Preserving the validity of the two-Higgs-doublet model up to the Planck scale

We examine the constraints on the two-Higgs-doublet model (2HDM) due to the stability of the scalar potential and absence of Landau poles at energy scales below the Planck scale. We employ the most general 2HDM that incorporates an approximately Standard Model (SM) Higgs boson with a flavor aligned Yukawa sector to eliminate potential tree-level Higgs-mediated flavor changing neutral currents. Using basis independent techniques, we exhibit regimes of the 2HDM parameter space with a 125 GeV SM-like Higgs boson that is stable and perturbative up to the Planck scale. Implications for the heavy scalar spectrum are exhibited.

Figure 1

Distribution of absolute values of the flavor alignment parameters, for regions of 2HDM parameter space which remain valid up to the Planck scale, assuming ${\mathrm{\Lambda }}_H=500\mathrm{GeV}$.

Figure 2

RG running of 2HDM quartic scalar couplings, with ${\mathrm{\Lambda }}_H=1\mathrm{TeV}$. Red points correspond to parameter choices for which an instability occurs in the scalar potential; blue points indicate the presence of a Landau pole. The upper solid black line indicates the occurrence of a Landau pole in the SM. The lower solid black line indicates the limit for which the SM potential becomes unstable.

Figure 3

Histograms of squared-mass differences of the heavy scalar states for ${\mathrm{\Lambda }}_H=500\mathrm{GeV}$. The left panel shows values of squared-mass difference between the two heavier neutral states. The right panel shows the values of the squared-mass difference between the lighter of the two heavy neutral states and the charged Higgs boson. The histograms correspond to 2HDM parameters for which there are no Landau poles and vacuum stability is satisfied at all energies below the Planck scale.

Figure 4

Left panel: Scale shift for converting the one-loop scalar potential instability boundary to the two-loop scalar potential instability boundary for a SM-like Higgs boson. Right panel: Higgs boson mass bounds in the flavor-aligned 2HDM, incorporating the scale shift shown in the left panel, assuming that ${\mathrm{\Lambda }}_H=1\mathrm{TeV}$. Red points indicate an instability in the running; blue points indicate the presence of a Landau pole.