Intrigued by some features of a small but significant fraction of the
multi-muon events recently published by the CDF collaboration, we show an
explicit attempt to describe them in terms of a light scalar singlet ϕ
which communicates with the standard quarks either through a heavy scalar or a
heavy fermion exchange. As suggested in arXiv:0810.7530, the singlet ϕ has
a chain decay into a final state made of four ττˉ pairs. We can
simulate most of the muon properties of the selected sample of events. Some of
these properties adhere rather well to the already published data; others
should allow a decisive test of the proposed interpretation. Assuming that the
test is positively passed, we show how the PAMELA excess can be fitted by the
annihilation of a TeV Dark Matter particle that communicates with the Standard
Model via the new light singlet(s).Comment: 19 pp, v2: small changes, agrees with the published versio