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Irreducible Bhabha background in the detection of muonium-antimuonium conversion

Mitrajyoti Ghosh, Kevin Liguori, Takemichi Okui, Kohsaku Tobioka

Abstract

Experiments such as MACS and the proposed MACE study muonium-antimuonium conversion by the energies of the final-state $e^\pm$. The $e^+$ and $e^-$ from an antimuonium decay tend to be non-relativistic and relativistic, respectively, and vice versa for muonium. However, these $e^\pm$ can exchange their energies by hard Bhabha scattering, causing muonium to fake an antimuonium decay signal. We compute the rate for this background and find that, while negligible for MACE, it will become larger than the signal for conversion probabilities less than $10^{-18}$. Measuring the helicity of the $e^-$ will reduce this to $10^{-22}$.

Irreducible Bhabha background in the detection of muonium-antimuonium conversion

Abstract

Experiments such as MACS and the proposed MACE study muonium-antimuonium conversion by the energies of the final-state . The and from an antimuonium decay tend to be non-relativistic and relativistic, respectively, and vice versa for muonium. However, these can exchange their energies by hard Bhabha scattering, causing muonium to fake an antimuonium decay signal. We compute the rate for this background and find that, while negligible for MACE, it will become larger than the signal for conversion probabilities less than . Measuring the helicity of the will reduce this to .

Paper Structure

This paper contains 13 equations, 4 figures.

Figures (4)

  • Figure 1: Diagram for the antimuonium ($\overline{\mathcal{M}}$) decay part of the signal, not including the conversion ($\mathcal{M} \to \overline{\mathcal{M}}$) part. Dashed lines carry muon number, while solid lines electron number. The momenta carried by the outgoing fermion lines are labelled next to the line, and $P$ is the 4-momentum of the $\overline{\mathcal{M}}$. Crucially, $e_\text{f}^-$ and $e_\text{s}^+$ are relativistic and non-relativistic, respectively.
  • Figure 2: Diagrams for the hard photon exchange background. Note that the final state $e^+_\text{s}$ and $e^-_\text{f}$ have the same four-momenta $p_\text{s}$ and $p_\text{f}$, respectively, as those in the signal (Fig. \ref{['fig:signal']}), and hence this final state is kinematically indistinguishable from that of the signal.
  • Figure 3: $N / \mathcal{Z}^2$ as a function of $P_\text{C}$ for different scenarios. The solid line uses the optimal cuts as shown in Fig. \ref{['fig:esfminmax']}, i.e., $N=N_\text{min}$. The dashed line uses the fixed cuts similar to those proposed by MACE Bai:2024skk ($\mathcal{E}_\text{f}^\text{min} = 0.4$ and ${\cal E}_\text{s}^\text{max} = 1.5$). The dotted line uses poorly chosen fixed cuts $\mathcal{E}_\text{f}^\text{min} = 0.1$ and ${\cal E}_\text{s}^\text{max} = 9$ to illustrate that non-optimal choices do lead to a higher $N$, but not significantly higher.
  • Figure 4: The optimal values of $\mathcal{E}_\text{f}^\text{min}$ (solid) and ${\cal E}_\text{s}^\text{max}$ (dashed) that yield $N = N_\text{min}$ for a given $P_\text{C}$.