On the interplay of constraints from D,  and K meson mixing in models with implications for transitions

Andrzej J. Buras; Peter Stangl

doi:10.1140/epjc/s10052-025-14168-z

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 519
https://doi.org/10.1140/epjc/s10052-025-14168-z

Regular Article - Theoretical Physics

On the interplay of constraints from $B_{s},$ $B_{s},$ D, and K meson mixing in $Z^{'}$ $Z^\prime$ models with implications for $b \to s ν \bar{ν}$ $b\!\rightarrow \! s \nu {\bar{\nu }}$ transitions

Andrzej J. Buras¹^,2 and Peter Stangl³^a

¹ TUM Institute for Advanced Study, Lichtenbergstr. 2a, 85747, Garching, Germany
² Physik Department, TUM School of Natural Sciences, TU München, James-Franck-Straße, 85748, Garching, Germany
³ Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland

^a peter.stangl@cern.ch

Received: 6 January 2025
Accepted: 7 April 2025
Published online: 12 May 2025

Abstract

Within $Z^{'}$ $Z^\prime$ models, neutral meson mixing severely constrains beyond the Standard Model (SM) effects in flavour changing neutral current (FCNC) processes. However, in certain regions of the $Z^{'}$ $Z^\prime$ parameter space, the contributions to meson mixing observables become negligibly small even for large $Z^{'}$ $Z^\prime$ couplings. While this a priori allows for significant new physics (NP) effects in FCNC decays, we discuss how large $Z^{'}$ $Z^\prime$ couplings in one neutral meson sector can generate effects in meson mixing observables of other neutral mesons, through correlations stemming from ${SU (2)}_{L}$ ${\text {SU}(2)}_L$ gauge invariance and through Renormalization Group (RG) effects in the SM Effective Field Theory (SMEFT). This is illustrated with the example of $B_{s}^{0} - {\bar{B}}_{s}^{0}$ $B_s^0-{\bar{B}}_s^0$ mixing, which in the presence of both left- and right-handed $Z^{'} b s$ $Z^\prime bs$ couplings $Δ_{L}^{bs}$ $\Delta _L^{bs}$ and $Δ_{R}^{bs}$ $\Delta _R^{bs}$ remains SM-like for $Δ_{R}^{bs} \approx 0.1 Δ_{L}^{bs} .$ $\Delta _R^{bs}\approx 0.1\,\Delta _L^{bs}.$ We show that in this case, large $Z^{'} b s$ $Z^\prime bs$ couplings generate effects in D and K meson mixing observables, but that the D and K mixing constraints and the relation between $Δ_{R}^{bs}$ $\Delta _R^{bs}$ and $Δ_{L}^{bs}$ $\Delta _L^{bs}$ are fully compatible with a lepton flavour universality (LFU) conserving explanation of the most recent $b \to s ℓ^{+} ℓ^{-}$ $b\rightarrow s\ell ^+\ell ^-$ experimental data without violating other constraints like $e^{+} e^{-} \to ℓ^{+} ℓ^{-}$ $e^+ e^-\rightarrow \ell ^+\ell ^-$ scattering. Assuming LFU, invariance under the ${SU (2)}_{L}$ ${\text {SU}(2)}_L$ gauge symmetry leads then to correlated effects in $b \to s ν \bar{ν}$ $b\rightarrow s\nu {\bar{\nu }}$ observables presently studied intensively by the Belle II experiment, which allow to probe the $Z^{'}$ $Z^\prime$ parameter space that is opened up by the vanishing NP contributions to $B_{s}^{0} - {\bar{B}}_{s}^{0}$ $B_s^0-{\bar{B}}_s^0$ mixing. In this scenario the suppression of $B \to K (K^{*}) μ^{+} μ^{-}$ $B\rightarrow K(K^*)\mu ^+\mu ^-$ branching ratios implies uniquely enhancements of $B \to K (K^{*}) ν \bar{ν}$ $B\rightarrow K(K^*)\nu {\bar{\nu }}$ branching ratios up to $20 % .$ $20\%.$

© The Author(s) 2025

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Funded by SCOAP³.

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On the interplay of constraints from Bs,D, and K meson mixing in Z′ models with implications for b→sνν¯ transitions

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On the interplay of constraints from $B_{s},$ $B_{s},$ D, and K meson mixing in $Z^{'}$ $Z^\prime$ models with implications for $b \to s ν \bar{ν}$ $b\!\rightarrow \! s \nu {\bar{\nu }}$ transitions