Scale of Dirac leptogenesis and left-right symmetry in the light of recent PTA results

Abstract: Motivated by the recent release of new results from five different pulsar timing array (PTA) experiments claiming to have found compelling evidence for primordial gravitational waves (GW) at nano-Hz frequencies, we study the consequences for two popular beyond the Standard Model (SM) frameworks, where such nano-Hz GW can arise due to annihilating domain walls (DW). Minimal framework of Dirac leptogenesis, as well as left-right symmetric model (LRSM) can lead to formation of DW due to spontaneous breaking of $Z_2$ symmetry. Considering the NANOGrav 15 yr data, we show that the scale of Dirac leptogenesis should be above $10^7$ GeV for conservative choices of Dirac Yukawa couplings with fine-tuning at the level of the SM. The scale of {\it minimal} LRSM is found to be more constrained $M_{\rm LR} \sim 10^6$ GeV in order to fit the NANOGrav 15 yr data. On the other hand, the {\it non-minimal} LRSM can be compatible with the NANOGrav data for $10^2 \, {\rm TeV} \lesssim M_{\rm LR} \lesssim 10^3$ TeV but with the corresponding $B-L$ breaking scale violating collider bounds.