Probing left-right symmetry via gravitational waves from domain walls

We study the possibility of probing the scale of left-right symmetry breaking in the context of left-right symmetric models (LRSM). In LRSM, the right handed fermions transform as doublets under a newly introduced $SU(2{)}_R$ gauge symmetry. This, along with a discrete parity symmetry $\mathcal{P}$ ensuring identical gauge couplings of left and right sectors make the model left-right symmetric, providing a dynamical origin of parity violation in electroweak interactions via spontaneous symmetry breaking. The spontaneous breaking of $\mathcal{P}$ leads to the formation of domain walls in the early universe. These walls, if made unstable by introducing an explicit parity breaking term, generate gravitational waves (GW) with a spectrum characterized by the wall tension or the spontaneous $\mathcal{P}$ breaking scale, and the explicit $\mathcal{P}$ breaking term. Considering explicit $\mathcal{P}$ breaking terms to originate from Planck suppressed operators provides one-to-one correspondence between the scale of left-right symmetry and sensitivities of near future GW experiments. This is not only complementary to collider and low energy probes of TeV scale LRSM but also to GW generated from first order phase transition in LRSM with different spectral shape, peak frequencies as well as symmetry breaking scales.

Figure 1

Gravitational wave spectrum from collapsing domain walls in LRSM for three different benchmark combination of $(M_{W_R},\mathrm{\Delta }V)$ given in Table 1. Different colored curves show the sensitivities from GW search experiments like LISA, BBO, DECIGO, HL (aLIGO), ET, CE, NANOGrav, SKA, EPTA, PPTA, IPTA, GAIA, THEIA, and $\mu \mathrm{ARES}$.

Figure 2

Contours of $\mathrm{SNR}=10$ for different GW experiments shown in $M_{W_R}-\mathrm{\Delta }V$ plane. The region above these contours correspond to $\mathrm{SNR}>10$ for the corresponding experiment. The region above the black solid line corresponds to ${\mathrm{\Omega }}_{\mathrm{GW}}{h}^2\gtrsim {10}^{-6}$ or equivalently $\mathrm{\Delta }{N}_{\mathrm{eff}}>0.3$ and hence disfavored. The shaded regions in upper part correspond to DW decaying after BBN $(t_{\mathrm{dec}}>t_{\mathrm{BBN}})$ and dominating before decaying $(t_{\mathrm{dom}}<t_{\mathrm{dec}})$ respectively and hence disfavored. The gray shaded region at the bottom is disfavored from the LHC bounds.

Figure 3

Gravitational wave spectrum from collapsing domain walls in LRSM for a particular benchmark value of $M_{W_R}$ but with two different ways of generating bias terms, labelled as minimal and nonminimal respectively (see text for details). Different colored curves show the sensitivities from GW search experiments like LISA, BBO, DECIGO, HL (aLIGO), ET, CE, NANOGrav, SKA, EPTA, PPTA, IPTA, GAIA, THEIA, and $\mu \mathrm{ARES}$.

Figure 4

Sensitivities of different GW experiments to the corresponding scale of left-right symmetry breaking or $M_{W_R}$ with $\mathrm{SNR}\ge 10$ by considering the bias term to originate from Planck suppressed dimension six and dimension five operators, labelled as minimal and nonminimal model respectively. The region below the red solid line is disfavored from the LHC bounds. The bounds on parameter space from $t_{\mathrm{dec}}<t_{\mathrm{BBN}}$, $t_{\mathrm{dom}}>t_{\mathrm{dec}}$ are also satisfied.