The scalar singlet extension of the Standard Model: gravitational waves versus baryogenesis

We study the possible gravitational wave signal and the viability of baryogenesis arising from the electroweak phase transition in an extension of the Standard Model (SM) by a scalar singlet field without a DOUBLE-STRUCK CAPITAL Z(2) symmetry. We first analyze the velocity of the expanding true-vacuum bubbles during the phase transition, confirming our previous finding in the unbroken DOUBLE-STRUCK CAPITAL Z(2) symmetry scenario, where the bubble wall velocity can be computed from first principles only for weak transitions with strength parameters alpha less than or similar to 0.05, and the Chapman-Jouguet velocity defines the maximum velocity for which the wall is stopped by the friction from the plasma. We further provide an analytical approximation to the wall velocity in the general scalar singlet scenario without DOUBLE-STRUCK CAPITAL Z(2) symmetry and test it against the results of a detailed calculation, finding good agreement. We show that in the singlet scenario with a spontaneously broken DOUBLE-STRUCK CAPITAL Z(2) symmetry, the phase transition is always weak and we see no hope for baryogenesis. In contrast, in the case with explicit DOUBLE-STRUCK CAPITAL Z(2) breaking there is a region of the parameter space producing a promising baryon yield in the presence of CP violating interactions via an effective operator involving the singlet scalar and the SM top quarks. Yet, we find that this region yields unobservable gravitational waves. Finally, we show that the promising region for baryogenesis in this model may be fully tested by direct searches for singlet-like scalars in di-boson final states at the HL-LHC, combined with present and future measurements of the electron electric dipole moment.

Automated summary

This study investigates the possible gravitational wave signal and baryogenesis in an extension of the Standard Model by a scalar singlet field without a DOUBLE-STRUCK CAPITAL Z(2) symmetry. The authors analyze the velocity of expanding true-vacuum bubbles during the phase transition, providing an analytical approximation and confirming their previous findings. They show that baryogenesis is not possible in the singlet scenario with a spontaneously broken DOUBLE-STRUCK CAPITAL Z(2) symmetry, but there is a promising region in the case with explicit DOUBLE-STRUCK CAPITAL Z(2) breaking. However, this region does not yield observable gravitational waves. The authors propose direct searches for singlet-like scalars in di-boson final states at the HL-LHC combined with electron electric dipole moment measurements to test the promising region for baryogenesis in this model.