Imprint of quark flavor violating SUSY in h(125) decays at future lepton colliders

We study the CP-even neutral Higgs boson decays $h \to c \bar{c}, b \bar{b}, b \bar{s}, \gamma \gamma, g g$ in the Minimal Supersymmetric Standard Model (MSSM) with general quark flavor violation (QFV), identifying the h as the Higgs boson with a mass of 125 GeV. We compute the widths of the h decays to $c \bar c, b \bar b, b \bar s (s \bar b)$ at full one-loop level. For the loop-induced h decays to photon photon and gluon gluon we compute the widths at NLO QCD level. {\it For the first time}, we perform a systematic MSSM parameter scan including Supersymmetric (SUSY) QFV parameters respecting all the relevant constraints, i.e. theoretical constraints from vacuum stability conditions and experimental constraints, such as those from K- and B-meson data, electroweak precision data, and the 125 GeV Higgs boson data from recent LHC experiments, as well as the limits on SUSY particle masses from the LHC experiment. We also take into account the expected SUSY particle mass limits from the future HL-LHC experiment in our analysis. {\it In strong contrast to} the usual studies in the MSSM with quark flavor conservation, we find that the deviations of these MSSM decay widths from the Standard Model (SM) values can be quite sizable and that there are significant correlations among these deviations. All of these sizable deviations in the h decays are due to (i) large scharm-stop mixing and large scharm/stop involved trilinear couplings $T_{U23}, T_{U32}, T_{U33}$, (ii) large sstrange-sbottom mixing and large sstrange/sbottom involved trilinear couplings $T_{D23}, T_{D32}, T_{D33}$ and (iii) large bottom Yukawa coupling $Y_b$ for large $\tan\beta$ and large top Yukawa coupling $Y_t$. Future lepton colliders such as ILC, CLIC, CEPC, FCC-ee and MuC can observe such sizable deviations from the SM at high signal significance {\it even after} the failure of SUSY particle discovery at the HL-LHC. In case the deviation pattern shown here is really observed at the lepton colliders, then it would strongly suggest the discovery of QFV SUSY (the MSSM with general QFV).