First-order electroweak phase transition in the standard model with a low cutoff

We study the possibility of a first-order electroweak phase transition due to a dimension-six operator in the effective Higgs potential. In contrast with previous attempts to make the electroweak phase transition strongly first-order as required by electroweak baryogenesis, we do not rely on large one-loop thermally generated cubic Higgs interactions. Instead, we augment the standard model effective theory with a dimension-six Higgs operator. This addition enables a strong first-order phase transition to develop even with a Higgs boson mass well above the current direct limit of 114 GeV. The ${\phi }^6$ term can be generated for instance by strong dynamics at the TeV scale or by integrating out heavy particles like an additional singlet scalar field. We discuss conditions to comply with electroweak precision constraints, and point out how future experimental measurements of the Higgs self-couplings could test the idea.

Figure 1

Contours of constant $T_c$ from 0 to 240 GeV. The shaded (blue) region satisfies the bounds of Eq. (5). Above it, the EWPT is second order and the critical temperature is no more given by Eq. (3) but instead by $T_c^2=(2{\Lambda }^2{m}_H^2-3v_0^4)/4c{\Lambda }^2$.

Figure 2

Contours of constant $v_c/T_c$ from 1 to $\infty$. The shaded (blue) region satisfies the bounds of Eq. (5).

Figure 3

Sphaleron energy at zero temperature in units of $4\pi v_0/g=4.75\mathrm{T}\mathrm{e}\mathrm{V}$.

Figure 4

Contours of constant $\mu /{\mu }_{\mathrm{S}\mathrm{M}}-1$ in the $\Lambda$ vs $m_H$ plane. The dashed lines delimit the allowed region defined in Eq. (5).