K⁺→π⁺νν¯ and K_L→π⁰νν¯ in the Standard Model: status and perspectives

Abstract: In view of the recent start of the NA62 experiment at CERN that is expected to measure the K⁺→π⁺νν¯ branching ratio with a precision of 10%, we summarise the present status of this promising decay within the Standard Model (SM). We do likewise for the closely related K_L→π⁰νν¯, which will be measured by the KOTO experiment around 2020. As the perturbative QCD and electroweak corrections in both decays are under full control, the dominant uncertainties within the SM presently originate from the CKM parameters |V_cb|, |V_ub| and γ. We show this dependence with the help of analytic expressions as well as accurate interpolating formulae. Unfortunately a clarification of the discrepancies between inclusive and exclusive determinations of |V_cb| and |V_ub| from tree-level decays will likely require results from the Belle II experiment available at the end of this decade. Thus we investigate whether higher precision on both branching ratios is achievable by determining |V_cb|, |V_ub| and γ by means of other observables that are already precisely measured. In this context ε_Kand ΔM_s,d, together with the expected progress in QCD lattice calculations will play a prominent role. We find ℬ(K⁺→π⁺νν¯)=(9.11±0.72)×10⁻¹¹and ℬ(K_L→π⁰νν¯)=(3.00±0.30)×10⁻¹¹, which is more precise than using averages of the present tree-level values of |V_cb|, |V_ub| and γ. Furthermore, we point out the correlation between ℬ(K⁺→π⁺νν¯),ℬ¯(B_s→μ⁺μ⁻and γ within the SM, that is only very weakly dependent on other CKM parameters. Finally, we update the correlation of K_L→π⁰νν¯ with the ratio ε^′/ε in the SM taking the recent progress on ε^′/ε from lattice QCD and the large N approach into account.