Kaon physics without new physics in $$$$ \varepsilon _K$$$$

Journal Article · Fri May 05 00:00:00 EDT 2023 · European Physical Journal. C, Particles and Fields (Online)

DOI:https://doi.org/10.1140/epjc/s10052-023-11474-2· OSTI ID:1972772

Aebischer, Jason; Buras, Andrzej J.; Kumar, Jacky

Abstract Despite the observation of significant suppressions of $$$$b\rightarrow s\mu ^+\mu ^-$$$$ $b\to s{\mu }^{+}{\mu }^{-}$ branching ratios no clear sign of New Physics (NP) has been identified in $$$$\Delta F=2$$$$ $\Delta F=2$ observables $$$$\Delta M_{d,s}$$$$ $\Delta M_{d,s}$ , $$$$\varepsilon _K$$$$ ${\epsilon }_K$ and the mixing induced CP asymmetries $$$$S_{\psi K_S}$$$$ $S_{\psi K_S}$ and $$$$S_{\psi \phi }$$$$ $S_{\psi \varphi }$ . Assuming negligible NP contributions to these observables allows to determine CKM parameters without being involved in the tensions between inclusive and exclusive determinations of $$$$|V_{cb}|$$$$ $|V_{\mathrm{cb}}|$ and $$$$|V_{ub}|$$$$ $|V_{\mathrm{ub}}|$ . Furthermore this method avoids the impact of NP on the determination of these parameters present likely in global fits. Simultaneously it provides SM predictions for numerous rare K and B branching ratios that are most accurate to date. Analyzing this scenario within $$$$Z^\prime $$$$ $Z^{\prime }$ models we point out, following the 2009 observations of Monika Blanke and ours of 2020, that despite the absence of NP contributions to $$$$\varepsilon _K$$$$ ${\epsilon }_K$ , significant NP contributions to $$$$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$$$ $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ , $$$$K_{L}\rightarrow \pi ^0\nu {\bar{\nu }}$$$$ $K_L\to {\pi }^0\nu \overline{\nu }$ , $$$$K_S\rightarrow \mu ^+\mu ^-$$$$ $K_S\to {\mu }^{+}{\mu }^{-}$ , $$$$K_L\rightarrow \pi ^0\ell ^+\ell ^-$$$$ $K_L\to {\pi }^0{\ell }^{+}{\ell }^{-}$ , $$$$\varepsilon '/\varepsilon $$$$ ${\epsilon }^{\prime }/\epsilon$ and $$$$\Delta M_K$$$$ $\Delta M_K$ can be present. In the simplest scenario, this is guaranteed, as far as flavour changes are concerned, by a single non-vanishing imaginary left-handed $$$$Z^\prime $$$$ $Z^{\prime }$ coupling $$$$g^L_{sd}$$$$ $g_{\mathrm{sd}}^L$ . This scenario implies very stringent correlations between the Kaon observables considered by us. In particular, the identification of NP in any of these observables implies automatically NP contributions to the remaining ones under the assumption of non-vanishing flavour conserving $$$$Z^\prime $$$$ $Z^{\prime }$ couplings to $$$$q{\bar{q}}$$$$ $q\overline{q}$ , $$$$\nu {\bar{\nu }}$$$$ $\nu \overline{\nu }$ , and $$$$\mu ^+\mu ^-$$$$ ${\mu }^{+}{\mu }^{-}$ . A characteristic feature of this scenario is a strict correlation between $$$$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$$$ $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $$$$K_{L}\rightarrow \pi ^0\nu {\bar{\nu }}$$$$ $K_L\to {\pi }^0\nu \overline{\nu }$ branching ratios on a branch parallel to the Grossman-Nir bound. Moreover, $$$$\Delta M_K$$$$ $\Delta M_K$ is automatically suppressed as seems to be required by the results of the RBC-UKQCD lattice QCD collaboration. Furthermore, there is no NP contribution to $$$$K_L\rightarrow \mu ^+\mu ^-$$$$ $K_L\to {\mu }^{+}{\mu }^{-}$ which otherwise would bound NP effects in $$$$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$$$ $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ . Of particular interest are the correlations of $$$$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$$$ $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $$$$K_{L}\rightarrow \pi ^0\nu {\bar{\nu }}$$$$ $K_L\to {\pi }^0\nu \overline{\nu }$ branching ratios and of $$$$\Delta M_K$$$$ $\Delta M_K$ with the ratio $$$$\varepsilon '/\varepsilon $$$$ ${\epsilon }^{\prime }/\epsilon$ . We investigate the impact of renormalization group effects in the context of the SMEFT on this simple scenario.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program; European Research Council (ERC); Swiss National Science Foundation (SNF); German Research Foundation (DFG)
• Grant/Contract Number: 20220706PRD1; 89233218CNA000001; 833280; 200020 204428; 390783311
• OSTI ID: 1972772
• Alternate ID(s): OSTI ID: 2204197
• Report Number(s): LA-UR-23-20868; 368; PII: 11474
• Journal Information: European Physical Journal. C, Particles and Fields (Online), Journal Name: European Physical Journal. C, Particles and Fields (Online) Vol. 83 Journal Issue: 5; ISSN 1434-6052
• Publisher: Springer Science + Business Media
• Country of Publication: Germany
• Language: English

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