K + → π + ν ν ¯ $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ and K L → π 0 ν ν ¯ $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$ 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 → π 0 νν, 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 K and ∆M 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 −11 and B(K L → π 0 νν) = (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 → π 0 νν 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.

New physics patterns in ε′/ε and ε K with implications for rare kaon decays and ∆M K

“…For the charm contribution, represented by P c (X), the calculations in [92][93][94][95][96] imply [45] P c (X) = 0.404 ± 0.024, (C.4) where the error is dominated by the long distance uncertainty estimated in [96]. Next…”

“…−11 (4.22) to be compared with the present SM estimates that include uncertainties in the tree-level determinations of CKM parameters [45] …”

New vector-like fermions and flavor physics

“…For K + → π + ν iνi [36][37][38][39][40] where λ K (q 2 ) is a phase space factor, f + and f T are q 2 -dependent form factors. The B → πµ + µ − rate is obtained with obvious replacements.…”

The CHarged particle ANTIcounter for the NA62 experiment at CERN

“…It is a theoretically very clean Flavour Changing Neutral Current process and represents a valid test for the flavor structure of the Standard Model (SM). The SM prediction is BR(K + → π + νν)=(0.84 ± 0.10) × 10 −10 [2], while the current best measurement, performed by the E787/E949 collaboration, is BR(K + → π + νν)=(1.73 +1.15 −1.05 ) × 10 −10 [3]. NA62 uses a 75 GeV/c unseparated hadron beam from the SPS with a 6% kaon component.…”