  We present our preliminary results concerning the charged/neutral pion mass
difference $M_{\pi^{+}} - M_{\pi^{0}}$ at order $\mathcal{O}(\alpha_{em})$ in
the QED interactions, and for $M_{\pi^{+}} - M_{\pi^{0}}$ at order
$\mathcal{O}\left( (m_{d}-m_{u})^{2}\right)$ in the strong isospin-breaking
term. The latter contribution provides a determination of the $\rm{SU}(2)$
chiral perturbation theory low-energy constant $\ell_{7}$, whose present
estimate is affected by a rather large uncertainty. The disconnected
contributions appearing in the diagrammatic expansion of $M_{\pi^{+}} -
M_{\pi^{0}}$, being very noisy, are notoriously difficult to evaluate and have
been neglected in our previous calculations. By making use of twisted mass
Lattice QCD simulations and adopting the RM123 method, we will show that taking
profit from our recently proposed rotated twisted-mass (RTM) scheme, tailored
to improve the signal on these kinds of observables, it is possible to evaluate
the disconnected diagrams with good precision. For the QED induced pion mass
difference, we obtain, after performing the extrapolation towards the continuum
and thermodynamic limit and at the physical point, the preliminary value
$M_{\pi^{+}}-M_{\pi^{0}} = 4.622~(95)~{\rm MeV}$, that is in good agreement
with the experimental result. For the determination of the low-energy constant
$\ell_{7}$, our result $\ell_{7} = 2.5~(1.4)\times 10^{-3}$, which is limited
so far to a single lattice spacing, is in agreement and improves
phenomenological estimates.
