Minimal spin-one isotriplet dark matter

In this work we present a simple extension of the Standard Model that contains, as the only new physics component, a massive spin-one matter field in the adjoint representation of $SU(2{)}_L$. In order to be consistent with perturbative unitarity, the vector field must be odd under a $Z_2$ symmetry. Radiative corrections make the neutral component of the triplet ($V^0$) slightly lighter than the charged ones. We show that $V^0$ can be the dark matter particle while satisfying all current bounds if it has a mass between 2.8 and 3.8 TeV. We present the current limit on the model parameter space from highly complementary experimental constraints, including dark matter relic density measurement, dark matter direct and indirect detection searches, LHC data on Higgs couplings to photons and LHC data on disappearing track searches. We also show that the two-dimensional parameter space can be fully covered by disappearing track searches at a future 100 TeV hadron collider, which will probe, in particular, the whole mass range relevant for dark matter, thus giving an opportunity to discover or exclude the model.

Figure 1

Left: The expected scale of perturbative unitarity loss as a function of $M_V$ and $a$. Areas shaded by colors indicate the scale of unitarity violation $\mathrm{\Lambda }$ according to Eq. (5), while area limited by the red contour and shaded by gray color (for both left and right panels) corresponds to a loss of perturbative unitarity at a scale lower than $10M_V$. Right: The expected scale of perturbative unitarity loss for the loop-induced $a$ (dashed), compared to the cases $a=0$., 1.0, 5.0 and $4\pi$.

Figure 2

The one-loop radiatively induced mass splitting between the charged and neutral components of the vector DM. The solid lines represent $\mathrm{\Delta }M$ computed at fixed values of the renormalization scale $Q$. The shaded green band indicates the range of values obtained by varying $Q$ continuously between $\min \{M_V/2,M_Z/2\}$ and $\max \{2M_V,2M_Z\}$ and thus constitutes an estimate of the uncertainty on $\mathrm{\Delta }M$. The solid black line is the one-loop mass splitting, Eq. (12), with all higher order terms truncated.

Figure 3

Thermal relic density for $V^0$ vs $M_V$ for various values of $a$. Perturbative unitarity loss at $\mathrm{\Lambda }<10M_V$ occurs where gray dashing overlays the relic density lines. The gray horizontal band corresponds to the range measured by Planck, ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.1186\pm 0.0020$, and the light gray region indicates ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2>0.1206$.

Figure 4

Spin-independent cross section for $V^0$-nucleon elastic scattering as a function of $M_V$ and for representative values of $a$. The cross section has been rescaled to take into account the actual thermal relic abundance. The continuous black curve represents the elastic cross section computed with the values of $M_V$ and $a$ that saturate the measured DM relic density. The gray dashing highlights the parameter space where perturbative unitarity loss occurs at a too low scale.

Figure 5

Annihilation cross section of $V^0$ compared to the most recent bounds from HESS in the $W^{+}{W}^{-}$ channel. The two bands consist of two different choices of the DM profile model (Einasto), showing the sensitivity of the bound to the DM distribution at the center of the Galaxy.

Figure 6

Contribution of the new vector isotriplet to the $h\to \gamma \gamma$ decay channel for $a=\pm 1$ (dashed) and $a=\pm 5$ (solid). The color code uses red for positive values and blue for negative. The colored bands are the experimentally allowed regions at 95% confidence level from ATLAS (pink) and CMS (yellow), while the orange band shows the overlap.

Figure 7

Contribution of the vector isotriplet to the DM relic abundance (top left), spin-independent direct detection cross section in terms of the ratio in Eq. (21) (top right) and $R_{\gamma \gamma }$ (bottom), as a function of $M_V$ and $a$.

Figure 8

Impact of experimental bounds on the vector isotriplet parameter space. We progressively impose the constraints from direct detection from XENON 1T 2018 (left), the upper bound on the relic abundance (center), and $R_{\gamma \gamma }$ (right). In Fig. 9 we showed a focused plot on the remaining parameter space with the constraint of the relic abundance within the sigma of the Planck measurement.

Figure 9

The remaining parameter space in the vector isotriplet model with constraints imposed from direct detection, the Higgs coupling to photons, and the relic abundance. For this case we demand that the relic abundance of vector DM is within one sigma of the Planck measured value.

Figure 10

Feynman diagram of the effective $V^{+}\to V^0{\pi }^{+}$ interaction, obtained by integrating out the off-shell $W$.

Figure 11

Left: The partial decay widths of the charged vector isotriplet component in $\mu \mathrm{eV}$ for the three allowed decay channels are given by solid lines. The dashed line indicates the naive perturbative result for the hadronic one. Right: The decay lifetime as a function of the mass, compared to the naive perturbative result.

Figure 12

The shapes of $p_T$ distributions for pair production of the charged component of the vector isotriplet and of a wino, for different values of the masses.

Figure 13

Production cross sections at leading order for the vector isotriplet model at various LHC energies and for a 100 TeV future collider. The solid lines represent Drell-Yann, while the dashed ones refer to the subleading vector boson fusion channel.

Figure 14

Effective cross sections ${\sigma }_{\mathrm{eff}}=\sigma (pp\to V^{\pm }{V}^0)+2\sigma (pp\to V^{+}{V}^{-})$ at leading order for the vector isotriplet model for 13 and 27 TeV LHC energies and for a 100 TeV future collider. The dashed black line corresponds the current LHC sensitivity of about 0.85 fb while the dashed red line corresponds to the expected 2 fb sensitivity of 27 TeV LHC and 100 TeV FCC collider in high luminosity regime.