On Lepton-Number-Violating Searches for Muon to Positron Conversion

Abstract

There is no guarantee that the violation of lepton number, assuming it exists, will primarily manifest itself in neutrinoless double beta decay ($0\nu \beta \beta$). Lepton-number violation and lepton-flavor violation may be related, and much-needed information regarding the physics that violates lepton number can be learned by exploring observables that violate lepton flavors other than electron flavor. One of the most promising observables is ${\mu }^{-}\to e^{+}$ conversion, which can be explored by experiments that are specifically designed to search for ${\mu }^{-}\to e^{-}$ conversion. We survey lepton-number-violating dimension-five, -seven, and -nine effective operators in the standard model and discuss the relationships between Majorana neutrino masses and the rates for $0\nu \beta \beta$ and ${\mu }^{-}\to e^{+}$ conversion. While $0\nu \beta \beta$ has the greatest sensitivity to new ultraviolet energy scales, its rate might be suppressed by the new physics relationship to lepton flavor, and ${\mu }^{-}\to e^{+}$ conversion offers a complementary probe of lepton-number-violating physics.

13 pages, 7 figures; updated to include modified results for two operators and additional references

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• Heavy neutral leptons and high-intensity observables
• Kiloton-scale xenon detectors for neutrinoless double beta decay and other new physics searches
• Probing nonstandard lepton number violating interactions in neutrino oscillations
• Accessible Lepton-Number-Violating Models and Negligible Neutrino Masses
• Future Experimental Improvement for the Search of LNV Process in $e\mu$ Sector
• Shining Light on the Mass Scale and Nature of Neutrinos with $e\gamma \to e\nu \overline{\nu }$
• Probing charged lepton number violation via ${\ell }^{\pm }{\ell }^{\prime \pm }{W}^{\mp }{W}^{\mp }$
• Electroweak baryogenesis in the three-loop neutrino mass model with dark matter
• RGE solver for the complete dim-7 SMEFT interactions and its application to $0\nu \beta \beta$ decay
• The high energy spectrum of internal positrons from radiative muon capture on nuclei
• QCD Running in Lepton Number Violating Meson and Tau Decays
• Muon to positron conversion