Similar results are found for the W $^{±}$Z $^{0}$, Z $^{0}$Z0 and h $^{0}$h0 final states. Thus a small v$_{L}$ required by the tiny neutrino masses naturally suppresses the triplet non-leptonic decays channels, such that our model can avoid the constraints from the PAMELA anti-proton data. The Yukawa interaction term ℓ c $_{L}$iτ$_{2}$ Δ$_{L}$ ℓ$_{L}$ requires that the couplings δ ±± L l $^{∓}$l$^{∓}$, δ 0 $_{L}$νν and δ ± $_{L}$l $^{∓}$ν are the same within each generation in the flavor basis. If the positron excesses reported by the PAMELA and Fermi-LAT are indeed from the DM decay through triplets, there must exist associating high energy neutrino flux which can be detected by the future experiments. The SU (2) triplet contains doubly as well as singly charged scalars. Besides the ordinary ICS and FSR caused by the final state charged leptons, the charged triplet scalars will emit gamma-rays through VIB processes in the cascade decay S$_{D}$ → δ ±± L δ $^{∓∓}$γ as shown in Fig. 2. The photon multiplicity for a decay process S → XX is defined as [19] where x = 2 E$_{γ}$$_{/}$√$_{s}$ and √$_{s}$ = m$_{S}$ is the center-of-mass energy. The radiation is dominated by the collinear photon emission case, which can be approximated by with F ( x ) = (1 + (1 − x ) $^{2}$) /x for fermions and (1 − x ) /x for bosons. For the decay process S$_{D}$ → δ ±± L δ ∓∓ L , one has s = m 2 D and m$_{X}$ = m$_{δ}$$_{L}$ . For the sequential decay δ ±± L → ℓ $^{±}$ℓ$^{±}$, s and m$_{X}$ are replaced by m$_{δ}$$_{L}$ and m$_{ℓ}$ respectively. For doubly charged particles there is a factor of four enhancement relative to that of singly charged ones. The final positron and gamma-ray energy spectra of cascade decays, such as S$_{D}$ → δ ±± L δ ∓∓ L → 4 ℓ , depend on the 8 dN$_{XX}$ dx ≈ αQ 2 π F ( x ) log$^{(}$ s (1 − x ) m 2 X ) (15) dN$_{XX}$ dx ≡ 1 σ$_{S}$$_{→}$$_{XX}$ dσ$_{S}$$_{→}$$_{XXγ}$ dx , (14) FIG. 2: Feynman diagrams for gamma-ray emission through internal bremsstrahlung. (Left) final state radiation (FSR) from final state charged leptons. (Right) virtual internal bremsstrahlung (VIB) from doubly charged triplet scalars. ℓ − ℓ − ℓ + ℓ + δ −− δ ++ S$_{D}$ ℓ − ℓ − ℓ + ℓ + δ −− δ ++ S$_{D}$ γ