Discovering intermediate mass sterile neutrinos through ${\tau }^{-}\to {\pi }^{-}{\mu }^{-}{e}^{+}\nu$ (or $\bar{\nu }$) decay

Abstract

Distinguishing the Dirac and Majorana nature of neutrinos remains one of the most important tasks in neutrino physics. By assuming that the ${\tau }^{-}\to {\pi }^{-}{\mu }^{-}{e}^{+}\nu$ (or $\bar{\nu }$) decay is resonantly enhanced by the exchange of an intermediate mass sterile neutrino $N$, we show that the energy spectrum of emitted pions and muons can be used to easily distinguish between the Dirac and Majorana nature of $N$. This method takes advantage of the fact that the flavor of light neutrinos is not identified in the tau decay under consideration. We find that it is particularly advantageous, because of no competing background events, to search for $N$ in the mass range $m_e+m_{\mu }⩽m_N⩽m_{\mu }+m_{\pi }$, where $m_X$ denotes the mass of particle $X\in \{e,\mu ,\pi ,N\}$.

arXiv comment6 pages, 5 figures, accepted for publication in Physical Review D

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• Four-body decays of $B$ meson with lepton number violation
• Search for light sterile neutrinos from $W^{\pm }$ decays at the LHC
• Discovering heavy neutrino oscillations in rare Bc meson decays at HL-LHCb
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• Sterile neutrinos in ${\Lambda }_b^0\to ({\Lambda }_c^{+},p^{+}){\ell }_1^{-}{\ell }_2^{-}{\ell }_3^{+}\nu$ decays
• CP violation in the rare Higgs decays via exchange of on-shell almost degenerate Majorana neutrinos, $H\to {\nu }_k{N}_j\to {\nu }_k{\ell }^{-}U\bar{D}$ and $H\to {\nu }_k{N}_j\to {\nu }_k{\ell }^{+}\bar{U}D$
• Dirac-Majorana neutrinos distinction in four-body decays