Assuming supersymmetry exists and a neutralino is stable, it's often seen as a leading dark matter candidate. What would be expected from the interaction of a neutralino and its anti-particle? Has there been any unambiguous detection of such an interaction?
Dear Michael, neutralino carries no conserved charges that can take arbitrarily large values (and no spin) and it is identical with its antiparticle, much like in the case of photons. That still allows two neutralinos to annihilate.
Neutralinos only carry a "1" charge under the $Z_2$ symmetry called R-parity. This means that the number of neutralinos must be conserved modulo 2. This is compatible with the annihilation of pairs of neutralinos. The annihilation of neutralino pairs was important when the Universe was young. With the right TeV-like mass and MSSM-like annihilation cross section, models may predict that the dark matter density has been diluted exactly to the observed value (plus minus a few orders of magnitude which is still a nontrivial agreement).
The products of this annihilation are most typically two photons (but two gluons or gamma-Z are also possible) and the resulting gamma rays are so rare in the present era that it's hard to observe them. However, people have still tried to argue that they should be observable, at least under various assumptions:
As far as I know, none of those gamma rays has been observed as of today.
It could be that the neutralino is a Majorana fermion. The $Z_2$ structure could be a signature of a Majorana fermion. The Majorana fermion is the charge conjugate fermion of the form $\psi_c~=~\gamma^2\psi^*$ with $\psi_c~=~\psi$. This has some interesting statistics. For fermions the exchange of a wave function introduces a negative sign. The additional constraint that $\psi~=~\gamma^2\psi^*$, means that the $\gamma^2$ introduces a braid structure into the exchange statistics of Majorana fermions. If this is the case the neutralino is its own anti-particle. The annihilation of the neutralino particle could then be a type of decay process.