  We present a study of the isospin-breaking (IB) corrections to pseudoscalar
(PS) meson masses using the gauge configurations produced by the ETM
Collaboration with $N_f=2+1+1$ dynamical quarks at three lattice spacings
varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of
the path integral in powers of the small parameters $(\widehat{m}_d -
\widehat{m}_u)/\Lambda_{QCD}$ and $\alpha_{em}$, where $\widehat{m}_f$ is the
renormalized quark mass and $\alpha_{em}$ the renormalized fine structure
constant. We obtain results for the pion, kaon and $D$-meson mass splitting;
for the Dashen's theorem violation parameters
$\epsilon_\gamma(\overline{\mathrm{MS}}, 2~\mbox{GeV})$, $\epsilon_{\pi^0}$,
$\epsilon_{K^0}(\overline{\mathrm{MS}}, 2~\mbox{GeV})$; for the light quark
masses $(\widehat{m}_d - \widehat{m}_u)(\overline{\mathrm{MS}}, 2~\mbox{GeV})$,
$(\widehat{m}_u / \widehat{m}_d)(\overline{\mathrm{MS}}, 2~\mbox{GeV})$; for
the flavour symmetry breaking parameters $R(\overline{\mathrm{MS}},
2~\mbox{GeV})$ and $Q(\overline{\mathrm{MS}}, 2~\mbox{GeV})$ and for the strong
IB effects on the kaon decay constants.
