Unitarity constraints on 2HDM with higher dimensional operators

TL;DR

The paper develops and applies a perturbative unitarity analysis to the 2HDM extended by bosonic dimension-six operators (2HDMEFT), focusing on how high-energy consistency constrains the Wilson coefficients and the new-physics scale $f$. By computing the full $2\to2$ bosonic scattering amplitudes and performing a partial-wave analysis, it delineates how $\varphi^4 D^2$ operators preserve a block-diagonal unitarity structure while $\varphi^6$ terms modify the eigenvalue spectrum, typically weakening bounds. The study highlights that unitarity bounds are strongest away from the alignment limit (cos(beta-alpha) not small) and can tighten complementary regions to electroweak precision and Higgs-data constraints, especially for custodial-symmetry-violating operators that are otherwise weakly probed. It demonstrates that high-energy consistency hence provides essential, model-independent limits that complement existing constraints from EWPD, Higgs measurements, and aQGC searches, helping to restrict the viable parameter space of 2HDMEFT in a way not accessible by low-energy data alone.

Abstract

We study how the requirement of perturbative unitarity restricts the parameter space of the two-Higgs-doublet model (2HDM) when higher-dimensional operators up to dimension six are included. We demonstrate that such operators can enhance scalar production cross sections in vector boson fusion relative to 2HDM. Using S-matrix unitarity, we place bounds on several dimension-six bosonic operators. We also find that certain blind directions in the Wilson coefficients of T-parameter violating operators which are poorly constrained by electroweak precision data can be partially excluded when unitarity constraints are taken into account. These results demonstrate how high-energy consistency can complement experimental limits in defining the allowed parameter space of 2HDM effective field theory.

Figures (6)

• Figure 1: The coefficient $A_2$ for $W_L^+ W_L^- \to W_L^+ W_L^-$ scattering as a function of $\cos(\beta-\alpha)$. Black line: Tree-level 2HDM (no dimension-six operators). Blue line: 2HDMEFT with $\varphi^4 D^2$ operators $O_{H1}$, $O_{H2}$, $O_{H12}$ ($c_{H1} = c_{H2} = c_{H12} = -1$, all other coefficients zero) and $\tan\beta = 1$. Red line: 2HDMEFT with same operators and coefficients as above but $\tan\beta = 5$. Parameters: $\sqrt{s} = 2~\text{TeV}$, $f = 1~\text{TeV}$.
• Figure 2: The coefficient $A_2$ for $W_L^+ W_L^+ \to W_L^+ W_L^+$ scattering as a function of $\cos(\beta-\alpha)$. Black line: Tree-level 2HDM. Blue line: 2HDMEFT with $\varphi^4 D^2$ operators $O_{H1}$, $O_{H2}$, $O_{H12}$ ($c_{H1} = c_{H2} = c_{H12} = -1$, all other coefficients zero) and $\tan\beta = 1$. Red line: 2HDMEFT with same operators and coefficients as above but $\tan\beta = 5$. Parameters: $\sqrt{s} = 2~\text{TeV}$, $f = 1~\text{TeV}$.
• Figure 3: The coefficient $A_2$ for $W_L^+ W_L^- \to Z_L Z_L$ scattering as a function of $\cos(\beta-\alpha)$. Black line: Tree-level 2HDM. Blue line: 2HDMEFT with $\varphi^4 D^2$ operators $O_{H1}$, $O_{H2}$, $O_{H12}$ ($c_{H1} = c_{H2} = c_{H12} = -1$, all other coefficients zero) and $\tan\beta = 1$. Red line: 2HDMEFT with same operators and coefficients as above but $\tan\beta = 5$. Parameters: $\sqrt{s} = 2~\text{TeV}$, $f = 1~\text{TeV}$.
• Figure 4: Cross sections for vector-boson scattering processes at $\cos(\beta-\alpha)=0.5$, $f=1\;\text{TeV}$, $\tan\beta=5$, with $\varphi^{4}D^{2}$ operators $O_{H1}$, $O_{H2}$, and $O_{H12}$ active ($c_{H1}=c_{H2}=c_{H12}=-1$, all other $\varphi^{4}D^{2}$ coefficients zero). Yellow solid line:$W_L^{\pm}W_L^{\mp}\to W_L^{\pm}W_L^{\mp}$; Orange dashed line:$W_L^{\pm}W_L^{\pm}\to W_L^{\pm}W_L^{\pm}$; Green dotted line:$W_L^{+}W_L^{-}\to Z_LZ_L$.
• Figure 5: Unitarity bounds in the $\sqrt{s}$–$f$ plane for different Wilson coefficients of $\varphi^4 D^2$ operators. Blue shaded regions are excluded by perturbative unitarity ($|\Lambda_i| > 8\pi$); white regions are allowed.