Sensitivity of High-Scale SUSY in Low Energy Hadronic FCNC

We discuss the sensitivity of the high-scale SUSY at $10$-$1000$ TeV in $B^0$, $B_s$, $K^0$ and $D$ meson systems together with the neutron EDM and the mercury EDM. In order to estimate the contribution of the squark flavor mixing to these FCNCs,we calculate the squark mass spectrum, which is consistent with the recent Higgs discovery. The SUSY contribution in $\epsilon_K$ could be large, around 40% in the region of the SUSY scale $10$-$100$ TeV. The neutron EDM and the mercury EDM are also sensitive to the SUSY contribution induced by the gluino-squark interaction. The predicted EDMs are roughly proportional to $|\epsilon_K^{\rm SUSY}|$. If the SUSY contribution is the level of O(10%) for epsilon_K, the neutron EDM is expected to be discovered in the region of $10^{-28}$-$10^{-26}$ecm. The mercury EDM also gives a strong constraint for the gluino-squark interaction. The SUSY contribution of $\Delta M_D$ is also discussed.


Introduction
The supersymmetry (SUSY) is one of the most attractive theories beyond the standard model (SM). Therefore, the SUSY has been expected to be observed at the LHC experiments. However, no signals of the SUSY have been discovered yet. The present searches for the SUSY particles give us important constraints for the SUSY. Since the lower bounds of the superparticle masses increase gradually, the squark and the gluino masses are supposed to be at the higher scale than 1 TeV [1,2,3]. On the other hand, the SUSY model has been seriously constrained by the Higgs discovery, in which the Higgs mass is 125 GeV [4]. Based on this theoretical and experimental situations, we consider the high-scale SUSY models, which have been widely discussed with a lot of attention [5]- [20].
If the squark and slepton masses are at the high-scale O(10-1000) TeV, the lightest Higgs mass can be pushed up to 125 GeV, whereas SUSY particles are out of the reach of the LHC experiment. Therefore, the indirect search of the SUSY particles becomes important in the low energy flavor physics [21,22,23].
The flavor physics is also on the new stage in the light of LHCb data. The LHCb collaboration has reported new data of the CP violation of the B s meson and the branching ratios of rare B s decays [24]- [36]. For many years the CP violation in the K and B 0 mesons has been successfully understood within the framework of the standard model (SM), so called Kobayashi-Maskawa (KM) model [37], where the source of the CP violation is the KM phase in the quark sector with three families. However, the new physics has been expected to be indirectly discovered in the precise data of B 0 and B s meson decays at the LHCb experiment and the further coming experiment, Belle-II.
There are new sources of the CP violation if the SM is extended to the SUSY models. The soft squark mass matrices contain the CP violating phases, which contribute to the flavor changing neutral current (FCNC) with the CP violation [38]. Therefore, we can expect the SUSY effect in the CP violating phenomena. However, the clear deviation from the SM prediction has not been observed yet in the LHCb experiment [24]- [36]. Actually, we have found that the CP violation of B 0 and B s meson systems are suppressed if the SUSY scale is above 10 TeV [39]. On the other hand, the CKMfitter group presented the current limits on new physics contributions of O(10%) in B 0 , B s and K 0 systems [40]. They have also estimated the sensitivity to new physics in B 0 and B s mixing achievable with 50ab −1 of Belle-II and 50fb −1 of LHCb data. Therefore, we should carefully study the sensitivity of the high-scale SUSY to the hadronic FCNC.
In this work, we discuss the high-scale SUSY contribution to the B 0 , B s and K 0 meson systems. Furthermore, we also discuss the sensitivity to the D meson and the electric dipole moment (EDM) of the neutron and the mercury. For these modes, the most important process of the SUSY contribution is the gluino-squark mediated flavor changing process [41]- [56]. The CP violation of K meson, ǫ K , provides a severe constraint to the gluino-squark mediated FCNC [57,58]. In addition, the recent work have found that the chromo-electric dipole moment (cEDM) is sensitive to the high-scale SUSY [59]. It is noted that the upperbound of the neutron EDM (nEDM) [60] gives a severe constraint for the gluino-squark interaction through the cEDM [61]- [66]. It is also remarked that the upper bound of the mercury EDM (HgEDM) [67] can give an important constraint [68].
