Search for lepton-flavor-violating $τ^- \to \ell^- K_s^0$ decays at Belle and Belle II

TL;DR

This work addresses charged-lepton-flavor violation in τ decays by searching for $τ^{-} \rightarrow \ell^{-}K_{S}^{0}$ with $\ell = e, μ$ using a combined data sample of $1.3\times 10^{9}$ $e^{+}e^{-} \rightarrow τ^{+}τ^{-}$ events from Belle II ($980~\mathrm{fb}^{-1}$) and Belle ($428~\mathrm{fb}^{-1}$). It employs a two-dimensional signal region in $M(\ell K_S^{0})$ and $ΔE(\ell K_S^{0})$, plus channel-specific boosted decision trees, to maximize background rejection while preserving signal efficiency. No significant excess is observed, yielding 90% C.L. upper limits: $B(τ^{-} \rightarrow e^{-}K_S^{0}) < 0.8\times 10^{-8}$ and $B(τ^{-} \rightarrow μ^{-}K_S^{0}) < 1.2\times 10^{-8}$, with the results representing the most stringent constraints on these LFV decays to date. These limits constrain new-physics scenarios that generate τ LFV interactions and provide valuable guidance for future high-statistics τ-lepton studies.

Abstract

We present the results of a search for charged-lepton-flavor violating decays $τ^{-} \rightarrow \ell^{-}K_{S}^{0}$, where $\ell^{-}$ is either an electron or a muon. We combine $e^+e^-$ data samples recorded by the Belle II experiment at the SuperKEKB collider (428 fb$^{-1}$) with samples recorded by the Belle experiment at the KEKB collider (980 fb$^{-1}$) to obtain a sample of 1.3 billion $e^+e^-\toτ^+τ^-$ events. We observe 0 and 1 events and set $90\%$ confidence level upper limits of $0.8 \times 10^{-8}$ and $1.2 \times 10^{-8}$ on the branching fractions of the decay modes $τ^{-} \rightarrow e^{-}K_{S}^{0}$ and $τ^{-} \rightarrow μ^{-}K_{S}^{0}$, respectively. These are the most stringent upper limits to date.

Figures (7)

• Figure 1: Distributions of simulated $\tau^-\rightarrow e^-K_S^0$ events for $\hbox{Belle II}\xspace{}$ (left) and $\tau^-\rightarrow e^-K_S^0$ for Belle (right) in the ($M(\ell K_S^0)$, $\Delta E(\ell K_S^0)$) plane. The lower row shows the $\tau^-\rightarrow \mu^- K_S^0$ channel. The large, dashed black box represents the $20\,\delta$ region, the small red rectangle is the SR and the green bands define the RSB.
• Figure 2: Comparison between data (black points with error bars) and background simulation (solid-filled histograms) in the sidebands before (left) and after (right) pre-selections are applied to reject low-multiplicity events. The signal in the $20\delta$ region is shown as a blue hatched histogram with an arbitrary scale. The statistical uncertainties are displayed in light gray shading. The upper row displays the $K_S^0$ mass reconstructed using the electron mass hypothesis for the pions, $M^{ee}(K_S^0)$, for the $\hbox{Belle II}\xspace{}$ electron channel. The lower row displays the thrust value for the Belle muon channel.
• Figure 3: Comparison between data (black points with error bars) and background simulation (solid-filled histograms) in the sideband regions after preselections for the $\Delta E(\ell K_S^0)$ and $M(\ell K_S^0)$ distributions, for both Belle (first and second rows) and Belle II (third and fourth rows) data sets. Only backgrounds with a non-null residual contribution after the selection is applied are shown in the plots. The signal in the $20\delta$ region is shown as a blue hatched histogram with an arbitrary scale. The statistical uncertainties are displayed in light gray shading. The left column shows the distributions for electron channels and the right column for the muon channels.
• Figure 4: Comparison between data (black points with error bars) and simulation (solid-filled histograms) for the BDT output distribution for events in the sideband region after preselection. The signal is shown as a blue hatched histogram with arbitrary scale. The statistical uncertainties are displayed as gray shaded areas. Top row shows the electron (left) and muon (right) channel for Belle, the bottom row shows electron (left) and muon (right) channel for Belle II.
• Figure 5: Fits (blue solid line) to selected events (points with error bars) in the RSB region as function of $M(\ell K_S^0)$. Top row shows the electron (left) and muon (right) channels for Belle, the bottom row shows the electron (left) and muon (right) channels for Belle II.