  We study the decay signatures of Asymmetric Dark Matter (ADM) via higher
dimension operators which are responsible for generating the primordial dark
matter (DM) asymmetry. Since the signatures are sensitive both to the nature of
the higher dimension operator generating the DM asymmetry and to the sign of
the baryon or lepton number that the DM carries, indirect detection may provide
a window into the nature of the mechanism which generates the DM asymmetry. We
consider in particular dimension-6 fermionic operators of the form ${\cal
O}_{ADM} = X {\cal O}_{B-L}/M^2$, where ${\cal O}_{B-L} = u^c d^c d^c,~\ell
\ell e^c,~q \ell d^c$ (or operators related through a Hermitian conjugate) with
the scale $M$ around or just below the GUT scale. We derive constraints on ADM
particles both in the natural mass range (around a few GeV), as well as in the
range between 100 GeV to 10 TeV. For light ADM, we focus on constraints from
both the low energy gamma ray data and proton/anti-proton fluxes. For heavy
ADM, we consider $\gamma$-rays and proton/anti-proton fluxes, and we fit
$e^+/e^-$ data from AMS-02 and H.E.S.S. (neglecting the Fermi charged particle
fluxes which disagree with AMS-02 below 100 GeV). We show that, although the
best fit regions from electron/positron measurement are still in tension with
other channels on account of the H.E.S.S. measurement at high energies,
compared to an ordinary symmetric dark matter scenario, the decay of DM with a
primordial asymmetry reduces the tension. Better measurement of the flux at
high energy will be necessary to draw a definite conclusion about the viability
of decaying DM as source for the signals.
