Rare kaon decays $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$: Standard Model predictions from lattice QCD
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| Natura: | Preprint |
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2026
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| author | Di Palma, R. Frezzotti, R. Gagliardi, G. Lubicz, V. Martinelli, G. Sachrajda, C. T. Sanfilippo, F. Simula, S. Tantalo, N. |
| author_facet | Di Palma, R. Frezzotti, R. Gagliardi, G. Lubicz, V. Martinelli, G. Sachrajda, C. T. Sanfilippo, F. Simula, S. Tantalo, N. |
| contents | Weak decays of charged kaons with an additional lepton-antilepton pair, $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$ ($K_{\ell2\ell'}$), are suppressed at order $O(G_{F}^{2}α_{\rm em}^{2})$ in the Standard Model (SM) and provide sensitive probes of its flavour structure, as well as independent determinations of the Cabibbo angle $|V_{us}|$. In this Letter we present the SM predictions for all four channels with $\ell,\ell' =e,μ$, based on the first complete lattice QCD calculation of the structure-dependent form factors reported in a companion paper [1]. Using the PDG value [2] $|V_{us}|^{\rm PDG}=0.22431(85)$, we obtain branching fractions with controlled uncertainties and precisions ranging from $2\%$ to $7\%$, depending on the channel. For the three modes with published measurements, our results agree with experiment. For the $K_{\mu2μ}$ mode, for which no published experimental result is available, we compare our prediction with the preliminary NA62 result, finding agreement at the $1.4σ$ level. Conversely, the measured decay rates can be used together with our results to extract $|V_{us}|$ from these modes. A weighted average over the two most precise channels, $K_{\mu2e}$ and $K_{\mu2μ}$, yields $|V_{us}|=0.2283(42)$, corresponding to a $1.8\%$ determination. These results pave the way for using $K_{\ell2\ell'}$ decays as precision probes of the SM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22727 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rare kaon decays $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$: Standard Model predictions from lattice QCD Di Palma, R. Frezzotti, R. Gagliardi, G. Lubicz, V. Martinelli, G. Sachrajda, C. T. Sanfilippo, F. Simula, S. Tantalo, N. High Energy Physics - Phenomenology High Energy Physics - Lattice Weak decays of charged kaons with an additional lepton-antilepton pair, $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$ ($K_{\ell2\ell'}$), are suppressed at order $O(G_{F}^{2}α_{\rm em}^{2})$ in the Standard Model (SM) and provide sensitive probes of its flavour structure, as well as independent determinations of the Cabibbo angle $|V_{us}|$. In this Letter we present the SM predictions for all four channels with $\ell,\ell' =e,μ$, based on the first complete lattice QCD calculation of the structure-dependent form factors reported in a companion paper [1]. Using the PDG value [2] $|V_{us}|^{\rm PDG}=0.22431(85)$, we obtain branching fractions with controlled uncertainties and precisions ranging from $2\%$ to $7\%$, depending on the channel. For the three modes with published measurements, our results agree with experiment. For the $K_{\mu2μ}$ mode, for which no published experimental result is available, we compare our prediction with the preliminary NA62 result, finding agreement at the $1.4σ$ level. Conversely, the measured decay rates can be used together with our results to extract $|V_{us}|$ from these modes. A weighted average over the two most precise channels, $K_{\mu2e}$ and $K_{\mu2μ}$, yields $|V_{us}|=0.2283(42)$, corresponding to a $1.8\%$ determination. These results pave the way for using $K_{\ell2\ell'}$ decays as precision probes of the SM. |
| title | Rare kaon decays $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$: Standard Model predictions from lattice QCD |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2605.22727 |