In order to estimate the gluino-squark mediated FCNC of the K, B 0 , B s and D mesons, we work in the basis of the squark mass eigenstate with the non-minimal squark (slepton) flavor mixing. There are three reasons why the SUSY contribution to the FCNC considerably depends on the squark mass spectrum. The first one is that the GIM mechanism works in the squark flavor mixing, and the second one is that the loop functions depend on the mass ratio of squark and gluino. The last one is that we need the mixing angle between the left-handed sbottom and right-handed sbottom, which dominates the ∆B = 1 decay processes. Therefore, we discuss the squark mass spectrum, which is consistent with the recent Higgs discovery. Taking the universal soft parameters at the SUSY breaking scale, we obtain the squark mass spectrum at the matching scale where the SM emerges, by using the Renormalization Group Equations (RGEs) of the soft masses. On the other hand, the 6 × 6 mixing matrix between squarks and quarks is taken to be free at the low energy.
In section 2, we discuss the squark and gluino mass spectrum and the squark mixing. In section 3, we present the formulation of the FCNC with ∆F = 2 in K, B 0 , B s and D meson systems together with nEDM and HgEDM. We present numerical results and discussions in section 4. Section 5 is devoted to the summary. The relevant formulations are presented in Appendices A, B, C and D.

SUSY Spectrum and Squark mixing
The low energy FCNCs depend significantly on the spectrum of the SUSY particles, which depend on the model. As well known, the lightest Higgs mass can be pushed up to 125 GeV if the squark masses are expected to be O(10) TeV. Therefore, let us consider the heavy SUSY particle mass spectrum in the framework of the minimal supersymmetric standard model (MSSM), which is consistent with the observed Higgs mass. The discussion how to obtain the SUSY spectrum have been given in Refs. [69,70].
We outline how to obtain the SUSY spectrum in our work. The details are presented in Appendix A. At the SUSY breaking scale Λ, we write the quadratic terms in the MSSM potential as Then, the Higgs mass parameter m 2 is expressed in terms of m 2 1 , m 2 2 and tan β as: After running down to the Q 0 scale, in which the SM emerges, by the one-loop SUSY Renormalization Group Equations (RGEs) [71], the scalar potential is the SM one as follows: Here, the Higgs coupling λ is given in terms of the SUSY parameters at the leading order as and h t is the top Yukawa coupling of the SM. The parameters m 2 and λ run with the two-loop SM RGEs with MS scheme [72] down to the electroweak scale Q EW = m H , and then give When m H = 125 GeV is put, λ(Q 0 ) and m 2 (Q 0 ) are obtained. This input constrains the SUSY mass spectrum of the MSSM. In our work, we take the universal soft breaking parameters at the SUSY breaking scale Λ as follows: By inputting m H = 125 GeV and taking the heavy scalar mass m H ≃ Q 0 (see Appendix A), we can obtain the SUSY spectrum for the fixed Q 0 and tan β. The details and numerical results are presented in Appendix A. Let us consider the squark flavor mixing. As discussed above, there is no flavor mixing at Λ in the MSSM. However, in order to consider the non-minimal flavor mixing framework, we allow the off diagonal components of the squark mass matrices at the 10% level, which leads to the flavor mixing of order 0.1. We take these flavor mixing angles as free parameters at low energies. Now we consider the 6 × 6 squark mass matrix Mq in the super-CKM basis. In order to move the mass eigenstate basis of squark masses, we should diagonalize the mass matrix by rotation matrix Γ (q) G as where Γ (q) G is the 6 × 6 unitary matrix, and we decompose it into the 3 × 6 matrices as Γ (q) GR ) T in the following expressions: where we use abbreviations c L,R ij = cos θ L,R ij , s L,R ij = sin θ L,R ij , c θ = cos θ and s θ = sin θ. Here θ is the left-right mixing angle betweenb L andb R , which is discussed in Appendix A. It is remarked that we take s L,R 12 = 0 due to the degenerate squark masses of the first and second families as discussed in Appendix A.
