  We investigate the viability of extending the Standard Model with $S_1$ and
$S_3$ scalar leptoquarks when the flavour structure is parametrized in terms of
Froggatt-Nielsen charges. In contrast to a similar analysis with a vector
leptoquark, we find essentially two solutions for the charges that fit the
experimental constraints, which are dominated by the current tensions in $B$
decays. These two scenarios differ in their estimate of the anomalous magnetic
moment of the muon, $(g-2)$, but they both predict sizeable contributions to
$\tau\to\mu\gamma$, $\bar B_s\to\tau^\pm\mu^\mp$ and $B^+\to K^+\tau^+\mu^-$
decays, whose branching ratios are close to the current experimental limits.

High Energy Physics - Phenomenology