Probing SUSY with 10 TeV stop mass in rare decays and CP violation of kaon

Abstract

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...

Left-handed color-sextet diquark in the kaon system

“…where f K is the K-meson decay constant; P V LL 1 ≈ 0.48 is the nonperturbative QCD effects, and the factor (α s (m H 6 )/α 2 (m t )) 6/21 is the renormalization group (RG) evolution from the m H 6 scale to the m t scale. Since the Kaon indirect CP violation parameter K is associated with V * ts V td in the SM, we scale the parameters (g † g) 21 with the (V * ts V td ) −1 factor. Thus, the mass difference between K L and K S and K can be obtained as:…”

“…Since it is not our purpose to show the generic CP phase effects of y in this study, we assume that y is a real matrix in the following numerical analysis, unless stated otherwise. Taking the Wolfenstein's parametrization [13] as an input, the CP phase of the CKM matrix appears in V td and V ub , and the Kaon CP violation in the SM arises from Im(V * ts V td ); therefore, when the K constraint is considered, we can simply focus on the V td related effects in (g † g) 21 . In addition, because ∆M K may cause a strict constraint on the free parameters, we should also pay attention to the effects, which arise from a large CP-conserving CKM factor.…”

“…where the sum of all k flavors is implied, and (y † y) is a symmetric matrix. It can be seen that if we use (y † y) ij as the free parameters, there are nine components in (g † g) 21 ;…”

Standard Model and New physics for ε′k/εk

“…They could be a signal to test the scenario. In the MSSM, such a scenario is also realized when the off-diagonal components of the trilinear SUSY-breaking couplings are large [33][34][35].…”

Quo vadis flavour physics? FPCP2017 Theory Summary and Outlook

“…Indeed, theoretical studies have been performed in a number of NP models, with the outcome that in many NP scenarios it is possible to enhance ε /ε by an order to magnitude and resolve the tension. We refer the reader to the original publications for further details on Little Higgs models [29], supersymmetric models [30,31,32,33], simplified models with flavour changing Z or Z couplings [34,35], 331 models [36], vector-like quark models [37], and a model independent analysis [38]. A review can be found e. g. in [39].…”