[Paper Review] Search for Darkonium in $e^+e^-$ Collisions

The BABAR Collaboration|arXiv (Cornell University)|Jun 16, 2021

Dark Matter and Cosmic Phenomena27 references4 citations

TL;DR

This paper presents the first search for a darkonium state—bound states of dark matter particles—produced in $e^+e^-$ collisions at the BESIII experiment. Using optimized event selection and machine learning classifiers for different dark photon lifetimes, the study sets 90% confidence level upper limits on the kinetic mixing parameter $\varepsilon$ down to $5 \times 10^{-5}$ across a broad mass range, improving on prior constraints for $m_{A'} < 1\,\text{GeV}$ and large dark sector coupling constants.

ABSTRACT

Collider searches for dark sectors, new particles interacting only feebly with ordinary matter, have largely focused on identifying signatures of new mediators, leaving much of dark sector structures unexplored. In particular, the existence of dark matter bound states (darkonia) remains to be investigated. This possibility could arise in a simple model in which a dark photon ($A'$) is light enough to generate an attractive force between dark fermions. We report herein a search for a $J^{PC}= 1^{--}$ darkonium state, the $Υ_D$, produced in the reaction $e^+e^- ightarrow γΥ_D, Υ_D ightarrow A' A' A'$, where the dark photons subsequently decay into pairs of leptons or pions, using $514 ext{ fb}^{-1}$ of data collected with the BABAR detector. No significant signal is observed, and we set bounds on the $γ- A'$ kinetic mixing as a function of the dark sector coupling constant for $0.001 &lt; m_{A'} &lt; 3.16 ext{ GeV}$ and $0.05 &lt; m_{Υ_D} &lt; 9.5 ext{ GeV}$.

Motivation & Objective

• To search for a darkonium state composed of bound states of dark matter particles decaying into three dark photons in $e^+e^-$ collisions.
• To improve constraints on the kinetic mixing parameter $\varepsilon$ between the Standard Model photon and the dark photon $A'$ in the dark sector.
• To explore the parameter space of dark photon masses $m_{A'}$ between 0.001 and 3.16 GeV and darkonium masses $m_{\Upsilon_D}$ between 0.05 and 9.5 GeV.
• To account for the dependence of signal sensitivity on the dark photon lifetime $c\tau_{A'}$ by optimizing selection criteria for $c\tau_{A'} = 0.1$, 1, and 10 mm.
• To derive model-independent limits on $\varepsilon$ for varying dark sector coupling constants $\alpha_D$ = 0.1, 0.3, 0.5, 0.7, 0.9, and 1.1.

Proposed method

• Event selection is optimized separately for three dark photon lifetimes: $c\tau_{A'} = 0.1$, 1, and 10 mm, based on reconstructed decay topology and vertex displacement.
• A machine learning classifier is trained for each $c\tau_{A'}$ value to distinguish signal-like events from background, improving sensitivity across the lifetime range.
• Signal extraction is performed independently on each $c\tau_{A'}$-optimized data sample, with background contributions estimated using control regions.
• Upper limits on the production cross section are derived at 90% confidence level (CL) for each $c\tau_{A'}$ and $m_{A'}$-mass bin.
• An iterative procedure is used to account for the dependence of the dark photon lifetime on the kinetic mixing $\varepsilon$, updating the limit at each step until convergence.
• Limits on $\varepsilon^2$ are derived for $\alpha_D = 0.5$, with additional results provided for other $\alpha_D$ values in the Supplemental Material.

Experimental results

Research questions

• RQ1 Can a darkonium state—bound states of dark matter particles—be produced and detected in $e^+e^-$ collisions via decay into three dark photons?
• RQ2 What are the sensitivity limits on the kinetic mixing parameter $\varepsilon$ between the Standard Model photon and the dark photon $A'$ across a broad range of $m_{A'}$ and $m_{\Upsilon_D}$?
• RQ3 How does the sensitivity of the search vary with the dark photon lifetime $c\tau_{A'}$, and can this be optimized using machine learning?
• RQ4 How do the derived limits compare to existing constraints, especially for $m_{A'} < 1\,\text{GeV}$ and large $\alpha_D$?
• RQ5 What is the impact of the dark sector coupling constant $\alpha_D$ on the sensitivity and the resulting upper limits on $\varepsilon$?

Key findings

• No significant signal is observed in any of the $c\tau_{A'}$-optimized data samples, with 56, 33, and 31 events selected for $c\tau_{A'} = 0.1$, 1, and 10 mm, respectively.
• The study sets 90% CL upper limits on the kinetic mixing parameter $\varepsilon$ down to $5 \times 10^{-5}$ across a large fraction of the parameter space for $m_{A'} < 1\,\text{GeV}$.
• For $\alpha_D = 0.5$, the limits on $\varepsilon^2$ are derived as a function of $m_{\Upsilon_D}$ and $m_{A'}$, with the strongest constraints in the low $m_{A'}$ and intermediate $m_{\Upsilon_D}$ region.
• The results improve upon existing constraints for $m_{A'} < 1\,\text{GeV}$, particularly for large values of the dark sector coupling constant $\alpha_D$.
• The iterative procedure to account for lifetime-dependent effects in the limit calculation ensures robustness and consistency across different $\varepsilon$ and $c\tau_{A'}$ values.
• Constraints for $\alpha_D = 0.1, 0.3, 0.7, 0.9, 1.1$ are provided in the Supplemental Material, showing a systematic improvement over previous limits in the explored region.