The chargino (neutralino)-squark-quark interaction can be also discussed in the similar way.

FCNC of ∆F = 2
In our previous work [39], we have probed the high-scale SUSY, which is at 10-50 TeV scale, in the CP violations of K, B 0 and B s mesons. It is found that ǫ K is most sensitive to the SUSY even if the SUSY scale is at 50 TeV. The SUSY contributions for the time dependent CP asymmetries of B 0 and B s with ∆B = 1 are suppresses at the SUSY scale of 10 TeV. Furthermore, the SUSY contribution for the b → sγ process is also suppressed since the left-right mixing angle, which induces the chiral enhancement, is very small as discussed in Appendix A. Therefore, we discuss the neutral meson mixing P 0 -P 0 (P 0 = K, B 0 , B s , D), which are FCNCs with ∆F = 2.
In those FCNCs, the dominant SUSY contribution is given through the gluino-squark interaction. Then, the dispersive part of meson mixing M P 0 12 (P 0 = K, B 0 , B s ) are written as where M q,SUSY 12 are given by the squark mixing parameters in Eq.(8) and its explicit formulation is given in Appendices B and C.
At first, we discuss the ∆B = 2 process, that is, the mass differences ∆M B 0 and ∆M Bs , and the CP-violating phases φ d and φ s . In general, the contribution of the new physics (NP) to the dispersive part M q 12 is parameterized as where M q,NP

12
are the NP contributions. The generic fits for B 0 and B s mixing have given the constraints on (h q , σ q ) [40], where it is assumed that the NP does not significantly affect the SM tree-level charged-current interaction, that is, the absorptive part Γ q 12 is dominated by the decay b → ccs. At present, the NP contribution h q are 10-35% and 15-25% depending on σ q for B 0 and B s , respectively. Thus, we can expect the sizable NP contribution of O(20%). We will discuss whether the high-scale SUSY can fill in the magnitude of the present NP contribution of O(20%).
Next, we discuss ∆S = 2 process, ∆M K 0 and the CP-violating parameter in the K meson, ǫ K . By the similar parametrization in Eq.(11), the allowed region of (h K , σ K ) has been estimated in Ref. [40]. The NP contribution is at least 50% although there is the strong σ K dependence. Therefore, it is important to examine carefully the CP violating parameter ǫ K , which is given as follows: with A K 0 being the isospin zero amplitude in K → ππ decays. Here, M K 12 is the dispersive part of the K 0 -K 0 mixing, and ∆M K is the mass difference in the neutral K meson. The effects of ξ = 0 and φ ǫ < π/4 give suppression effect in ǫ K , and it is parameterized as κ ǫ and estimated by Buras and Guadagnoli [73] as: In the SM, the dispersive part M K 12 is given as follows, where s are the one-loop functions [74] and η cc,tt,ct are the QCD corrections [73]. Then, |ǫ SM K | is given in terms of the Wolfenstein parameters λ, ρ and η as follows: with Note that |ǫ SM K | depends on the non-perturbative parameterB K in Eq. (15). Recently, the error of this parameter shrank dramatically in the lattice calculations [75]. In our calculation we use the updated value by the Flavor Lattice Averaging Group [76]: Let us write down ǫ K as: where ǫ SUSY K is induced by the imaginary part of the gluino-squark box diagram, which is presented in Appendices B and C. Since s L(R) 12 vanishes in our scheme, ǫ SU SY K is given in the second order of the squark mixing s 23 . In addition to the above FCNC processes, the neutron EDM, d n arises through the cEDM of the quarks, d C q due to the gluino-squark mixing [61]- [66]. By using the QCD sum rules, d n is given as where d q and d C q denote the EDM and cEDM of quarks d C q defined in Appendix D. On the other hand, by using the chiral perturbation theory Therefore, the experimental upper bound [60] |d n | < 0.29 × 10 −25 ecm , provides us a strong constraint to the gluino-squark mixing. The HgEDM can also probe the gluino-squark mixing [68]. The QCD sum rule approach gives [77] d and the chiral Lagrangian method gives [78] d The experimental upper bound [67] |d constrains the gluino-squark mixing. At the last step, we discuss the charm sector, which is a promising field to probe for the new physics beyond the SM. The D 0 −D 0 mixing is now well established [79] as follows: where ∆M D and ∆Γ D are the differences of the masses and the decay widths between the mass eigenstates of the D meson, respectively, and Γ D is the averaged decay width of the D meson. Since the SM prediction of ∆M D at the short distance is much suppressed compared with the experimental value due to the bottom quark loop, the SUSY contribution may be enhanced.

