The decays \( {h}^0\to b\overline{b} \) and \( {h}^0\to c\overline{c} \) in the light of the MSSM with quark flavour violation

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