Probing the electroweak phase transition with Higgs factories and gravitational waves

After the discovery of the Higgs boson, understanding the nature of electroweak symmetry breaking and the associated electroweak phase transition has become the most pressing question in particle physics. Answering this question is a priority for experimental studies. Data from the LHC and future lepton collider-based Higgs factories may uncover new physics coupled to the Higgs boson, which can induce the electroweak phase transition to become first order. Such a phase transition generates a stochastic background of gravitational waves, which could potentially be detected by a space-based gravitational wave interferometer. In this paper, we survey a few classes of models in which the electroweak phase transition is strongly first order. We identify the observables that would provide evidence of these models at the LHC and next-generation lepton colliders, and we assess whether the corresponding gravitational wave signal could be detected by eLISA. We find that most of the models with first-order electroweak phase transition can be covered by the precise measurements of Higgs couplings at the proposed Higgs factories. We also map out the model space that can be probed with gravitational wave detection by eLISA.

Figure 1

Parameter space scan for the singlet model of 2a. An orange point indicates a first-order phase transition, a blue point indicates a strongly first-order phase transition (3.4), and a green point indicates a very strong first-order phase transition with potentially detectable gravitational wave signal at eLISA. The right panels shows the predicted gravitational wave spectrum today along with the projected sensitivity of eLISA [2].

Figure 2

Parameter space scan for the singlet model of 2a1 where a discrete ${\mathbb{Z}}_2$ symmetry forbids the Higgs-singlet mixing and suppresses the BSM modification to the $hZZ$ coupling.

Figure 3

Parameter space scan for the singlet model of 2a2 where the Higgs-singlet mixing is tuned to zero.

Figure 4

Parameter space scan for the top-squark-like model of 2b. The projected sensitivity of figure Higgs factories (CEPC, ILC-500, FCC-ee) is sufficient to test the entire region of parameter space where the phase transition is first order (orange, blue, and green points).

Figure 5

Results for the heavy chiral fermion model of 2c. The Higgs-to-diphoton decay rate is shown as a function of the chargino mass. We fix the Higgs-bino-Higgsino Yukawa coupling $h^{\prime }=0$ and we show various values of the Higgs-wino-Higgsino Yukawa coupling $h$. Thick lines indicates parameters with a strongly first-order phase transition (3.4), dashed lines indicate a weakly first-order transition, and thin lines indicate a crossover or second-order transition.

Figure 6

Results for the varying Yukawas model of 2c2. In the top row, the quark Yukawa couplings are allowed to vary with lepton couplings fixed to their SM values. In the middle and bottom rows, the lepton couplings vary, and the quark couplings are fixed. In the first two rows, the Yukawa coupling changes by a flavor-independent shift, and in the bottom row it is a flavor-independent rescaling instead.