Results and Discussions
Let us estimate the SUSY contribution of the low energy FCNC. We calculate the SUSY mass spectrum at Q 0 = 10, 50, 100, 1000 TeV and interpolate the each mass of the SUSY particle in the region of Q 0 = 10-1000 TeV. This approximation is satisfied within O(10%). Therefore, our numerical results should be taken with the ambiguity of O(10%). The mass spectrum at Q 0 = 10 TeV is presented in Appendix A. See Refs. [39], [58] for the mass spectrum at Q 0 = 50 TeV. Then, we have four mixing angles θ We reduce the number of parameters by taking sin θ L ij = sin θ R ij ≡ s ij for simplicity. In the numerical calculations, we scan the phases of Eq. (8) in the region of 0 ∼ 2π for fixed s ij , where the Cabibbo angle 0.22 and the large angle 0.5 are taken as the typical mixing. Other relevant input parameters such as quark masses m c , m b , the CKM parameters V us , V cb ,ρ,η and f B , f K , etc. have been presented in our previous paper Ref. [55], which are referred from UTfit Collaboration [80] and PDG [60]. There is no phase dependence in our predictions. It is found that the SUSY contributions in ∆M B 0 and ∆M Bs are at most 1.5% and 0.1% at mQ = 10 TeV, respectively. Namely, the high-scale SUSY cannot explain the NP contributions of h d = 0.1-0.35 and h s = 0.15-0.25, which have been discussed in Eq. (11). As mQ increases, the SUSY contributions of both ∆M B 0 and ∆M Bs decrease approximately with the power of 1/m 2Q . Thus, there is no hope to observe the SUSY contribution in the ∆B = 2 process for the high-scale SUSY. It should be noted that the SM predictions are comparable to these experimental data.
The related phenomena are the CP violation of the non-leptonic decays B 0 → J/ψK S and B s → J/ψφ. The recent experimental data of these phases are [27,34,35,36] sin φ d = 0.679 ± 0.020 , φ s = 0.07 ± 0.09 ± 0.01 , in which the contribution of the gluino-squark-quark interaction may be included. The NP contributions in φ d and φ s are expressed in terms of the parameters of Eq.(11) as [55]:

Neutral K meson system
At the second step, we examine the neutral K meson. We show the SUSY contributions of ∆M K 0 and ǫ K versus mQ ≡ Q 0 in Figure 2 On the other hand, ǫ K is very sensitive to the SUSY contribution up to 100TeV as seen in Figure 2(b). The plot is scattered due to the random phases of the squark mixing. The experimental data of ǫ K constrains the squark mixing and phases considerably. Actually, we have already pointed out that the SUSY contribution in ǫ K could be 40% and 35% at mQ = 10, 50 TeV, respectively [39]. It is found that this seizable SUSY contribution still exist up to 100 TeV in this work.
In the SM, there is only one CP violating phase. Therefore, the observed value of φ d in Eq. (27), should be correlated with ǫ K in the SM. According to the recent experimental results, it is found that the consistency between the SM prediction and the experimental data of sin φ d and ǫ K is marginal. This fact was pointed out by Buras and Guadagnoli [73] and called as the tension between ǫ K and sin φ d . Considering the effect of the SUSY contribution O(10%) in ǫ K , this tension can be relaxed even if mQ = 100 TeV. The precise determination of the unitarity triangle of B 0 is required in order to find the SUSY contribution of this level.
