Testing scalar versus vector dark matter

We investigate and compare two simple models of dark matter (DM): a vector and a scalar DM model. Both models require the presence of two physical Higgs bosons $h_1$ and $h_2$ which come from mixed components of the standard Higgs doublet $H$ and a complex singlet $S$. In the vector model, the extra $U(1)$ symmetry is spontaneously broken by the vacuum of the complex field $S$. This leads to a massive gauge boson $X^{\mu }$ that is a DM candidate stabilized by the dark charge conjugation symmetry $S\to S^{*}$, $X^{\mu }\to -X^{\mu }$. On the other hand, in the scalar model the gauge group remains the standard one. The DM field $A$ is the imaginary component of $S$ and the stabilizing symmetry is also the dark charge conjugation $S\to S^{*}$ ($A\to -A$). In this case, in order to avoid spontaneous breaking, the $U(1)$ symmetry is broken explicitly, but softly, in the scalar potential. The possibility to disentangle the two models has been investigated. We have analyzed collider, cosmological, DM direct and indirect detection constraints and shown that there are regions in the space spanned by the mass of the nonstandard Higgs boson and the mass of the DM particle where the experimental bounds exclude one of the models. We have also considered possibility to disentangle the models at $e^{+}{e}^{-}$ collider and concluded that the process $e^{+}{e}^{-}\to Z+\mathrm{DM}$ provides a useful tool to distinguish the models.

Figure 1

Feynman diagram for considered channel of DM production. $\chi$ denotes the dark particle ($\chi =A$, $X$).

Figure 2

An exemplary plot of $\frac{d\sigma }{d{E}_Z}$ function for the SDM model. Different curves correspond to different cases: for the purple one, $2·m_{\mathrm{DM}}<m_1,m_2$; for the brown $m_1<2·m_{\mathrm{DM}}<m_2$; and for the green $m_1$, $m_2<2·m_{\mathrm{DM}}$.

Figure 3

Comparison of cross sections for the $e^{+}{e}^{-}\to Z{h}_i(\chi \chi )$ process ($\chi =A$, $X$) for the SDM and for the VDM, in the two-pole case: $2·m_{\mathrm{DM}}<m_1,m_2$. The upper right panel shows $d\sigma /d{E}_Z$ for both models while the lower one shows the ratio of the distributions between the SDM and the VDM. The parameters chosen for the plot in the right panels are specified in the lower left corner and above the upper left panel. The chosen values for $(m_{\mathrm{DM}},m_2)$ correspond to the point denoted by the star in the left upper panel. The colour bar shows the value of the ratio of total cross sections for $e^{+}{e}^{-}\to Z{h}_i(\chi \chi )$. The thick gray line on the upper right panel represents the SM background for our process (see Sec. 4d). Polarizations of the beams are $(P_{+},P_{-})=(-30\%,80\%)$.

Figure 4

As in Fig. 3, however for the one-pole case, i.e., for $m_1<2·m_{\mathrm{DM}}<m_2$.

Figure 5

As in Fig. 3, however for the no-pole case: $m_1$, $m_2<2·m_{\mathrm{DM}}$.

Figure 6

Exemplary diagrams of the standard model background processes. Neutrinos contribute to missing energy and can therefore mimic dark particles. The background cross section could be reduced by polarizing the initial $e^{+}$ and $e^{-}$ beams.

Figure 7

Branching ratio of $h_2\to h_1{h}_1$ as a function of $m_2$ for the scalar model and for the vector model (color code in the legend).

Figure 8

Branching ratio of the SM-like Higgs (a) and of the second Higgs (b) into DM particles as a function of the DM mass.

Figure 9

Left: $m_{\mathrm{DM}}/v_S$ as a function of the DM mass; right: $\sin \alpha$ as a function of $m_2$.

Figure 10

$\mathrm{BR}(h_2\to h_1{h}_1)+\mathrm{BR}(h_2\to \mathrm{DM}\mathrm{DM})$ vs $m_2$ for points that survive the bounds coming from heavy resonances and in particular $\sigma (pp(gg)\to h_2\to ZZ)$ with still large values $\sin \alpha$. Only points located outside of the pattern in the right panel of Fig. 9 are shown.

Figure 11

Second Higgs mass ($m_2$) as a function of the DM mass ($m_{\mathrm{DM}}$).

Figure 12

DM-nucleon cross section as a function of the DM mass. Scalar DM-nucleon nucleon cross section is computed at one-loop level. The latest results from Xenon1T are shown as the solid line that makes the upper edge of the plot.

Figure 13

Scalar DM-nucleon cross section as a function of the DM mass ($m_{\mathrm{DM}}=m_A$) with the latest result from Xenon1T and relic abundance within $5\sigma$ of experimental value.

Figure 14

Thermal average DM annihilation cross section (into the SM) times velocity (at zero temperature) vs DM mass.