First-order Transition Triggered By U(1) Symmetry Breaking Can Generate Gravitational Waves (Quantum)

An extra U(1) gauge interaction is one of the promising and interesting extensions of the standard model (SM) of particle physics. Since tiny but non-vanishing neutrino masses are a clear evidence for the existence of the beyond the SM, one of the simplest and the most interesting models is the one based on the gauge group SU(3)c×SU(2)L× U(1)Y× U(1)BL, where the additional interaction is from the gauged U(1)BL (baryon number minus lepton number) symmetry. In the standard U(1)BL charge assignment, three right-handed (RH) neutrinos have to be introduced to fulfill the gauge and gravitational anomaly cancellation conditions. After Majorana masses of RH neutrinos are generated by the spontaneous U(1)BL gauge symmetry breaking at a high energy scale, the observed tiny neutrino masses are naturally explained by the so-called seesaw mechanism with the heavy Majorana RH neutrinos through their Yukawa interactions with the SM left-handed neutrinos. In addition, one of the three RH neutrinos can be a candidate for the dark matter in our universe.

Although it is very difficult for any collider experiments to test an additional gauge symmetry if it is broken at very high energies, the detection of a gravitational wave (GW) can be a probe for such an extra U(1) symmetry breaking. This is because the first-order phase transition in the early universe is one of the promising sources of stochastic GW background. If a first-order phase transition occurred in the early universe, the dynamics of bubble collision followed by the turbulence of the plasma and sonic waves would have generated GWs, which can be detected by the future experiments, such as Big Bang Observer (BBO), DECi-hertz Interferometer Observatory (DECIGO), Advanced LIGO (aLIGO), and Einstein Telescope (ET).

Now, Nobuchika and colleagues in their recent paper, considered the U(1)X extended SM and studied the spectrum of stochastic GWs generated by the first-order phase transition associated with the extra U(1)X, symmetry breaking in the early universe. This breaking is responsible for the generation of Majorana masses of RH neutrinos. They have investigated a UV completion of the U(1)X extended SM by an SO(10) GUT. In this UV completion, the extra U(1) gauge coupling is unified with the SM gauge couplings, and thus the extra U(1) gauge coupling at the phase transition epoch is no longer a free parameter and g_χ ∼ 0.4 from the gauge coupling unification condition. They have found that the first-order phase transition triggered by this extra U(1) symmetry breaking can be strong enough to generate GWs with a detectable size of amplitude if the U(1)X Higgs quartic coupling is small enough and the symmetry breaking scale (the bubble nucleation temperature T⋆) is smaller than about 105 (104) TeV.

FIG. 1: The predicted GW spectrum for various values of Y_N and λ_2 for g_χ = 0.463 and v_2 = 1 PeV. Parameters in the legend denote (Y_N , λ_2 × 10³) © Nobuchika et al.

They have also clarified the dependence of the resultant GW spectrum on the RH neutrino Majorana Yukawa couplings, in other words, the mass scale of RH neutrinos. As the Yukawa couplings increase, the amplitude of GW background reduces and the peak frequency slightly increases. They have found a similar behavior in the GW spectrum as they change the U(1)X Higgs quartic coupling. Thus, different combinations of the Yukawa and the quartic couplings can result in almost the same GW spectrum. In order to extract the information about RH neutrino masses from the spectral shape of GW background, the information on the U(1)X Higgs quartic coupling is necessary.

Featured image: The predicted GW spectrum for various symmetry breaking scales for λ_2 = 6 × 10¯4. The difference of the symmetry breaking scale is indicated by colors as shown in the legends. Black solid curves are the expected sensitivities of each indicated experiments derived in K. Schmitz (2021) © Nobuchika et al.

Reference: Nobuchika Okada, Osamu Seto, Hikaru Uchida, “Gravitational waves from breaking of an extra U(1) in SO(10) grand unification”, Progress of Theoretical and Experimental Physics, Volume 2021, Issue 3, March 2021, 033B01,

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