[Paper Review] On the conversion of mass eigenstates

Mikhail V. Medvedev|arXiv (Cornell University)|Apr 20, 2010

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper demonstrates that stable, massive flavor-mixed particles can undergo incoherent conversion between heavy and light mass eigenstates via elastic scattering, even in non-relativistic regimes where standard flavor oscillations fail. The key result is that such conversions can lead to gradual 'evaporation' of particles from gravitational potentials—offering a novel mechanism for cosmic neutrino background distortions and cold dark matter halo evaporation.

ABSTRACT

In this paper we consider a stable particle with flavor mixing. We demonstrate that incoherent conversion of heavy mass eigenstates into light ones and vice versa can occur, as a result of elastic scattering. This effect is nontrivial for non-relativistic particles, for which the standard flavor oscillation ceases rapidly due to incoherence. We also prove that if a heavy state is bound in a gravitational potential and a light state is unbound, the mass-state conversion can lead to gradual "evaporation" of the mixed particle from the potential. A number of implications, ranging from the cosmic neutrino background distortions to scenarios of cold dark matter evaporation from halos, are addressed.

Motivation & Objective

• To investigate whether stable, non-relativistic particles with flavor mixing can undergo incoherent conversion between mass eigenstates.
• To explore the physical mechanism enabling such conversions through elastic scattering in spatially separated wave packets.
• To examine astrophysical and cosmological implications, including distortions in the cosmic neutrino background and evaporation of cold dark matter from galactic halos.
• To assess the viability of this mechanism in scenarios involving axions, WIMPs, and weakly interacting massive particles with mass degeneracy.
• To provide a theoretical framework for mass-state conversion that operates independently of flavor oscillations, relying on wave packet dynamics and scattering.

Proposed method

• Uses a two-flavor system with mass eigenstates |m_h> and |m_l> connected by a unitary mixing matrix U.
• Applies wave packet formalism where mass states propagate with different velocities and separate spatially, breaking coherence.
• Models elastic scattering via a localized potential V with off-diagonal terms V_lh = (V_α - V_β)cosθsinθ, enabling transitions between mass states.
• Introduces operators ÂV and ÂM to describe scattering and membrane-induced state separation, respectively, in a formal operator framework.
• Analyzes a one-dimensional box model with semi-transparent membranes that reflect heavy states but transmit light states, simulating particle evaporation.
• Estimates scattering rates and conversion probabilities using cross-sections and interaction parameters, including coherent scattering effects and velocity-dependent cross-sections.

Experimental results

Research questions

• RQ1 Can stable massive particles with flavor mixing undergo incoherent conversion between heavy and light mass eigenstates via elastic scattering?
• RQ2 What are the conditions under which such conversions lead to observable effects like particle evaporation from gravitational potentials?
• RQ3 How does this mechanism differ from standard flavor oscillations, particularly in non-relativistic regimes?
• RQ4 What are the cosmological implications of this conversion process for the cosmic neutrino background and dark matter halos?
• RQ5 Can this mechanism explain or affect phenomena such as the missing satellite problem in cold dark matter models?

Key findings

• Incoherent conversion between mass eigenstates via elastic scattering is possible even for stable, non-relativistic particles, where standard flavor oscillations cease due to wave packet separation.
• In a box with membranes that reflect heavy states but transmit light states, repeated scattering and reflection cycles lead to gradual evaporation of the particle as a wave-packet train of light states.
• For cosmological neutrinos, the interaction cross-section is too small (σ_ν ~ 10^{-60} cm²) to produce observable effects over the Hubble time, though the effect may accumulate asymptotically.
• In axion-photon mixing scenarios, conversion probability per passage can reach order unity in galactic halos (B ~ 1–3 μG, L ~ 30–100 kpc), enabling significant halo evaporation on Hubble timescales.
• For WIMPs with mass degeneracy (Δm ~ MeV, m ~ TeV), conversion can produce light-state velocities ~300 km/s—comparable to escape velocities in dwarf galaxies, potentially explaining the missing satellite problem.
• The mechanism requires strong mass degeneracy and high self-interaction cross-sections, which may be accommodated by velocity-dependent or Sommerfeld-enhanced models, though such models face theoretical constraints.