It is noted that the SUSY contribution of both ∆M K 0 and ǫ K also decrease approximately with the power of 1/m 2Q as mQ increases up to 1000 TeV.

The nEDM and HgEDM with ǫ K
The nEDM and HgEDM are also sensitive to the SUSY contribution [59,68]. The gluinosquark interaction leads to the cEDM of quarks, which give the nEDM as shown in Eqs. (19) and (20). We show the predicted nEDM versus mQ for the case of the QCD sum rules of  Eqs. (19) in Figure 3(a), where the upper bound of |d n | is shown by the red line. The plot is scattered due to the random phases of the squark mixing as well as in the case of ǫ K . We find that the contribution of EDM, d d and d u occupy around 25% of the neutron EDM. The SUSY contribution is close to the experimental upper bound up to 50TeV. Since the predicted nEDM depends on the phases of the squark mixing matrix significantly, we plot the nEDM versus |ǫ SUSY K | in Figure 3(b). It is found that the predicted nEDM is roughly proportional to |ǫ SUSY K |. If the SUSY contribution is the level of O(10%) for ǫ K , the nEDM is expected to be discovered in the region of 10 −27 -10 −26 ecm. On the other hand, if the nEDM is not observed above 10 −28 ecm, the SUSY contribution of ǫ K is below a few %. Thus, there is the correlation between d n and ǫ SUSY K . We also show the predicted HgEDM versus mQ for the case of the QCD sum rules of Eq. (22) in Figure 4(a), where the upper bound of |d Hg | is shown by the red line. The SUSY contribution is close to the experimental upper bound up to 200TeV, which is much higher than the one of the nEDM. In Figure 4(b), we plot the HgEDM versus |ǫ SUSY K |. It is found that the experimental upper bound of the HgEDM excludes completely |ǫ SUSY K | which is inconsistent with the experimental data. If the SUSY contribution is the level of O(10%) for ǫ K , the nEDM is expected to be discovered in the region of 10 −27 -10 −26 ecm. If the HgEDM is not observed above 10 −29 ecm, the SUSY contribution of ǫ K is below a few %. Thus, the mercury EDM gives more significant information for the gluino-squark interaction compared with the neutron EDM.
However, these correlations strongly depend on the assumptions of θ L 23 = θ L 13 and θ L ij = θ R ij . The deviation from these relations destroys these correlations. For instance, for the case of is much suppressed whereas the nEDM and HgEDM are still sizable. On the other hand, if θ L ij ≫ θ R ij or θ L ij ≫ θ R ij is realized, the cEDMs are suppressed because they require the chirality flipping. In conclusion, the careful studies of the mixing angle relations are required to test the correlations between EDMs and ǫ SUSY K . We should comment on the hadronic model dependence of our numerical result. For both nEDM and HgEDM, we show the numerical result by using the hadronic model of the QCD sum rules in Eqs. (19) and (22). We have also calculated the EDMs by using the hadronic model of the chiral perturbation theory in Eqs. (20) and (23). For the neutron EDM, the prediction of the chiral perturbation theory is larger than the one of the QCD sum rule at most of factor two. However, for the mercury EDM, the prediction of the QCD sum rule is more than three times larger compared with the one of the chiral perturbation theory. Thus, predicted EDMs have the ambiguity with the factor 2 − 3 from the hadronic model.

D-D mixing
Since the SM prediction of ∆M D at the short distance is O(10 −18 ) GeV, which is very small compared with the experimental value due to the bottom quark loop, it is important to estimate the SUSY contribution of ∆M D . The mixing angle θ L(R) ij also appears in the uptype squark mixing matrix whereas the down-type squark mixing matrix contributes to K 0 , B 0 and B s meson systems induced by the gluino-squark-quark interaction.
We show the SUSY component of ∆M D and x D versus mQ for s 13 = s 23 = 0.22, 0.5 in Figure 5. At the SUSY scale of 10 TeV, the SUSY component may be comparable to the observed value. Although the accurate estimate of the long-distance effect is difficult, Cheng and Chiang estimated x D of order 10 −3 from the two body hadronic modes [81]. This obtained value is consistent with the experimental one. Therefore, we should take into account the long-distance effect properly in order to constrain the SUSY contribution from ∆M D .
