3rd International Conference on Charged Lepton Flavor Violation Lepton-flavor-violating decays into axion-like particles Lorenzo Calibbi (Nankai University) Mainly based on work in progress with D. Redigolo, R. Ziegler, and J. Zupan Kyushu University, Fukuoka June 18 th 2019
Motivation Belle/BaBar Mu3e I Mu3e II Definitely worth to keep searching, but… Lorenzo Calibbi (Nankai) LFV into ALPs
Motivation Belle/BaBar Mu3e I Mu3e II What if we haven’t looked (enough) in the right place? Lorenzo Calibbi (Nankai) LFV into ALPs
Introduction Assume there is a light , invisible , new particle “ a” with FV couplings to leptons Light : Invisible : • Neutral m a < m μ , m τ • Feebly coupled (long-lived) CLFV modes would then be μ → e a , τ → μ a , μ → e γ a , etc . Interesting interplay with cosmo/astro: • DM candidate? (if long-lived enough) • Bounds from star cooling/supernovae (if light and feeble enough) Lorenzo Calibbi (Nankai) LFV into ALPs
Lepton-flavor-violating ALPs Why should a be light and feebly-coupled? That’s natural, if it is the (pseudo) Nambu-Goldstone boson (PNGB) of a broken global U(1), aka an axion-like particle (ALP) Examples: Global symmetry: PNGB: • Lepton Number Majoron • Peccei-Quinn Axion Wilczek ‘82 • Flavor symmetry Familon Pilaftsis ‘93 … Feng et al. ‘97 Equivalent possibility: light Z ′ of a local U(1), e.g. L i -L j (with g ≪ 1) Heeck ‘16 Lorenzo Calibbi (Nankai) LFV into ALPs
<latexit sha1_base64="+IolpgmdWYoOPH+Lgq5kmoxRFSI=">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</latexit> Lepton-flavor-violating ALPs Where does lepton flavor violation come from? General couplings to leptons: L a `` = @ µ a C V ij ` i � µ ` j + C A � � ij ` i � µ � 5 ` j 2 f a • If lepton U(1) charges are flavor non-universal naturally flavor-violating couplings • Alternatively, loop-induced flavor-violating couplings Explicit examples at the end of the talk… Lorenzo Calibbi (Nankai) LFV into ALPs
<latexit sha1_base64="+IolpgmdWYoOPH+Lgq5kmoxRFSI=">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</latexit> Lepton-flavor-violating ALPs Where does lepton flavor violation come from? General couplings to leptons: Shift symmetry (PNGB!) → m a from (small) explicit U(1) breaking L a `` = @ µ a C V ij ` i � µ ` j + C A � � ij ` i � µ � 5 ` j 2 f a U(1)-breaking scale → coupling suppression • If lepton U(1) charges are flavor non-universal naturally flavor-violating couplings • Alternatively, loop-induced flavor-violating couplings Explicit examples at the end of the talk… Lorenzo Calibbi (Nankai) LFV into ALPs
<latexit sha1_base64="+IolpgmdWYoOPH+Lgq5kmoxRFSI=">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</latexit> <latexit sha1_base64="UgJGgFEiKJwhr5AYNxEv5pPyXI=">ACKXicbVDLSgMxFM3UV62vqks3wSIQpmpgi6rBXFZwT6g0w6ZNPGZh5NMoWSzu+48VfcKCjq1h8xfSDaeiBwOdcbu5xI0aFNM0PI7W0vLK6l7PbGxube9kd/eqIow5JhUcspDXSQIowGpSCoZqUecIN9lpOb2SmO/NiBc0DC4k8OINH3UCahHMZJacrLFa0fR+8Qm/ZgObI8jrArQc1CibNHnUo1KLVNJplRqwBP4Fi4/BGSxMnmzLw5AVwk1ozkwAxlJ/tit0Mc+ySQmCEhGpYZyaZCXFLMSJKxY0EihHuoQxqaBsgnoqkmlybwSCt6IVcv0DCifp7QiFfiKHv6qSPZFfMe2PxP68RS+iqWgQxZIEeLrIixmUIRzXBtuUEyzZUBOEOdV/hbiLdF1Sl5vRJVjzJy+SaiFvneYLt2e54tWsjQ4AIfgGFjgHBTBDSiDCsDgATyBV/BmPBrPxrvxOY2mjNnMPvgD4+sb5WoOw=</latexit> <latexit sha1_base64="DnXvEscDeIybi8iGp/syNEWX9+Y=">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</latexit> LFV decays into ALPs: model-independent approach L a `` = @ µ a C V ij ` i � µ ` j + C A � � ij ` i � µ � 5 ` j 2 f a This generic Lagrangian induces 2-body LFV decays such as: ! 2 m 3 1 − m 2 1 2 f a ` i a Γ ( ` i → ` j a ) = F ij ≡ q F 2 m 2 16 ⇡ ij | 2 + | C A | C V ij | 2 ij ` i Feng et al. ‘97 Goal: constrain the effective LFV scales F ij using experimental data • Which experiments? • What are the future prospects? Lorenzo Calibbi (Nankai) LFV into ALPs
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