  We study sub-GeV dark matter (DM) particles that may annihilate or decay into
Standard Model (SM) particles producing an electron-positron cascade that
results in positronium bound state formation after energy losses. This
comprises an exotic injection component in the Milky Way that leaves an imprint
in the 511 keV photon line due to the decay of positronium into two photons. In
this work, we use $\sim16$~yr of SPI spectrometer data from the INTEGRAL
satellite to constrain DM properties. We include three major novelties in our
study: i) we account for positron diffusion and propagation, as well as
positron losses due to annihilation in flight and other energy losses, ii) we
include the free electron density suppression away from the Galactic plane and
iii) we derive limits for decaying DM for the first time with SPI data. We show
that the predicted longitude and latitude profiles change significantly for
different DM masses, contrary to what has previously been assumed. In addition,
we find that the limits derived from this new set of SPI data are the strongest
on sub-GeV DM to date across almost the entire DM mass range considered (from
MeV to a few GeV), excluding cross-sections down to $10^{-32}$ cm$^3$ s$^{-1}
\, \, (\text{for} \,\, m_{\chi}\sim1 \,\text{MeV}) \lesssim \langle \sigma
v\rangle \lesssim10^{-26}$ cm$^3$ s$^{-1} \, \, (m_{\chi}\sim5\,\text{GeV})$
and lifetimes up to $10^{29}\, \textrm{s} \,
(m_{\chi}\sim1\,\text{MeV})\lesssim \tau \lesssim 10^{27}\,\textrm{s}$
($m_{\chi}\sim5$~GeV), whilst considering best-fit cosmic ray (CR) propagation
and diffusion parameters. These limits surpass even the most stringent
complementary cosmological and astrophysical limits over most of the mass range
considered.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena