MeV gamma rays from $Q$-ball decay

We study the supersymmetric $Q$ balls which decay at present and find that they create a distinctive spectrum of gamma rays at around O(10) MeV. The charge of the $Q$ ball is lepton numbers in order for the lifetime to be as long as the present age of the Universe, and the main decay products are light leptons. However, as the charge of the $Q$ ball decreases, the decay channel into pions becomes kinematically allowed towards the end of the decay, and the pions are produced at rest. Immediately, ${\pi }^0$ decays into two photons with the energy of 67.5 MeV, half the pion mass, which exhibits a unique emission line. In addition, ${\pi }^{\pm }$ decay into ${\mu }^{\pm }$, which further decay with emitting internal bremsstrahlung, whose spectrum has a sharp cutoff at $\sim 50\mathrm{MeV}$. If the observations find these peculiar features of the gamma-ray spectrum in the future, it could be a smoking gun of the supersymmetric $Q$-ball decay at present.

Figure 1

Evolution of the $Q$-ball charge is shown in the purple arrow. We show the charge at the formation (5), that for the decay at present (8), that when the transformation from the new-type into the gauge-mediation type takes place (11), and that when the decay channel to pions opens (12) as the function of $m_{3/2}$, for ${\varphi }_0=0.3M_{\mathrm{P}}$ and $|K|=0.02$, in blue, red, magenta, and green lines, respectively.

Figure 2

Photon spectra from the $Q$-ball decay. We display the spectra (13), (17), and (19) in blue, green, and red lines, respectively. Observations of the Galactic diffuse gamma-ray emission are also shown in cyan (COMPTEL) and gray points (EGRET).

Figure 3

Extragalactic photon spectra from the $Q$-ball decay. We display the spectra (22) in blue, (24) in green, and (27) in red lines. Solid and dashed lines denote the cases with $\xi =0.1$ and 0.5, respectively. Observations of the extragalactic diffuse gamma-ray emission are also shown in cyan (COMPTEL) and gray (EGRET) points, and in orange lines (SMM).