[Paper Review] Neutrino masses from the GSI anomaly

A. N. Ivanov, E. Kryshen+2 more|ArXiv.org|Apr 8, 2008

Neutrino Physics Research1 references3 citations

TL;DR

This paper proposes that corrections to neutrino masses from virtual charged lepton–W⁺ boson pairs in the strong Coulomb field of a heavy ion explain the 2.9-fold discrepancy between the neutrino mass-squared difference extracted from GSI's electron-capture decay modulation (2.18×10⁻⁴ eV²) and the KamLAND value (7.59×10⁻⁵ eV²). The calculated mass corrections reconcile the GSI result with global neutrino data, yielding neutrino masses around 0.11–0.12 eV, consistent with cosmological constraints.

ABSTRACT

We investigate the influence of the strong Coulomb field of a heavy nucleus on massive neutrinos, produced in the K-shell electron capture (EC) decays of the H-like 140Pr58+ and 142Pm60+ ions. The corrections to the neutrino masses due to virtually produced charged lepton W-boson pairs in the strong Coulomb field of a nucleus with charge Ze are calculated and discussed with respect to their influence on the period of the time-modulation of the number of daughter ions, observed recently in the EC-decays of the H-like 140Pr58+ and 142Pm60+ ions at GSI in Darmstadt. These corrections explain the 2.9 times higher difference of the squared neutrino masses obtained from the time-modulation of the EC-decays with respect to the value deduced from the antineutrino-oscillation experiments of KamLAND.

Motivation & Objective

• To resolve the discrepancy between the neutrino mass-squared difference (Δm²₂₁) extracted from GSI's time-modulated electron-capture decays of H-like ¹⁴⁰Pr⁵⁸⁺ and ¹⁴²Pm⁶⁰⁺ ions and the value from KamLAND solar neutrino experiments.
• To investigate whether virtual W⁺-boson and charged lepton (e⁻, μ⁻, τ⁻) pair production in the strong Coulomb field of the daughter ion induces measurable corrections to neutrino masses.
• To reconcile the GSI-modulated decay rate period (T_EC ≈ 7 s) with the standard model value of Δm²₂₁ by including these field-induced mass corrections.
• To estimate absolute neutrino masses consistent with cosmological upper bounds on the sum of neutrino masses.

Proposed method

• The authors calculate corrections δm_j(r) to the mass of each neutrino mass eigenstate ν_j due to virtual charged lepton–W⁺ pair production in the Coulomb field of a nucleus with charge Ze, using the weak interaction Lagrangian with Fermi coupling constant G_F.
• They employ the energy-dependent Green's function for charged leptons in a strong Coulomb field, derived from relativistic quantum mechanics, to compute the matrix element M_ℓ(r) responsible for the mass shift.
• The total mass correction δm_j(r) is obtained by summing over all charged lepton flavors ℓ (e⁻, μ⁻, τ⁻), weighted by the unitary neutrino mixing matrix elements U_jℓ and U*ℓj.
• The corrected mass-squared difference (m₂ + δm₂)² − (m₁ + δm₁)² is used to recompute the decay rate modulation period T_EC, matching the observed 7.06 s.
• The method incorporates mixing angles θ₁₂ = 34° and θ₂₃ = 45°, and neglects second-order terms (δm_j)² for analytical tractability.
• The heaviest neutrino mass m₃ is estimated using the known Δm²₃₂ = 2.4×10⁻³ eV² and the corrected m₁, m₂ values.

Experimental results

Research questions

• RQ1 Can the observed 2.9× higher Δm²₂₁ in GSI's electron-capture decay experiments be explained by radiative corrections to neutrino masses in a strong Coulomb field?
• RQ2 What is the magnitude and flavor dependence of the neutrino mass corrections induced by virtual ℓ⁻W⁺ pair production in the Coulomb field of a heavy ion?
• RQ3 Does the inclusion of these corrections reconcile the GSI-extracted Δm²₂₁ with the globally fitted KamLAND value of 7.59×10⁻⁵ eV²?
• RQ4 What are the absolute neutrino masses consistent with the corrected Δm²₂₁ and cosmological constraints?
• RQ5 How significant are Z⁰-boson exchange contributions compared to W⁺-boson exchange in inducing these mass shifts?

Key findings

• The correction to the electron-neutrino mass is δm₁(R) = −14.74×10⁻⁴ eV, and to the muon-neutrino mass is δm₂(R) = −8.22×10⁻⁴ eV, due to virtual e⁻, μ⁻, τ⁻ pairs in the Coulomb field.
• The corrected mass-squared difference (Δm²₂₁)_GSI is reconciled with the KamLAND value (Δm²₂₁)_KL = 7.59×10⁻⁵ eV² through these field-induced corrections.
• The absolute neutrino masses are calculated as m₁ = 0.11 + 4.26×10⁻⁴ eV, m₂ = 0.11 + 0.82×10⁻⁴ eV, and m₃ = 0.12 + 8.05×10⁻⁴ eV.
• The sum of neutrino masses is ∑m_j = 0.34 eV, which is consistent with the cosmological upper limit ∑m_j < 1 eV.
• The correction from Z⁰-boson exchange is negligible compared to experimental uncertainties in mixing angles, justifying the omission of Z⁰ contributions.
• The model successfully explains the 7.06 s modulation period observed in GSI's EC decays using corrected neutrino masses, resolving the long-standing discrepancy.