Probing Lepton Flavour Universality with $K\to \pi \nu \bar{\nu }$ decays

Abstract

We analyse the rare processes $K\to \pi \nu \bar{\nu }$ in view of the recent hints of violations of Lepton Flavour Universality (LFU) observed in B meson decays. If, as suggested by present data, the new interactions responsible for LFU violations couple mainly to the third generation of left-handed fermions, $K\to \pi \nu \bar{\nu }$ decays turn out to be particularly interesting: these are the only kaon decays with third-generation leptons (the $\tau$ neutrinos) in the final state. In order to relate B-physics anomalies and K decays we adopt an Effective Field Theory approach, assuming that the new interactions satisfy an approximate $U(2{)}_q\times U(2{)}_{\ell }$ flavour symmetry. In this framework we show that O(1) deviations from the Standard Model predictions in $K\to \pi \nu \bar{\nu }$ branching ratios, closely correlated to similar effects in $B\to K^{(\ast )}\nu \bar{\nu }$, are naturally expected. The correlation of $\mathcal{B}(K\to \pi \nu \bar{\nu })$, $\mathcal{B}(B\to K^{(\ast )}\nu \bar{\nu })$, and the LFU violations in B decays would provide a very valuable tool to shed more light on this interesting phenomenon.

11 pages, 2 figures

References in corpus (10)

• Confronting lepton flavor universality violation in B decays with high-$p_T$ tau lepton searches at LHC
• Simultaneous Explanation of the $R_K$ and $R(D^{(\ast )})$ Puzzles
• Lepton Flavor Violation in B Decays?
• Leptoquark model to explain the $B$-physics anomalies, $R_K$ and $R_D$
• B-decay Anomalies in a Composite Leptoquark Model
• Simultaneous Explanation of the $R_K$ and $R_{D^{(\ast )}}$ Puzzles: a Model Analysis
• Improved estimates of rare K decay matrix-elements from Kl3 decays
• Leptoquark Flavor Patterns & B Decay Anomalies
• New strategies for New Physics search in B -> K* nu anti-nu, B -> K nu anti-nu and B -> X(s) nu anti-nu decays
• Phenomenology of an $SU(2)\times SU(2)\times U(1)$ model with lepton-flavour non-universality

Cited by in corpus (7)

• B-physics anomalies: a guide to combined explanations
• Explaining $(g-2{)}_{\mu ,e}$, the KOTO anomaly and the MiniBooNE excess in an extended Higgs model with sterile neutrinos
• Vector Leptoquarks Beyond Tree Level
• Effective Theory Approach to New Physics with Flavour: General Framework and a Leptoquark Example
• Implications of $b\to s\mu \mu$ Anomalies for Future Measurements of $B\to K^{(\ast )}\nu \bar{\nu }$ and $K\to \pi \nu \bar{\nu }$
• Flavor Non-universal Vector Leptoquark Imprints in $K\to \pi \nu \bar{\nu }$ and $\Delta F=2$ Transitions
• Rare B, D and K decays, radiative and electroweak penguin decays, including constraints on $V_{td}/V_{ts}$ and ${\epsilon }^{\prime }/\epsilon$: Summary of CKM 2018 working group 3