Quark-flavour violating Higgs decays to charm and bottom pairs in the MSSM

We calculate the decay width of $h^0\to b\bar{b}$ in the Minimal Supersymmetric Standard Model (MSSM) with quark-flavour violation (QFV) at full one-loop level. The effect of $\tilde{c}-\tilde{t}$ mixing and $\tilde{s}-\tilde{b}$ mixing is studied taking into account the constraints from the B-meson data. We discuss and compare in detail the decays $h^0 \to c \bar{c}$and$h^0 \to b \bar{b}$ within the framework of the perturbative mass insertion technique using the Flavour Expansion Theorem. The deviation of both decay widths from the Standard Model results can be quite large. While in $h^0 \to c \bar{c}$ it is almost entirely due to the flavour violating part of the MSSM, in $h^0\to b\bar{b}$ it is mainly due to the flavour conserving part. Nevertheless, $\mathrm{\Gamma }(h^0\to b\bar{b})$ can fluctuate up to $\sim 7\mathrm{\%}$ due to QFV chargino exchange with large $\tilde{c}-\tilde{t}$ mixing. due to QFV chargino exchange with large $\tilde{c}-\tilde{t}$ mixing.