We consider a weakly interacting massive particle (WIMP) dark matter (DM) annihilating into all possible Standard Model (SM) particle pairs, including the SM neutrinos, via -wave processes and derive the branching ratio independent upper limit on the total annihilation cross-section using the data of CMB, gamma-ray, cosmic-ray and several neutrino observations. For conservative choices of all relevant astrophysical parameters, we obtain upper limits of on the total for the WIMP mass range , thus making the entire mass range consistent with the observed relic density. An important input that goes into our analysis is the assumption that thermal WIMPs can have significant coupling to the SM neutrinos.

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