Probing $\mu e\gamma \gamma$ contact interactions with $\mu \to e$ conversion

Abstract

Contact interactions of a muon, an electron and two photons can contribute to the decay $\mu \to e\gamma \gamma$, but also to the conversion of a muon into an electron in the electric field of a nucleus. We calculate the $\mu \to e$ conversion rate, and show that for the coefficients of operators involving the combination $FF\propto |\vec{E}{|}^2$ (as opposed to $F\tilde{F}\propto \vec{E}\cdot \vec{B}$), the current bound on $\mu \to e$ conversion is more sensitive than the bound on $\mu \to e\gamma \gamma$.

arXiv comment14 pages, version accepted for publication

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• Completeness and Complementarity for $\mu \to e\gamma$, $\mu \to 3e$ and $\mu \to e$ conversion
• What is Leading Order for LFV in SMEFT?
• Introduction to Charged Lepton Flavour Violation
• Search for muon-to-electron conversion with the COMET experiment
• Reach and complementarity of $\mu \to e$ searches
• Upper limits on branching ratios of the lepton-flavor-violating decays $\tau \to \ell \gamma \gamma$ and $\tau \to \ell X$
• Indirect upper limits on ${\ell }_i\to {\ell }_j\gamma \gamma$ from ${\ell }_i\to {\ell }_j\gamma$
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• SMEFT analysis of charged lepton flavor violating $B$-meson decays
• General Signals for Charged Lepton Flavor Violating Decays
• Exploring hadronic de-excitation via Lepton Flavor Violation
• Two-to-two processes at an electron-muon collider
• Constraining lepton flavor violating SMEFT $2q2\ell$ operators from low-energy cLFV processes