Before closing the presentation of the numerical results, we add a comment on the other gaugino contribution. There are additional contributions to the FCNC induced by chargino exchanging diagrams. The chargino contribution to the gluino one is approximately 10% in the above numerical study of ∆F = 2. Thus, the chargino contributions are the sub-leading ones.

Summary
We discussed the sensitivity of the high-scale SUSY at 10-1000 TeV in the B 0 , B s and K 0 meson systems. Furthermore, we have also discussed the sensitivity to the D-D mixing, the neutron EDM and the mercury EDM. In order to estimate the contribution of the squark flavor mixing to these FCNC, we calculate the squark mass spectrum, which is consistent with the recent Higgs discovery.
The SUSY contributions in ∆M B 0 and ∆M Bs are at most 1.5% and 0.1% at mQ = 10 TeV, respectively. As mQ increases, the SUSY contributions of both ∆M B 0 and ∆M Bs decrease approximately with the power of 1/m 2Q . Therefore, the SUSY scale increases to more than 10 TeV, no signal of the SUSY is expected. On the other hand, the SUSY contribution in ∆M K 0 can be comparable to the experimental value in the case of s 13 = s 23 = 0.5 whereas it is suppressed in the case of s 13 = s 23 = 0.22 at mQ = 10 TeV. Furthermore, the SUSY contribution in ǫ K could be large, around 40% in the region of the SUSY scale 10-100 TeV. By considering the effect of the SUSY contribution O(10%) in ǫ K , the tension between ǫ K and sin φ d can be relaxed even if the SUSY scale is 100 TeV.
The neutron EDM and the mercury EDM are also sensitive to the SUSY contribution induced by the gluino-squark interaction. The |d n | is expected to be close to the experimental upper bound even if the SUSY scale is 50 TeV. The predicted nEDM is roughly proportional to |ǫ SUSY K |. If the SUSY contribution is the level of O(10%) for ǫ K , the |d n | is expected to be discovered in the region of 10 −27 -10 −26 cm. For the |d Hg |, the SUSY contribution is close to the experimental upper bound up to 200TeV, which is much higher than the one of the nEDM. If the HgEDM is not observed above 10 −29 cm, the SUSY contribution of ǫ K is below a few %. Thus, the mercury EDM gives more significant information for the gluinosquark interaction compared with the neutron EDM. It may be important to give a comment that these predictions depend strongly on the assumptions of θ L 23 = θ L 13 and θ L ij = θ R ij . The deviation from these relations destroys these correlations. In conclusion, the careful studies of the mixing angle relations are required to test the correlations between EDMs and ǫ SUSY K .
The predicted EDMs have also the ambiguity with the factor 2 − 3 from the hadronic model.
Since the SM prediction of ∆M D at the short distance is O(10 −18 ) GeV, which is very small compared with the experimental value, it is important to estimate the SUSY contribution of ∆M D .
In conclusion, the more detailed studies of K 0 meson system, the EDMs of the neutron and mercury are required in order to probe the high-scale SUSY at 10-1000 TeV.
