  Recently evidence for gamma ray lines at energies of approximately 111 and
128 GeV has been found in Fermi-LAT data from the center of the galaxy and from
unassociated point sources. Many explanations in terms of dark matter particle
pairs annihilating to gamma gamma and gamma Z have been suggested, but these
typically require very large couplings or mysterious coincidences in the masses
of several new particles to fit the signal strength. We propose a simple novel
explanation in which dark matter is part of a multiplet of new states which all
have mass near 260 GeV as a result of symmetry. Two dark matter particles
annihilate to a pair of neutral particles in this multiplet which subsequently
decay to gamma gamma and gamma Z. For example, one may have a triplet of
pseudo-Nambu-Goldstone bosons, charged pions and a neutral pion, where the
charged pions are stabilized by their charge under a new U(1) symmetry and the
slightly lighter neutral pion state decays to gamma gamma and gamma Z. The
symmetry structure of such a model explains the near degeneracy in masses
needed for the resulting photons to have a line-like shape and the large
observed flux. The tunable lifetime of the neutral state allows such models to
go unseen at direct detection or collider experiments that can constrain most
other explanations. However, nucleosynthesis constraints on the neutral pion
lifetime fix a minimum necessary coupling between the new multiplet and the
Standard Model. The spectrum is predicted to be not a line but a box with a
width of order a few GeV, smaller than but on the order of the Fermi-LAT
resolution.
