Correlating $$B\rightarrow K^{(*)} \nu \bar{\nu }$$ B → K ( ∗ ) ν ν ¯ and flavor anomalies in SMEFT

Abstract

Abstract The recent measurement of $$\mathcal {B}(B^+\rightarrow K^+\nu \bar{\nu })$$ B ( B + → K + ν ν ¯ ) by Belle-II reveals a $$2.8~\sigma $$ 2.8 σ deviation from the Standard Model (SM) prediction. Combining this with a prior Belle measurement of $$\mathcal {B}(B^{0}\rightarrow K^{*0}\nu \bar{\nu })$$ B ( B 0 → K ∗ 0 ν ν ¯ ) , the upper bound of the ratio $$\mathcal {B}(B^{0}\rightarrow K^{*0}\nu \bar{\nu })/\mathcal {B}(B^+\rightarrow K^+\nu \bar{\nu })$$ B ( B 0 → K ∗ 0 ν ν ¯ ) / B ( B + → K + ν ν ¯ ) is notably smaller than the SM prediction. In this work, tensions are solved within the framework of Standard Model effective field theory (SMEFT). The flavor-changing-neutral-current (FCNC) and charged-current observables of either down-type ( $$b\rightarrow s\nu \bar{\nu }$$ b → s ν ν ¯ , $$b\rightarrow s\ell ^+\ell ^-$$ b → s ℓ + ℓ - , and $$b\rightarrow u_i\ell \bar{\nu }$$ b → u i ℓ ν ¯ ) or up-type ( $$u_j\rightarrow u_i\nu \bar{\nu }$$ u j → u i ν ν ¯ , $$u_j\rightarrow u_i\ell ^+\ell ^-$$ u j → u i ℓ + ℓ - , and $$u_j\rightarrow s\ell \bar{\nu }$$ u j → s ℓ ν ¯ ) processes, described by low-energy effective field theory (LEFT) operators, are interconnected by a minimal set of four SMEFT operators at the electroweak scale. Subsequently, we obtain the latest ranges of Wilson coefficients for these four operators through a global fit that accommodates flavor anomalies such as $$R_{K^{(*)}}$$ R K ( ∗ ) , $$R_{D^{(*)}}$$ R D ( ∗ ) , and $$\mathcal {B}(B\rightarrow K^{(*)}\nu \bar{\nu })$$ B ( B → K ( ∗ ) ν ν ¯ ) . Our findings reveal that predictions for $$\mathcal {B}(B^+\rightarrow \tau ^+\nu _\tau )$$ B ( B + → τ + ν τ ) and $$\mathcal {B}(D_s^+\rightarrow \tau ^+\nu _\tau )$$ B ( D s + → τ + ν τ ) align well with measured values from Belle and BESIII, based on the fitted coefficients. The predicted branching fraction for $$B^0\rightarrow K^{*0}\nu \bar{\nu }$$ B 0 → K ∗ 0 ν ν ¯ is $$(1.42\pm 0.74)\times 10^{-5}$$ ( 1.42 ± 0.74 ) × 10 - 5 , closely approaching the current experimental upper limit. Anticipation surrounds the rare decay $$B_s\rightarrow \tau ^+ \tau ^-$$ B s → τ + τ - , expected in the near future with a branching fraction on the order of $$10^{-4}$$ 10 - 4 .