B$_s$ → μ$^+$μ$^-$ in a two-Higgs-doublet model with flavour-changing up-type Yukawa couplings

We present a Two-Higgs-Doublet Model in which the structure of the quark
Yukawa matrices is governed by three spurions breaking the flavour symmetries of the quark
Yukawa sector. The model naturally suppresses flavour-changing neutral current (FCNC)
amplitudes in the down-type sector, but permits sizable FCNC couplings in the up sector.
We calculate the branching ratio of Bs → μ+μ− to leading and next-to-leading order of
QCD for the case with FCNC couplings of the heavy neutral Higgs bosons to up-type quarks
and verify that all counterterms follow the pattern dictated by the spurion expansion of the
Yukawa matrices. We find correlations between Bs → μ$^+$μ$^-$, b → sγ, and the Higgs masses.
The B$_s$ − $\overline{B}$$_s$ mixing amplitude is naturally suppressed in the model but can probe a portion
of the parameter space with very heavy Higgs bosons.