New physics contributions to the Z penguin are revisited in the light of the recently-reported discrepancy of the direct CP violation in K → ππ. Interference effects between the standard model and new physics contributions to ∆S = 2 observables are taken into account. Although the effects are overlooked in the literature, they make experimental bounds significantly severer. It is shown that the new physics contributions must be tuned to enhance B(K L → π 0 νν), if the discrepancy of the direct CP violation is explained with satisfying the experimental constraints. The branching ratio can be as large as 6 × 10 −10 when the contributions are tuned at the 10 % level.

Polarization measurements in $$ \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} $$ B ¯ → D ∗ τ ν ¯ are useful to check consistency in new physics explanations for the R D and $$ {R}_{D^{*}} $$ R D * anomalies. In this paper, we investigate the D * and τ polarizations and focus on the new physics contributions to the fraction of a longitudinal D * polarization (F L D * ), which is recently measured by the Belle collaboration F L D * = 0.60 ± 0.09, in model-independent manner and in each single leptoquark model (R2, S1 and U1) that can naturally explain the $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ anomalies. It is found that ℬ(B c +  → τ + ν) severely restricts deviation from the Standard Model (SM) prediction of F L,SM D * = 0.46±0.04 in the leptoquark models: [0.43, 0.44], [0.42, 0.48], and [0.43, 0.47] are predicted as a range of F L D * for the R2, S1, and U1 leptoquark models, respectively, where the current data of $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ is satisfied at 1σ level. It is also shown that the τ polarization observables can much deviate from the SM predictions. The Belle II experiment, therefore, can check such correlations between $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ and the polarization observables, and discriminate among the leptoquark models.

We probe the SUSY at the 10 TeV scale in the rare decays and the CP violation of the kaon. We focus on the processes of K L → π 0 νν and K + → π + νν combined with the CP violating parameters ǫ K and ǫ ′ K /ǫ K . The Z-penguin mediated by the chargino loop cannot enhance K L → π 0 νν and K + → π + νν because the left-right mixing of the stop is constrained by the 125 GeV Higgs mass. On the other hand, the Z-penguin mediated by the gluino loop can enhance the branching ratios of both K L → π 0 νν and K + → π + νν. The former increases up to more than 1.0 × 10 −10 , which is much larger than the SM prediction even if the constraint of ǫ K is imposed. It is remarkable that the Z-penguin mediated by the gluino loop can enhance simultaneously ǫ ′ K /ǫ K and the branching ratio of K L → π 0 νν, which increases up to 1.0 × 10 −10 . We also study the decay rates of K L → µ + µ − , B 0 → µ + µ − and B s → µ + µ − , which correlate with the K L → π 0 νν decay through the Z penguin. It is important to examine the B 0 → µ + µ − process since we expect the enough sensitivity of this decay mode to the SUSY at LHCb.The rare decays and the CP violation of the kaon have given us important constraints for new physics (NP) since the standard model (SM) contributions are suppressed due to the flavor structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix [1,2]. Typical examples are the rare decay processes K L → π 0 νν and K + → π + νν, which are clean theoretically [3,4]. These processes have been considered to be one of the powerful probes of NP [5]- [17]. In order to improve the previous experimental measurements [18,19], new experiments are going on. One is the J-PARC KOTO experiment, which is to measure the decay rate of K L → π 0 νν approaching to the SM predicted precision [20,21]. Another one is the CERN NA62 experiment to observe the K + → π + νν decay [22].Especially, the K L → π 0 νν process is the CP violating one and provides the direct measurement of the CP violating phase in the CKM matrix. On the other hand, the indirect CP violating parameter ǫ K , which is induced by the K 0 −K 0 mixing, has given us the precise information of the CP violating phase of the CKM matrix. Another CP violating parameter ǫ ′ K /ǫ K was measured in the K → ππ decay. Therefore, the K L → π 0 νν process is expected to open the NP window in the CP violation by combining with ǫ K and ǫ ′ K /ǫ K . The K L → π 0 νν and K + → π + νν decays are dominated by the Z-penguin process, which is the flavor changing neutral current (FCNC) through loop diagrams. The Z-penguin process also gives the large contribution to ǫ ′ K /ǫ K due to the enhancement of the ∆I = 1/2 amplitude [23]. Actually, it cancels the dominant QCD penguin contribution significantly in the SM since it has the opposite sign to the QCD penguin amplitude. On the other hand, ǫ K is given by the box diagram. We expect the deviation from the SM prediction with correlating among K L → π 0 νν, K + → π + νν, ǫ K and ǫ ′ K /ǫ K due to the NP effect. Furthermore, there may be other correlatio...

Motivated by the recent hints of lepton flavor universality violation observed in semileptonic B decays, we analyze how to test flavor and helicity structures of the corresponding amplitudes in view of future data. We show that the general assumption that such non-standard effects are controlled by a U (2)q × U (2) flavor symmetry, minimally broken as in the Standard Model Yukawa sector, leads to stringent predictions on leptonic and semileptonic B decays. Future measurements of R D ( * ) , R K ( * ) , B(Bc,u → ν), B(B → π ν), B(B → π ¯ ), B(B s,d → ¯ ( ) ), as well as various polarization asymmetries inB → D ( * ) τν decays, will allow to prove or falsify this general hypothesis independently of its dynamical origin.