Constraining the interaction strength between dark matter and visible matter: II. scalar, vector and spin-3/2 dark matter

We investigate the constraints on the scalar, vector and spin-3/2 dark matter interaction with the standard model particles, from the observations of dark matter relic density, the direct detection experiments of CDMS and XENON, and the indirect detection of the antiproton-to-proton ratio by PAMELA. A model independent way is adopted by constructing general 4-particle operators up to dimension 6 for the effective interaction between dark matter and standard model particles. We find that the constraints from different experiments are complementary with each other. Comparison among these constraints may exclude some effective models of dark matter and limit some parameters of others. The spin-independent direct detection gives strong constraints for some operators, while the indirect detection of antiproton-to-proton data can be more sensitive than direct detection or relic density for light dark matter (whose mass less than 70 GeV) in some cases. The constraints on some operators for spin-3/2 dark matter are shown to be similar to those on their analogous operators for Dirac fermionic dark matter. There are still some operators not sensitive to the current dark matter direct and indirect search experiments.

💡 Research Summary

This paper presents a comprehensive, model‑independent study of dark‑matter (DM) interactions for three classes of weakly interacting massive particles (WIMPs): complex scalar, vector, and spin‑3/2 particles. For each class the authors construct all possible four‑particle effective operators up to dimension six that respect Hermiticity, Lorentz invariance, and CPT symmetry. The scalar sector includes four operators: scalar (S), vector‑derivative (V), scalar‑pseudoscalar (SP), and vector‑axial‑vector (VA). The vector and spin‑3/2 sectors are treated analogously, with the same operator basis but different field content. Two coupling‑parameterizations are considered: universal couplings (F_f = constant for all SM fermions) and Yukawa‑like couplings proportional to the fermion mass (F_f ∝ m_f).

The relic‑density calculation follows the standard thermal freeze‑out formalism. The authors compute the annihilation cross sections σ_ann for each operator, expand the thermally averaged product ⟨σ_ann v⟩ in powers of the relative velocity (a_0 + a_1 v^2), and solve the Boltzmann equation to obtain the freeze‑out temperature x_f and the present DM abundance Ω_DM h^2. They emphasize that dimension‑5 operators (S, SP) have a_0 essentially independent of the DM mass, whereas dimension‑6 operators (V, VA) acquire an extra M_φ^2 factor, leading to stronger annihilation for heavy DM. By imposing the WMAP/Planck measurement Ω_DM h^2 = 0.1109 ± 0.0056, they derive the required values of the effective couplings F_f as functions of the DM mass M_φ (Fig. 1). The curves display characteristic kinks at the thresholds for heavy‑quark final states (c, b, t), especially pronounced in the Yukawa‑like scenario where the top‑quark channel opens near M_φ ≈ 171 GeV.

Direct‑detection constraints are applied using the latest spin‑independent (SI) limits from XENON10 00 and spin‑dependent (SD) limits from CDMS. Operators S and SP generate SI scattering, while V and VA generate SD scattering. The SI limits are particularly powerful for dimension‑5 operators, forcing F_f ≲ 10^–4 GeV^–1, whereas the SD limits constrain dimension‑6 couplings to F_f ≲ 10^–8 GeV^–2. The authors also discuss the validity of the effective‑field‑theory description, noting that for very light mediators the EFT may break down, but they remain within the regime where the momentum transfer is well below the cutoff scale.

Indirect detection is examined through the antiproton‑to‑proton ratio measured by PAMELA. The authors compute the halo‑averaged annihilation rate ⟨σ_ann v⟩_halo for each operator and compare the predicted antiproton flux with PAMELA data. They find that for light DM (M_φ < 70 GeV) the p‑wave contribution of dimension‑6 operators can dominate, leading to an antiproton excess that is already excluded. In contrast, dimension‑5 operators are largely p‑wave suppressed and remain compatible with current antiproton measurements. Consequently, PAMELA provides the strongest bounds on V and VA operators in the low‑mass region, complementing the SI limits from direct searches.

The spin‑3/2 analysis, presented more briefly, shows that many constraints mirror those for Dirac fermion DM because the effective operators have analogous Lorentz structures. Nevertheless, certain tensor‑type operators unique to spin‑3/2 are identified as being essentially invisible to present direct and indirect searches, highlighting opportunities for future experiments.

Overall, the paper demonstrates that relic‑density, direct‑detection, and indirect‑detection data probe complementary slices of the effective‑operator parameter space. Dimension‑5 scalar‑type operators are most tightly constrained by SI direct searches, while dimension‑6 vector‑type operators are most sensitive to antiproton data for light masses. The study also underscores that current experiments leave several operator directions unconstrained, motivating higher‑sensitivity detectors and collider searches to fully explore the landscape of possible DM–SM interactions.