[Paper Review] Probing the explanation of the muon (g-2) anomaly and thermal light dark matter with the semi-visible dark photon channel

NA64 Collaboration, P. Odagiu+7 more|arXiv (Cornell University)|Jan 1, 2021

Dark Matter and Cosmic Phenomena40 references26 citations

TL;DR

This paper proposes a semi-visible dark photon (A′) decay channel, A′ → χ₁χ₂ followed by χ₂ → χ₁e⁺e⁻, to simultaneously explain the muon (g-2) anomaly and thermal dark matter relic density. Using a full re-analysis of NA64 data, it excludes 90% CL parameter space for mA′ < 0.39 GeV and ε between 3×10⁻⁵ and 2×10⁻², covering a significant region of the (g-2) anomaly and dark matter relic density band.

ABSTRACT

We report the results of a search for a new vector boson ($A'$) decaying into two dark matter particles $\chi_1 \chi_2$ of different mass. The heavier $\chi_2$ particle subsequently decays to $\chi_1$ and $A' o e^- e^+$. For a sufficiently large mass splitting, this model can explain in terms of new physics the recently confirmed discrepancy observed in the muon anomalous magnetic moment at Fermilab. Remarkably, it also predicts the observed yield of thermal dark matter relic abundance. A detailed Monte-Carlo simulation was used to determine the signal yield and detection efficiency for this channel in the NA64 setup. The results were obtained re-analyzing the previous NA64 searches for an invisible decay $A' o \chi \overline{\chi}$ and axion-like or pseudo-scalar particles $a o \gamma \gamma$. With this method, we exclude a significant portion of the parameter space justifying the muon g-2 anomaly and being compatible with the observed dark matter relic density for $A'$ masses from 2$m_e$ up to 390 MeV and mixing parameter $\epsilon$ between $3 imes10^{-5}$ and $2 imes10^{-2}$.

Motivation & Objective

• To explore a semi-visible decay channel of a dark photon A′ that can simultaneously explain the muon (g-2) anomaly and the observed thermal dark matter relic density.
• To improve experimental constraints on the parameter space of a U(1)D dark sector model with a pseudo-Dirac dark matter state and kinetic mixing with the SM photon.
• To re-analyze NA64 data collected in 'invisible-mode' to search for signatures of A′ → χ₁χ₂(χ₂ → χ₁e⁺e⁻), combining features of both visible and invisible decay modes.
• To assess the sensitivity of the NA64 experiment to this model and project future improvements with optimized detector configurations.
• To identify and exclude previously unexplored regions of parameter space compatible with both the (g-2) anomaly and the observed dark matter abundance.

Proposed method

• Adopt a U(1)D gauge symmetry with spontaneous breaking via a dark Higgs field hD, leading to a massive dark photon A′ with kinetic mixing ε to the SM photon.
• Implement a pseudo-Dirac fermion field Ψ charged under U(1)D, which after symmetry breaking yields two dark matter eigenstates: a light stable χ₁ and a heavier metastable χ₂ with mass difference ∆ = mχ₂ − mχ₁.
• Use the effective Lagrangian (Eq. 1) to describe the interaction, with off-diagonal coupling gD between χ₂ and A′, and εe coupling between A′ and SM electrons.
• Calculate the 3-body decay width Γ(χ₂ → χ₁e⁺e⁻) using MadGraph5aMC@NLO’s MadWidth module, obtaining a corrected formula (Eq. 2) with a K ≈ 0.640 ± 0.004 correction factor.
• Perform a full Monte Carlo simulation of the signal process in the NA64 detector setup, including detector response, reconstruction efficiencies, and all systematic uncertainties.
• Re-analyze existing NA64 data from three runs in 'invisible-mode' to extract 90% confidence level exclusion limits in the (mA′, ε), (mA′, αD), and (mχ₁, ∆/mχ₁) planes.

Experimental results

Research questions

• RQ1 Can a semi-visible decay channel A′ → χ₁χ₂(χ₂ → χ₁e⁺e⁻) explain both the muon (g-2) anomaly and the observed thermal dark matter relic density?
• RQ2 What are the experimental limits on the parameter space of this model, particularly for A′ masses below 0.39 GeV and mixing parameters ε in the range 3×10⁻⁵ to 2×10⁻²?
• RQ3 How does the decay width scaling ∝ ∆⁵ affect the detectability of short-lived χ₂ states, and what are the implications for future sensitivity?
• RQ4 To what extent can the NA64 experiment exclude previously unexplored regions of the (g-2) anomaly and dark matter relic density parameter space?
• RQ5 What improvements in sensitivity can be achieved with a compact HCAL1 and increased EOT (electrons on target) for detecting short-lived χ₂ decays?

Key findings

• The NA64 experiment excludes 90% confidence level (CL) a significant portion of the parameter space that explains both the muon (g-2) anomaly and the thermal dark matter relic density, for A′ masses up to 0.39 GeV.
• The analysis improves upon previous bounds by excluding regions of parameter space previously uncovered, particularly for mA′ ≲ 0.39 GeV and ε ∈ [3×10⁻⁵, 2×10⁻²], assuming αD = 0.1 and ∆/mχ₁ = 0.4.
• For mA′ ≳ 0.3 GeV, the model is excluded within the central band of the (g-2) anomaly, indicating that only models with mA′ > 0.4 GeV or large mass splitting ∆ can still be viable.
• The signal yield is exponentially suppressed for ∆/mχ₁ ≳ 0.5 due to the ∆⁵ scaling in the decay width, making detection increasingly unlikely for large mass splittings.
• With 5×10¹² EOT and a compact HCAL1 of 50 cm, the experiment would be limited only by very large ∆/mχ₁ values, suggesting full coverage of the phenomenologically interesting region is achievable in future runs.
• The study demonstrates that the NA64 setup is sensitive to semi-visible decays and that a compact detector configuration could fully probe the viable parameter space for both (g-2) and dark matter relic density.