Bounds on lepton flavor violating physics and decays of neutral mesons from $τ(μ) \to 3 \ell, \ell γγ$-decays

Abstract: We study two- and three-body lepton flavor violating (LFV) decays involving leptons and neutral vector bosons $V=\rho^0, \omega, \phi, J/\psi, \Upsilon, Z^0$, as well as pseudo-scalar $P=\pi^0, \eta, \eta', \eta_c$ and scalar $S=f_0(500), f_0(980), a_0(980), \chi_{c0}(1P)$ mesons, without referring to a specific mechanism of LFV realization. In particular, we relate the rates of the three-body LFV decays $\tau(\mu) \to 3 \ell$, where $\ell = \mu$ or $e$, to the two-body LFV decays $(V,P) \to \tau\mu(\tau e, \mu e)$, where $V$ and $P$ play the role of intermediate resonances in the decay process $\tau(\mu) \to 3 \ell$. From the experimental upper bounds for the branching ratios of $\tau(\mu) \to 3 \ell$ decays, we derive upper limits for the branching ratios of $(V,P) \to \tau\mu(\tau e, \mu e)$. We compare our results to the available experimental data and known theoretical upper limits from previous studies of LFV processes, and find that some of our limits are several orders of magnitude more stringent. Using the idea of quark-hadron duality, we extract limits on various quark-lepton dimension-six LFV operators from data on lepton decays. Some of these limits are either new or stronger than those existing in the literature.