Leptogenesis and neutral gauge bosons

We consider low-scale leptogenesis via right-handed neutrinos $N$ coupled to a $Z^{\prime }$ boson, with gauged $U(1{)}_{B-L}$ as a simple realization. Keeping the neutrinos sufficiently out of equilibrium puts strong bounds on the $Z^{\prime }$ coupling strength and mass, our focus being on light $Z^{\prime }$ and $N$, testable in the near future by SHiP, HPS, Belle II, and at the LHC. We show that leptogenesis could be robustly falsified in a large region of parameter space by the double observation of $Z^{\prime }$ and $N$, e.g. in the channel $pp\to Z^{\prime }\to NN$ with displaced $N$-decay vertex, and by several experiments searching for light $Z^{\prime }$, according to the mass of $N$.

Figure 1

The deviation of the $N$ number density from equilibrium in the presence (continuous line) or absence (dashed line) of gauge interactions. For illustrative purposes, we have chosen $M_N=10\mathrm{TeV}$, $M_{Z^{\prime }}=5\mathrm{TeV}$, $M_S=30\mathrm{TeV}$, and $\tilde{m}=1\mathrm{eV}$.

Figure 2

Contours of ${\log }_{10}ϵ$ needed for successful leptogenesis for $M_{Z^{\prime }}=5\mathrm{TeV}$, $M_S=30\mathrm{TeV}$, and $g^{\prime }=0.2$. Perturbative unitarity excludes the region $M_N>44\mathrm{TeV}$.

Figure 3

Upper limit on $g^{\prime }/M_{Z^{\prime }}=(2w{)}^{-1}$ vs $M_{Z^{\prime }}$ for decoupled $S$, $M_N=1\mathrm{TeV}$, and $ϵ=1$.

Figure 4

Upper limit on $g^{\prime }/M_{Z^{\prime }}$ vs $M_N$ for $M_{Z^{\prime }}=1\mathrm{GeV}$ (valid for any $M_{Z^{\prime }}\ll M_N$) and decoupled $S$ for various $CP$ asymmetries. In the shaded region perturbative unitarity would be violated.

Figure 5

Upper limit on $g^{\prime }/M_{Z^{\prime }}$ vs $M_N$ for $M_{Z^{\prime }}=1\mathrm{GeV}$ (valid for any $M_{Z^{\prime }}\ll M_N$), $ϵ=1$, and various $S$ masses. The shaded regions (left and right) and the dashed parts of the lines (right) correspond to the perturbative-unitarity bounds (8).

Figure 6

Parameter space of a gauge boson $Z^{\prime }$ coupled to $B-L$. The shaded areas are excluded at 90% C.L., and future reach is shown in dashed lines; see text for details. The diagonal black and blue lines show the upper bound for successful leptogenesis with $CP$ asymmetries $ϵ=1$ and $10^{-3}$, respectively, for various $N$ masses. The black line $ϵ=1$, $M_N=1.6\mathrm{TeV}$ corresponds to the most conservative limit from leptogenesis within the perturbative region.

Figure 7

Upper limit on $g^{\prime }$ vs $M_{Z^{\prime }}=3M_N$ for decoupled $S$ and $ϵ=1$ (thick black line). Existing limits (shaded) and future prospects (dashed) under the assumption $M_{Z^{\prime }}/M_N=3$ and the seesaw relation for the active-sterile mixing angle are taken from Ref. [56]. In particular, the dark red dotted-dashed (blue dashed) lines show the projections for the HL-LHC ($3{\mathrm{ab}}^{-1}$) in the channel $pp\to Z^{\prime }\to {\ell }^{+}{\ell }^{-}$ ($pp\to Z^{\prime }\to NN$ with displaced vertices), while the dashed green line shows the SHiP reach for displaced vertices. For $M_N$ lighter than a few GeV the leptogenesis bound reported should be considered very conservative; see the discussion in Sec. 3a.

Figure 8

Upper limit on $g^{\prime }$ vs $M_{Z^{\prime }}=X{M}_N$ for $X\in \{0.1,1,2,3,10,100\}$, decoupled $S$ and $ϵ=1$. The dashed part of the line corresponds to the perturbative-unitarity bound (8). For $M_N$ lighter than a few GeV the leptogenesis bounds reported should be considered very conservative; see the discussion in Sec. 3a.