Natural $Z^{\prime }$ model with an inverse seesaw mechanism and leptonic dark matter

We consider a model for a $Z^{\prime }$-boson coupled only to baryon minus lepton number and hypercharge. Besides the usual right-handed neutrinos, we add a pair of fermions with a fractional lepton charge, which we therefore call leptinos. One of the leptinos is taken to be odd under an additional $Z_2$ charge, the other even. This allows for a natural (inverse) seesaw mechanism for neutrino masses. The odd leptino is a candidate for dark matter, but has to be resonantly annihilated by the $Z^{\prime }$-boson or the Higgs-boson responsible for giving mass to the former. Considering collider and cosmological bounds on the model, we find that the $Z^{\prime }$-boson and/or the extra Higgs-boson can be seen at the LHC. With more pairs of leptinos leptogenesis is possible.

Figure 1

$Z^{\prime }$ exclusions from CMS data, at $\sqrt{s}=7\mathrm{TeV}$ for the combination of $4.7{\mathrm{fb}}^{-1}$ in the electron channel and $4.9{\mathrm{fb}}^{-1}$ in the muon channel. The dotted black lines refer to the two main benchmark models of this analysis.

Figure 2

DM relic abundance as a function of the candidate mass for $M_{H_2}=800\mathrm{GeV}$ and $M_{Z^{\prime }}=2\mathrm{TeV}$, for two different choices of the scalar mixing angle. Also, $g_{BL}=0.1$ and $g_2=0$.

Figure 3

(Left) DM relic abundance as a function of the DM mass for $M_{H_2}=800\mathrm{GeV}$, for some values of the vev $v^{\prime }$ and $\sin \alpha =0.1$. The blue shading represents values of the vev for which an allowed DM mass exists, for this $M_{H_2}$, as taken from the right panel. (Right) Allowed region for $v^{\prime }$ for which a DM mass yields the correct relic density, as a function of the heavy Higgs boson mass, for the three values of $\sin \alpha =0.05$, 0.1, 0.3. The LEP exclusion is as in Eqs. (10, 11).

Figure 4

Relic density as a function of the DM candidate mass around the $Z^{\prime }$ peak. The lower curve, for $g_{BL}=0.5$, is for illustrative purposes only, being already excluded by LEP.

Figure 5

Variation of the relic density (at the $Z^{\prime }$ resonance) with $g_2$ for a choice of $g_{BL}$ (see the text for further details), for (left) $M_{Z^{\prime }}=2\mathrm{TeV}$ and (right) $M_{Z^{\prime }}=3\mathrm{TeV}$.

Figure 6

Existence of a suitable DM candidate: the allowed region is the one above the dashed curves, in the $g_{BL}-M_{Z^{\prime }}$ plane, (left) for $g_2=0$ and (right) for $g_2=g_2^{\min }(g_{BL})$, which minimizes the $Z^{\prime }$ width, hence allowing for a smaller $g_{BL}$ (and therefore a smaller cross section) per fixed $M_{Z^{\prime }}$. The red shading combinations are forbidden by LEP [Eqs. (10, 11), respectively], the black (solid) lines are the LHC exclusion, as in Table .

Figure 7

Spin-independent direct searches for maximum Yukawa couplings $y_{S_2}\sim M_{S_2}/v^{\prime }$. Only allowed masses are plotted, from Fig. 3 (right), for $g_2=g_2^{\min }$.

Figure 8

(Left) Higgs resonance, $n\equiv N_{\ell }=3$ is not shown as always disallowed in this case. Here, $\sin \alpha =0.1$. (Right) Allowed parameter range for resonant $Z^{\prime }$ boson annihilation for $n\equiv N_{\ell }=1\dots 3$ families of leptinos. The curves are for $g_2=g_2^{\min }(g_{BL})$.

Figure 9

(a) Total $Z^{\prime }$ width for selected $g_{BL}$ values (solid lines refer to $N_{\ell }=1$, dashed lines to $N_{\ell }=3$) and (b) percentage variation between the 2 models in the $g_{BL}-g_2$ plane, for $M_{Z^{\prime }}=2.0\mathrm{TeV}$. For the heavy neutrino masses, see the text.