  Among the different scenarios of New Physics, those with an extended Higgs
sector are examined with a lot of attention. Recent experimental observations
of several anomalies in flavour physics with respect to expectations of the
Standard Model further motivate the effort of phenomenologists. First,
informations about the $R_{D_s}$ ratio, a test of lepton flavour universality
equivalent to $R_D$, already measured, but with the $s$ quark as spectator, are
awaited in coming years to constrain the corner of an extended Higgs sector
with charged doublets. On another side, leptonic widths of pseudoscalar
quarkonia are particularly interesting to test an extended Higgs sector with a
light CP-odd Higgs boson singlet, through the study of its mixing with
quarkonia states. Hadronic parameters entering those processes have to be
determined from lattice QCD with enough confidence on the control of systematic
errors. We report on the very first step of a long-term program tackled with
${\rm N_f}=2$ Wilson-Clover fermions to put relevant constraints on extensions
of the Higgs sector: extraction of decay constants of $D^*_s$, $\eta_c$,
$\eta_c(2S)$, $J/\psi$ and $\psi(2S)$ with lattice ensembles provided by the
CLS effort, considering 2 lattice spacings and a large range of pion masses to
estimate cut-off effects and extrapolate results to the chiral limit.
