Baryon and lepton number violation from gravitational waves

We describe a unique gravitational wave signature for a class of models with a vast hierarchy between the symmetry breaking scales. The unusual shape of the signal is a result of the overlapping contributions to the stochastic gravitational wave background from cosmic strings produced at a high scale and a cosmological phase transition at a low scale. We apply this idea to a simple model with gauged baryon and lepton numbers, in which the high-scale breaking of the lepton number is motivated by the seesaw mechanism for the neutrinos, whereas the low scale of baryon number breaking is required by the observed dark matter relic density. The novel signature can be searched for in upcoming gravitational wave experiments.

Figure 1

Stochastic gravitational wave background from the cosmic string network produced from gauged $\mathrm{U}(1{)}_L$ breaking for several choices of the scale $v_L$.

Figure 2

Plot of the effective potential $V_{\mathrm{eff}}({\varphi }_B,T)-V_{\mathrm{eff}}(0,T)$ for the choice of parameters in Eq. (14) and several temperatures.

Figure 3

Stochastic gravitational wave background produced by sound waves and turbulence during a first order phase transition triggered by the breaking of gauged $\mathrm{U}(1{)}_B$, for the benchmark scenario in Eq. (14). The dashed line corresponds to the signal from sound waves without the suppression factor $\mathrm{\Upsilon }$.

Figure 4

The parameter space region $({\lambda }_B,g_B)$ for which a phase transition triggered by $\mathrm{U}(1{)}_B$ breaking with $v_B=20\mathrm{TeV}$ gives rise to a gravitational wave signal detectable at LISA (green), DECIGO (green and blue), and BBO (green, blue, and purple) with a signal-to-noise ratio greater than five after one year of collecting data. The orange dot denotes the benchmark parameters used in Fig. 5.

Figure 5

Stochastic gravitational wave signature of the model with gauged baryon and lepton numbers for $v_B=20\mathrm{TeV}$ and $v_L={10}^{11}\mathrm{GeV}$ (black solid line). Sensitivities of future detectors are also shown: Big Bang Observer [88] (purple), DECIGO [88] (blue), LISA (in the C1 configuration) [81] (green), Cosmic Explorer [5] (gray), and Einstein Telescope [89] (red). The dashed line denotes the contribution from the phase transition associated with $\mathrm{U}(1{)}_B$ breaking, whereas the dotted line corresponds to the cosmic string signal from $\mathrm{U}(1{)}_L$ breaking.