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Enhanced Rare Pion Decays from a Model of MeV Dark Matter

Yonatan Kahn, Michael Schmitt, Tim Tait

TL;DR

The study addresses a potential discrepancy in the rare decay π0 → e+e− by introducing a light vector boson U from a Boehm–Fayet light dark matter framework. It computes the U-mediated contribution to the decay amplitude, derives constraints on axial couplings (notably (g_A^u − g_A^d) g_A^e/m_U^2 ≈ 4.0×10^{-10} MeV^{-2}), and finds that for m_U ≈ 10 MeV the required couplings g_A are around 2×10^{-4}. The results are broadly consistent with other bounds and relic-density considerations, suggesting a viable but tightly constrained parameter space for the U-boson; the paper also outlines experimental paths to sharpen or challenge this interpretation, including improved Dalitz-decay measurements and η decays as cross-checks.

Abstract

A model has been proposed in which neutral scalar particles chi, of mass 1-10 MeV, annihilate through the exchange of a light vector boson U, of mass 10-100 MeV, to produce the 511 keV line observed emanating from the center of the galaxy. The chi interacts weakly with normal matter and is a viable dark matter candidate. If the U-boson couples to quarks as well as to electrons, it could enhance the branching ratio for the rare decay pi0 -> e+e-. A recent measurement by the KTeV Collaboration lies three standard deviations above a prediction by Dorokhov and Ivanov, and we relate this excess to the couplings of the U-boson. The values are consistent with other constraints and considerations. We make some comments on possible improvements in the data.

Enhanced Rare Pion Decays from a Model of MeV Dark Matter

TL;DR

The study addresses a potential discrepancy in the rare decay π0 → e+e− by introducing a light vector boson U from a Boehm–Fayet light dark matter framework. It computes the U-mediated contribution to the decay amplitude, derives constraints on axial couplings (notably (g_A^u − g_A^d) g_A^e/m_U^2 ≈ 4.0×10^{-10} MeV^{-2}), and finds that for m_U ≈ 10 MeV the required couplings g_A are around 2×10^{-4}. The results are broadly consistent with other bounds and relic-density considerations, suggesting a viable but tightly constrained parameter space for the U-boson; the paper also outlines experimental paths to sharpen or challenge this interpretation, including improved Dalitz-decay measurements and η decays as cross-checks.

Abstract

A model has been proposed in which neutral scalar particles chi, of mass 1-10 MeV, annihilate through the exchange of a light vector boson U, of mass 10-100 MeV, to produce the 511 keV line observed emanating from the center of the galaxy. The chi interacts weakly with normal matter and is a viable dark matter candidate. If the U-boson couples to quarks as well as to electrons, it could enhance the branching ratio for the rare decay pi0 -> e+e-. A recent measurement by the KTeV Collaboration lies three standard deviations above a prediction by Dorokhov and Ivanov, and we relate this excess to the couplings of the U-boson. The values are consistent with other constraints and considerations. We make some comments on possible improvements in the data.

Paper Structure

This paper contains 6 sections, 12 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Pion decay
  3. Bounds on U-quark couplings
  4. Possible Improvements
  5. Summary
  6. Matrix element calculation

Figures (2)

  • Figure 1: Feynman diagram for $\pi^0 \to e^+e^-$.
  • Figure 2: Constraints on the couplings as a function of $m_U$. The thick (red) line labeled "$\pi^0$" shows our result Eq. (\ref{['E:constraint']}). The dotted line comes from constraints on $(g-2)_e$ and the dashed line from $\nu$-$e$ scattering FayetLatest. The solid (blue) lines labeled with "$n$ MeV" are based on relic density calculations FayetLatest.