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Indirect and direct signatures of Higgs portal decaying vector dark matter for positron excess in cosmic rays

We investigate the indirect signatures of the Higgs portal $U(1)_X$ vector dark matter (VDM) $X_μ$ from both its pair annihilation and decay. The VDM is stable at renormalizable level by $Z_2$ symmetry, and thermalized by Higgs-portal interactions. It can also decay by some nonrenormalizable operators with very long lifetime at cosmological time scale. If dim-6 operators for VDM decays are suppressed by $10^{16}$ GeV scale, the lifetime of VDM with mass $\sim$ 2 TeV is just right for explaining the positron excess in cosmic ray recent observed by PAMELA and AMS02 Collaborations. The VDM decaying into $μ^+ μ^-$ can fit the data, evading various constraints on cosmic rays. We give one UV-complete model as an example. This scenario for Higgs portal decaying VDM with mass around $\sim2$ TeV can be tested by DM direct search at XENON1T and at the future colliders by measuring the Higgs self-couplings.