  We recently proposed to cross-correlate the diffuse extragalactic gamma-ray
background with the gravitational lensing signal of cosmic shear. This
represents a novel and promising strategy to search for annihilating or
decaying particle dark matter (DM) candidates. In the present work, we
demonstrate the potential of a tomographic-spectral approach: measuring the
cross-correlation in separate bins of redshift and energy significantly
improves the sensitivity to a DM signal. Indeed, the technique proposed here
takes advantage of the different scaling of the astrophysical and DM components
with redshift and, simultaneously, of their different energy spectra and
different angular extensions. The sensitivity to a particle DM signal is
extremely promising even when the DM-induced emission is quite faint. We first
quantify the prospects of detecting DM by cross-correlating the Fermi Large
Area Telescope (LAT) diffuse gamma-ray background with the cosmic shear
expected from the Dark Energy Survey. Under the hypothesis of a significant
subhalo boost, such a measurement can deliver a 5-sigma detection of DM, if the
DM particle is lighter than 300 GeV and has a thermal annihilation rate. We
then forecast the capability of the European Space Agency Euclid satellite
(whose launch is planned for 2020), in combination with an hypothetical future
gamma-ray detector with slightly improved specifications compared to current
telescopes. We predict that the cross-correlation of their data will allow a
measurement of the DM mass with an uncertainty of a factor of 1.5-2, even for
moderate subhalo boosts, for DM masses up to few hundreds of GeV and thermal
annihilation rates.
