On the Importance of Rare Kaon Decays: A Snowmass 2021 White Paper

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

doi:10.48550/arxiv.2203.09524

“…The measurement of γ combined with the 16 |V cb |-independent ratios constructed in [7] and with γ-dependence of various observables presented here will also play an important role in the search for NP. The importance of rare K decays in the search for NP has been recently summarized in [51] and the prospects for reducing hadronic uncertainties in K decays through intensive LQCD computations in the coming years are very good [52].…”

Section: Discussionmentioning

confidence: 99%

The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

Buras,

Venturini

2022

Preprint

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The most common predictions for rare K and B decay branching ratios in the Standard Model in the literature are based on the CKM elements |V cb | and |V ub | resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route, which to our knowledge has not been explored for ∆M s,d and rare K and B decays by anybody to date. We assume, in contrast to the prevailing inclusive expectations for |V cb |, that the future true values of |V cb | and |V ub | will be both from exclusive determinations and set them equal to the most recent ones from FLAG. With the precisely known |V us | the resulting rare decay branching ratios, ε K , ∆M d , ∆M s and S ψK S depend then only on the angles β and γ in the unitarity triangle that moreover are correlated through the CKM unitarity. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using HPQCD B 0 s,d − B0 s,d hadronic matrix elements a 3.1σ tension in ∆M s independently of γ is found. For 60 • ≤ γ ≤ 75 • the tension in ∆M d between 4.0σ and 1.1σ is found and in the case of ε K between 5.2σ and 2.1σ. Moreover, the room for new physics indecays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which |V cb | in the former scenario is replaced by the most recent inclusive |V cb | and present the dependence of all observables considered by us in both scenarios as functions of γ. As a byproduct we compare the determination of |V cb | from ∆M s , ∆M d , ε K and S ψK S using B 0 s,d − B0 s,d hadronic matrix elements from LQCD with 2 + 1 + 1 flavours, 2 + 1 flavours and their average. Only for the 2 + 1 + 1 case values for β and γ exist for which the same value of |V cb | is found: |V cb | = 42.6(7) × 10 −3 , γ = 64.6(4.0) • and β = 22.2(7) • . This in turn implies a 2.7σ anomaly in B s → µ + µ − .

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“…The measurement of γ combined with the 16 |V cb |independent ratios constructed in [7] and with γ -dependence of various observables presented here will also play an important role in the search for NP. The importance of rare K decays in the search for NP has been recently summarized in [63] and the prospects for reducing hadronic uncertainties in K decays through intensive LQCD computations in the coming years are very good [64].…”

Section: Discussionmentioning

confidence: 99%

The exclusive vision of rare K and B decays and of the quark mixing in the standard model

Buras

¹

,

Venturini

²

2022

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The most common predictions for rare K and B decay branching ratios in the Standard Model in the literature are based on the CKM elements $$|V_{cb}|$$ | V cb | and $$|V_{ub}|$$ | V ub | resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route, which to our knowledge has not been explored for $$\Delta M_{s,d}$$ Δ M s , d and rare K and B decays by anybody to date. We assume, in contrast to the prevailing inclusive expectations for $$|V_{cb}|$$ | V cb | , that the future true values of $$|V_{cb}|$$ | V cb | and $$|V_{ub}|$$ | V ub | will be both from exclusive determinations; in practice we use the most recent averages from FLAG. With the precisely known $$|V_{us}|$$ | V us | the resulting rare decay branching ratios, $$\varepsilon _K$$ ε K , $$\Delta M_d$$ Δ M d , $$\Delta M_s$$ Δ M s and $$S_{\psi K_S}$$ S ψ K S depend then only on the angles $$\beta $$ β and $$\gamma $$ γ in the unitarity triangle that moreover are correlated through the CKM unitarity. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using HPQCD $$B^0_{s,d}-{{\bar{B}}}^0_{s,d}$$ B s , d 0 - B ¯ s , d 0 hadronic matrix elements a $$3.1\sigma $$ 3.1 σ tension in $$\Delta M_s$$ Δ M s independently of $$\gamma $$ γ is found. For $$60^\circ \le \gamma \le 75^\circ $$ 60 ∘ ≤ γ ≤ 75 ∘ the tension in $$\Delta M_d$$ Δ M d between $$4.0\sigma $$ 4.0 σ and $$1.1\sigma $$ 1.1 σ is found and in the case of $$\varepsilon _K$$ ε K between $$5.2\sigma $$ 5.2 σ and $$2.1\sigma $$ 2.1 σ . Moreover, the room for new physics in $$K^+\rightarrow \pi ^+\nu {\bar{\nu }}$$ K + → π + ν ν ¯ , $$K_L\rightarrow \pi ^0\nu {\bar{\nu }}$$ K L → π 0 ν ν ¯ and $$B\rightarrow K(K^*)\nu {\bar{\nu }}$$ B → K ( K ∗ ) ν ν ¯ decays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which $$|V_{cb}|$$ | V cb | in the former scenario is replaced by the most recent inclusive $$|V_{cb}|$$ | V cb | and present the dependence of all observables considered by us in both scenarios as functions of $$\gamma $$ γ . As a byproduct we compare the determination of $$|V_{cb}|$$ | V cb | from $$\Delta M_s$$ Δ M s , $$\Delta M_d$$ Δ M d , $$\varepsilon _K$$ ε K and $$S_{\psi K_S}$$ S ψ K S using $$B^0_{s,d}-{{\bar{B}}}^0_{s,d}$$ B s , d 0 - B ¯ s , d 0 hadronic matrix elements from LQCD with $$2+1+1$$ 2 + 1 + 1 flavours, $$2+1$$ 2 + 1 flavours and their average. Only for the $$2+1+1$$ 2 + 1 + 1 case values for $$\beta $$ β and $$\gamma $$ γ exist for which the same value of $$|V_{cb}|$$ | V cb | is found: $$|V_{cb}|=42.6(4)\times 10^{-3}$$ | V cb | = 42.6 ( 4 ) × 10 - 3 , $$\gamma =64.6(16)^\circ $$ γ = 64.6 ( 16 ) ∘ and $$\beta =22.2(7)^\circ $$ β = 22.2 ( 7 ) ∘ . This in turn implies a $$2.7\sigma $$ 2.7 σ anomaly in $$B_s\rightarrow \mu ^+\mu ^-$$ B s → μ + μ - .

