Sensitivity for four-body tau-lepton decays at Belle and Belle II experiments

Abstract

We study the expected sensitivity at Belle and Belle II for four-body $\ddot{I}{„}^{\mp }\to X^{\pm }{l}^{\mp }{l}^{\mp }\hat{I}{½}_{\ddot{I}}„$ decays where $l=e$ or $\hat{I}¼$ and $X=\ddot{I}€$, $K$, $\ddot{I}$ and $K^{\ast }$ mesons. These decay processes violate the total lepton number ($|\hat{I}”L|=2$ ) and they can be induced by the exchange of Majorana neutrinos. In particular, we consider lifetimes in the accessible ranges of $\ddot{I}{„}_N$ = 5, 100 ps and extract the limits on $|V_{\ell N}{|}^2$ without any additional assumption on the relative size of the mixing matrix elements. For an integrated luminosity collected of 1 ab${}^{-1}$ at Belle, we found significant sensitivity on branching fractions of the order BR($\ddot{I}{„}^{\mp }\to X^{\pm }{l}^{\mp }{l}^{\mp }\hat{I}{½}_{\ddot{I}}„$) $\sim 10^{-8}$. For an integrated luminosity expected of 50 ab${}^{-1}$ and intermediate luminosity of 10 ab${}^{-1}$ at the Belle II, we found significant sensitivity on branching fractions of the order BR($\ddot{I}{„}^{\mp }\to X^{\pm }{l}^{\mp }{l}^{\mp }\hat{I}{½}_{\ddot{I}}„$) $\sim 10^{-9}-10^{-8}$. We use these sensitivities to set limits for the exclusion regions on the parameter space $(m_N,|V_{\ell N}{|}^2)$ associated with the heavy neutrino; such that for a $|V_{\ell N}{|}^2\sim \mathcal{O}(10^{-5})$ at $\ddot{I}{„}_N=100$ ps, we find the bounds as $0.140<m_N<1.776$ GeV for $\ddot{I}{„}^{-}\to X^{+}{e}^{-}{e}^{-}\hat{I}{½}_{\ddot{I}}„$ and $0.245<m_N<1.671$ GeV for $\ddot{I}{„}^{-}\to X^{+}\hat{I}{¼}^{-}\hat{I}{¼}^{-}\hat{I}{½}_{\ddot{I}}„$.