We present a study of the isospin-breaking corrections to pseudoscalar 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 $(m_d - m_u)/\Lambda_{QCD}$ and $\alpha_{em}$, where $m_f$ 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 $\epsilon_\gamma(\mathrm{\overline{MS}}, 2\,\mathrm{GeV})$, $\epsilon_{\pi^0}$, $\epsilon_{K^0}(\mathrm{\overline{MS}}, 2\,\mathrm{GeV})$; for the light quark masses $(m_d - m_u)(\mathrm{\overline{MS}}, 2\,\mathrm{GeV})$, $(m_u / m_d)(\mathrm{\overline{MS}}, 2\,\mathrm{GeV})$ and for the flavour symmetry breaking parameters $R(\mathrm{\overline{MS}}, 2\,\mathrm{GeV})$ and $Q(\mathrm{\overline{MS}}, 2\,\mathrm{GeV})$.

Hadron Structure