New physics in multi-lepton tau decays

Abstract

Dark particles with lepton-flavor-violating couplings to the tau lepton can induce rare neutrinoless $τ$ decays with large final state multiplicities. We study models where transitions of the type $τ^\pm\to \ell^\pm\,φ$, with $φ$ a light new particle, initiate a chain of decays in the dark sector that terminate with decays into electrons, muons, or pions. These decay cascades appear as rare five or even seven-body $τ$ decays with multiple reconstructable resonances. We survey several representative models: kinetically mixed dark photon, gauged $L_i-L_j$ models, and other more exotic charge assignments such as chiral $U(1)'$ extensions of the Standard Model. The main new ingredient is the possibility of flavor violation at very high scales. In these models, a number of channels that have not yet been searched for experimentally, such as $τ\to 5μ$, $τ\to 3μ\,2e$, $τ\to μ\,4e$, and hadronic channels like $τ\to μ\,4π$, typically dominate over the previously-considered signatures such as $τ\to 3μ$. While some of the models, such as the gauged $L_i-L_j$ ones, also contain more challenging channels with missing energy due to decays to neutrinos, they can still be searched for via fully visible channels.

Figures (6)

• Figure 1: Dark cascaded decays of the type $\tau \to {\ell} (2A) (2B)$ for $A,B \in \{{\ell},h\}$ (top) and $\tau \to {\ell} (2A) (2B) (2C)$ for $A,B,C \in \{{\ell},h\}$ (bottom).
• Figure 2: Viable parameter space for prompt and on-shell light new physics sourcing $\tau \to$ multi-lepton cascade decay signatures assuming $\varepsilon = 10^{-4}, \alpha_d = \alpha$.
• Figure 3: Predicted branching ratios for $\tau \to \mu\phi \to \mu VV$ cascade decays in Model I (kinetic mixing) as a function of the dark photon mass $m_V$. The scalar mass is set to its maximal value, $m_\phi = m_\tau - m_\mu \approx 1.67$ GeV, for which both $\phi$ and $V$ decay promptly and on-shell for benchmark couplings $\varepsilon = 10^{-4}$ and $\alpha_D = \alpha$. For simplicity, we assume only $\kappa_{\tau \mu}$ is non-zero, the resulting Wilson coefficient $c_{\tau\mu}$ is then determined at each $m_V$ by saturating the preliminary LHCb $\tau \to 5\mu$ sensitivity of $4.2 \times 10^{-8}$ (black dashed horizontal line), pinning the $\tau \to 5\mu$ channel to this value across all masses. Consequently, any channel with predicted branching ratio above this line would be observable with comparable experimental sensitivity. The solid blue curve shows $\tau \to 5\mu$, while dashed and dot-dashed curves show mixed leptonic ($3\mu 2e$, $\mu 4e$) states. Hadronic channels are separated into $2\pi$ ($\rho^0$) and $3\pi$ ($\omega/\phi$) contributions using the VMD decomposition of Ilten:2018crw; solid lines show the $\pi^+\pi^-$ channels ($3\mu\,2\pi$, $\mu\,4\pi$, $\mu\,2\pi\,2e$) and dashed lines the corresponding $3\pi$ channels. The red shaded region at $m_V > m_\phi/2$ indicates where $\phi \to VV$ becomes kinematically forbidden. Horizontal lines show the projected Belle II reach (purple band, $\sim 3 \times 10^{-10}$) and FCC-ee sensitivity (magenta band, $\sim 9\times 10^{-11}$), obtained by rescaling current upper limits by the expected increase in tau statistics (see \ref{['sec:exp:prospects']}). Inset: Dark photon branching ratios $\mathcal{B}(V \to X)$ for $X = e^+e^-$, $\mu^+\mu^-$, $\pi^+\pi^-$ and $\pi^+\pi^-\pi^0$, computed using the experimentally measured $R$-ratio. Near the $\rho$ resonance ($m_V \approx 775$ MeV), hadronic channels dominate, causing $\tau \to \mu(n\pi)$ final states to dominate over the purely leptonic channels by an order of magnitude.
• Figure 4: Sensitivity to the new physics scale $\Lambda$ in the secluded $U(1)'$ model with kinetic mixing (Model I). Left: The NP scale $\Lambda$ reach of $\tau \to 5\mu$ corresponding to the LHCb preliminary sensitivity $\mathcal{B}(\tau\to 5\mu) < 4.2\times 10^{-8}$, shown in the $(m_V, m_\phi)$ plane. The red shaded region is kinematically forbidden ($m_V > m_\phi/2$). Right: Discovery reach as a function of $m_V$, maximized over $m_\phi$ for each $m_V$. The shaded regions show existing constraints from the $\tau$ lifetime (blue, $\sum \mathcal{B}_{\slashed{\rm SM}} < 5\times10^{-3}$, maximized over all kinematically allowed $m_\phi$) and from $\tau\to 3\mu$ (orange), the latter requiring a nonzero diagonal coupling $c_{\mu\mu} = c_{\tau\mu}$ (see text). All other curves are maximized over $m_\phi > 2m_V$, i.e., the on-shell cascade regime $\phi \to VV$. Solid and dashed curves show the $\Lambda$ reach of LHCb (preliminary, best channel and $5\mu$-only), In both panels $\varepsilon = 10^{-4}$, $\alpha_d = \alpha$, $c_{\mu\mu} = c_{\tau\mu} = 1$, and $c_{\tau e} = 0$.
• Figure 5: Same as \ref{['fig:model1_BRs']} but for the gauged $L_e + L_\mu - 2L_\tau$ model (Model III) with $m_\phi = 1$ GeV. In this model the $Z'$ carries lepton-flavor-violating couplings ($R_{\phi Z'}\simeq 1$), giving rise to both five-body cascade decays ($\tau\to\mu,\phi\to\mu,Z'Z'$) and direct three-body decays ($\tau\to\mu,Z'$). At each $m_V$ the LFV coupling is fixed by saturating the strongest existing bound among the Belle $\tau\to\mu e^+e^-$ (orange line, $1.8\times10^{-8}$), Belle II $\tau\to 3\mu$ limit (dark red line, $1.9\times10^{-8}$), and the preliminary LHCb $\tau\to 5\mu$ estimate of sensitivity (black line, $4.2\times10^{-8}$). The gray shaded region above the Belle and Belle II lines is excluded. Because the $Z'$ decays to $e^+e^-$, $\mu^+\mu^-$, and $\nu\bar{\nu}$ with approximate branching ratios $0.2:0.2:0.6$, channels with missing energy dominate the cascade rate, while the purely leptonic five-body modes ($5\mu$, $\mu,4e$, $3\mu,2e$) account for $\sim 16\%$. Inset:$Z'$ branching ratios as a function of $m_V$, showing the $\mu^+\mu^-$ threshold at $2m_\mu$.