We employ the two independent Casimir operators of the Poincaré group, the squared fourmomentum, p 2 , and the squared Pauli-Lubanski vector, W 2 , in the construction of a covariant mass-m, and spin-3 2 projector in the four-vector-spinor, ψµ. This projector provides the basis for the construction of an interacting Lagrangian that describes a causally propagating spin-3 2 particle coupled to the electromagnetic field by a gyromagnetic ratio of g 3 2 = 2.

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We study multipole decompositions of the electromagnetic currents of spin-1/2, 1, and 3/2 particles described in terms of representation specific wave equations which are second order in the momenta and which emerge within the recently elaborated Poincaré covariant projector method, where the respective Lagrangians explicitly depend on the Lorentz group generators of the representations of interest. The currents are then the ordinary linear Noether currents related to phase invariance, and present themselves always as two-terms motion-plus spin-magnetization currents. The spin-magnetization currents appear weighted by the gyromagnetic ratio, g, a free parameter in the method which we fix either by unitarity of forward Compton scattering amplitudes in the ultraviolet for spin-1, and spin-3/2, or, in the spin-1/2 case, by their asymptotic vanishing, thus ending up in all three cases with the universal g value of g = 2. Within the method under discussion we calculate the electric multipoles of the above spins for the spinor-, the four-vector, and the fourvector-spinor representations, and find it favorable in some aspects specifically in comparison with the conventional Proca-, and Rarita-Schwinger frameworks. We furthermore attend to the most general non-Lagrangian spin-3/2 currents which are allowed by Lorentz invariance to be up to third order in the momenta and construct the linear-current equivalent of identical multipole moments of one of them. We conclude that non-linear non-Lagrangian spin-3/2 currents are not necessarily more general and more advantageous than the linear spin-3/2 Lagrangian current emerging within the covariant projector formalism. Finally, we test the representation dependence of the multipoles by placing spin-1 and spin-3/2 in the respective (1,0)⊕(0,1), and (3/2,0)⊕(0,3/2) single-spin representations. We observe representation independence of the charge monopoles and the magnetic dipoles, in contrast to the higher multipoles, which turn out to be representation dependent. In particular, we find the bi-vector (1, 0) ⊕ (0, 1) to be characterized by an electric quadrupole moment of opposite sign to the one found in (1/2, 1/2), and consequently, to the W boson. This observation allows to explain the positive electric quadrupole moment of the ρ meson extracted from recent analyzes of the ρ meson electric form factor. Our finding points toward the possibility that the ρ meson could transform as part of an anti-symmetric tensor with an a1 meson-like state as its representation companion, a possibility consistent with the empirically established ρ-, and a1 vector meson dominance of the hadronic vector-, and axial-vector currents.

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In this work, we study the possibility that dark matter fields transform in the ð1; 0Þ ⊕ ð0; 1Þ representation of the homogeneous Lorentz group. In an effective theory approach, we study the lowest-dimension interacting terms of dark matter with standard model fields, assuming that dark matter fields transform as singlets under the standard model gauge group. There are three dimension-four operators, two of them yielding a Higgs portal to dark matter. The third operator couples the photon and Z 0 fields to the higher multipoles of dark matter, yielding a spin portal to dark matter. For low mass dark matter (D), the decays Z 0 →DD and H →DD are kinematically allowed and contribute to the invisible widths of the Z 0 and H bosons. We use experimental results on these invisible widths to constrain the values of the low-energy constants g t (for the spin portal) and g s , g p (for the Higgs portal) for this mass region. We calculate the dark matter relic density in our formalism and, using the above constraints, we find that consistency with the experimental value requires dark matter to have a mass M > 43 GeV in the case of the spin portal and M > 62 GeV for the Higgs portal. For higher mass dark matter (M > M H =2), we calculate the velocity averaged cross section for the annihilation of dark matter intobb and τ þ τ − and compare with the upper bounds recently reported by Fermi-LAT and DES Collaborations, finding that both portals yield results consistent with the reported upper bounds. Finally, we study direct detection by elastic scattering on nuclei. The Higgs portal yields results consistent with the upper bounds reported recently by the XENON Collaboration. The spin portal can also accommodate this data but requires higher values of the dark matter mass or smaller values of the corresponding coupling.