In the framework of the MSSM, one obtains the SUSY particle spectrum which is consistent with the observed Higgs mass. The numerical analyses have been given in Refs. [69,70]. At the SUSY breaking scale Λ, the quadratic terms in the MSSM potential is given as The mass eigenvalues at the H 1 andH 2 ≡ ǫH * 2 system are given Suppose that the MSSM matches with the SM at the SUSY mass scale Q 0 ≡ m 0 . Then, the smaller one m 2 − is identified to be the mass squared of the SM Higgs H with the tachyonic mass. The larger one m 2 + is the mass squared of the orthogonal combination H, which is decoupled from the SM at Q 0 , that is, m H ≃ Q 0 . Therefore, we have with which leads to the mixing angle between H 1 andH 2 , β as follows: Thus, the Higgs mass parameter m 2 is expressed in terms of m 2 1 , m 2 2 and tan β: Below the Q 0 scale, in which the SM emerges, the scalar potential is the SM one as follows: Here, the Higgs coupling λ is given in terms of the SUSY parameters at the leading order as and h t is the top Yukawa coupling of the SM. The parameters m 2 and λ run with the SM Renormalization Group Equation down to the electroweak scale Q EW = m H , and then give It is easily seen that the VEV of Higgs, H is v, and H = 0, taking account of H 1 = v cos β and H 2 = v sin β, where v = 246 GeV. Let us fix m H = 125 GeV, which gives λ(Q 0 ) and m 2 (Q 0 ). This experimental input constrains the SUSY mass spectrum of the MSSM. We consider the some universal soft breaking parameters at the SUSY breaking scale Λ as follows: Therefore, there is no flavor mixing at Λ in the MSSM. However, in order to consider the non-minimal flavor mixing framework, we allow the off diagonal components of the squark mass matrices at the 10% level, which leads to the flavor mixing of order 0.1. We take these flavor mixing angles as free parameters at low energies. Now, we have the SUSY five parameters, Λ, tan β, m 0 , m 1/2 , A 0 , where Q 0 = m 0 . In addition to these parameters, we take µ = Q 0 . Inputing m H = 125 GeV and taking m H ≃ Q 0 , we can obtain the SUSY spectrum for the fixed Q 0 and tan β.
We present the SUSY mass spectrum at Q 0 = 10 TeV. The input parameter set and the obtained SUSY mass spectra at Q 0 are summarized in Table 1, where we use m t (m t ) = 163.5 ± 2 GeV [60,80]. These parameter sets are easily found from the work in Ref. [69].  Table 1: Input parameters at Λ and the obtained SUSY spectra at Q 0 = 10 TeV.
As seen in Table 1, the first and second family squarks are degenerate in their masses, on the other hand, the third ones split due to the large RGE's effect. Therefore, the mixing angle between the first and second family squarks vanishes, but the mixing angles between the first-third and the second-third family squarks are produced at the Q 0 scale. The left-right mixing angle betweenb L andb R is given as which is very small, O(0.01) at 10 TeV. The lightest squark is the right-handed stop and the lightest gaugino is the Bino.

Appendix B : Squark contribution in ∆F = 2 process
The ∆F = 2 effective Lagrangian from the gluino-sbottom-quark interaction is given as [82]: where with (P, Q, q) = (B 0 , b, d), (B s , b, s), (K 0 , s, d). The L, R denote (1 ±γ 5 )/2, and a, b are color indices. Then, the P 0 -P 0 mixing, M 12 , is written as: The hadronic matrix elements are given in terms of the non-perturbative parameters B i as: where The Wilson coefficients for the gluino contribution in Eq. (39) are written as [82]: where (λ (d) Here we take (i, j) = (1, 3), (2, 3), (1, 2) which correspond to B 0 , B s , and K 0 mesons, respectively. The loop functions are given as follows: • If xg I = xg J , Taking account of the case that the gluino mass is much smaller than the squark mass scale Q 0 , the effective Wilson coefficients are given by using the RGEs for higher-dimensional operators in Eq.(39) at the leading order of QCD as follows: where 6 15 α s (mg) α s (m t ) 6 21 α s (m t ) α s (m b ) 6 23 , For the parameters B On the other hand, we use the most updated values forB For the paremeters B K i (i = 2 − 5), we use following values [84], B and we take recent value of Eq.(17) for deriving B

Appendix D : EDM and Chromo-EDM of quarks
We present the EDM of the strange quark from the gluino contribution as the typical example [82]: where A γ22 s (Q 0 ) = Q s α s (mg) 4π 22 3 + m s (λ (d) On the other hand, the chromo-EDM (cEDM) of the strange quark from gluino contribution is given as: where A g22 s (Q 0 ) = − α s (mg) 4π Including the RGE effect of QCD [87], the cEDM of the strange quark is given as 14 21 α s (m t ) α s (m b ) 14 23 α s (m b ) α s (2GeV) 14 25 .
The EDMs and cEDMs of the down-and up-quarks induced by the gluino interaction are also given by the similar formulas.