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“…Setting the values of the four ∆F = 2 observables in (1) to their experimental values and including all experimental and theoretical uncertainties one finds [5] B(K + → π + ν ν) SM = (8.60 ± 0.42) × 10 Note that relative to the usually quoted values by experimentalists in (3) the central values for K + → π + ν ν and K L → π 0 ν ν did not change by much but the uncertainties decreased by factors 2.5 and 4.0, respectively. Therefore, referring to (3) as the present best values instead of ( 12) totally misreprents the situation and should be abandoned as already emphasized in [5,6,9,10]. The values in (13) are rather close to those in (8), although the value for B s → µ + µ − is by one σ larger.…”

mentioning

confidence: 85%

“…In this note I want to stress again, as done already in [5,6,9,10], that in view of the tensions between exclusive and inclusive determinations of |V cb | and |V ub | [11,12], presently the only trustable SM predictions for the branching ratios in question can be obtained by eliminating their dependence on CKM parameters with the help of the ∆F = 2 observables…”

Section: Introductionmentioning

confidence: 92%

On the Standard Model Predictions for Rare K and B Decay Branching Ratios: 2022

Buras¹

2022

Preprint

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In this decade one expects a very significant progress in measuring the branching ratios for several rare K and B decays, in particular for the decaysOn the theory side a very significant progress on calculating these branching ratios has been achieved in the last thirty years culminating recently in rather precise SM predictions for them. It is then unfortunate that some papers still cite the results for K + → π + ν ν and K L → π 0 ν ν presented by us in 2015. They are clearly out of date. Similar comments apply to predictions for B s,d → µ + µ − . In this note I want to stress again that, in view of the tensions between various determinations of |V cb | in tree-level decays, presently, the only trustable SM predictions for the branching ratios in question can be obtained by eliminating their dependence on the CKM parameters with the help of |ε K |, ∆M s , ∆M d and S ψK S , evaluated in the SM. In this context I am astonished by statements made by some computer code practitioners that setting in this strategy these four ∆F = 2 observables to their experimental values is an assumption. The goal of this strategy is not to make an overall SM fit but to predict the SM branching ratios. In the SM there are no new physics (NP) contributions to ∆F = 2 transitions and no assumption on the absence of NP is needed. Moreover, presently NP is not required to describe simultaneously the very precise data on |ε K |, ∆M s , ∆M d and S ψK S . This strategy for obtaining true SM predictions for rare decay branching ratios is moreover not polluted by hadronic uncertainies and observed anomalies in semi-leptonic decays used often in global analyses.

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On the Importance of Rare Kaon Decays: A Snowmass 2021 White Paper

Cited by 8 publications

References 120 publications

The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

The exclusive vision of rare K and B decays and of the quark mixing in the standard model

On the Standard Model Predictions for Rare K and B Decay Branching Ratios: 2022

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