Tensor gauge boson dark matter extension of the electroweak sector

The existence of dark matter is explained by a new, massive, neutral, non-symmetric, rank-2 tensor gauge boson (Z${}_{\mu \nu }$-boson). The Z${}_{\mu \nu }$-boson can be predicted by the tensor gauge boson extension of the Electro Weak (EW) theory, proposed by Savvidy (Phys Lett B 625:341, 2005). The non-symmetric rank-2 tensor Z${}_{\mu \nu }$ can be decomposed into a symmetric (Z${}_{\left(\mu \nu \right)}$) and anti-symmetric (Z${}_{\left[\mu \nu \right]}$) part. Based on the non-Lagrangian formulation for the free sector of the R${}_2$-theory proposed recently by Criado et al. (Phys Rev D 102:125031, arXiv:2010.02224, 2020), our massive anti-symmetric tensor field Z${}_{\left[\mu \nu \right]}$ corresponds to the massive symmetric spinor field Z${}_{\alpha \beta \gamma \delta }$ in the (2,0) irrep. For the massive Z${}_{\alpha \beta \gamma \delta }$ with the Z${}_2$-symmetric Higgs portal couplings to a Standard Model (SM) particle, we compute the self-annihilation cross-section of the Z${}_{\alpha \beta \gamma \delta }$ dark matter and calculate its relic abundance. We also study the SM-SM particle scattering due to the exchange of the massive-Z${}_{\left(\mu \nu \right)}$ symmetric field at a high energy scale. This proposition may have far reaching applications in astrophysics and cosmology.