational wave background. These limits have been obtained through the upper bound on Model E investigated in DeRomeri:2023dht. The grey region represents the excluded area.