Relevance of one-loop SMEFT matching in the 2HDM

The two-Higgs doublet model (2HDM) is a well understood alternative to the Standard Model of particle physics. If the new particles included in the 2HDM are at an energy scale much greater than the weak scale, the theory can be matched to the Standard Model effective field theory (SMEFT). We compute for the first time the complete one-loop matching at dimension-6. We compare its numerical impact with that of tree-level matching at dimension-8 by performing a global fit to single Higgs and precision electroweak measurements, and we emphasize the importance of comparing one-loop SMEFT results with corresponding one-loop results in the full 2HDM model. In the SMEFT, we consider the relative importance of both one-loop matching and the inclusion of renormalization group evolution. Our results demonstrate the necessity of studying the impact of various expansions to quantify the uncertainties of the SMEFT matching.

Figure 1

Comparison of constraints on the 2HDM from electroweak precision observables in the full 2HDM (via a fit to the oblique parameters $S$, $T$ and $U$) and in the SMEFT matched to the 2HDM (with loop matching). The region satisfying the theoretical constraints outlined in Sec. 2b is shaded gray.

Figure 2

Comparison of the constraints from Higgs precision observables on the 2HDM with the constraints set by a fit to the SMEFT coefficients. The dotted and solid black lines show the constraints in the exact model with the Higgs coupling modifiers evaluated at LO and NLO, respectively (see Appendix pp1 for details). The red and blue lines show the SMEFT result with and without the inclusion of the dimension-eight operators ($d_8^{\mathrm{tree}}$). The solid red and blue lines include the contributions to the dimension-six operators generated at one-loop in the SMEFT matching ($d_6^{\mathrm{loop}}$), while the dashed ones do not. In all four panels, the additional heavy states are assumed to be degenerate and equal to the matching scale, $\mathrm{\Lambda }$. Note that the EFT expansion is only formally consistent if $c_{\beta -\alpha }$ is small (i.e., close to the alignment limit, $c_{\beta -\alpha }=0$).

Figure 3

Plots of the WCs $C_{tH}$, $C_{bH}$, and $C_{\varphi }$ vs. $\tan \beta$, that are generated in the type-I 2HDM at tree-level (dashed lines) and one-loop (solid lines), for various values of the alignment parameter, $\cos (\beta -\alpha )$.

Figure 4

Additional plots showing the constraints from Higgs measurements at the LHC on the fits to the type-I 2HDM. The upper left panel shows the constraints on the exact model (using the NLO predictions, with the heavy Higgs states separated from the matching scale by various values of $\mathrm{\Delta }{m}^2$) and compares these constraints to the theoretically allowed regions described in the text. The LO prediction for the exact model (which does not depend on the mass splitting) is shown as a dashed black curve for comparison. In the upper right panel, we show the same curves, now evaluated using the SMEFT matching at dimension-6 at tree-level (dashed) and one-loop (solid). In the lower left panel, we show the effects of including indirect information from single Higgs production on the Higgs self coupling ($C_{\varphi }$) for different values of the matching scale. The lower right panel illustrates the effects of including RGE of the WCs generated at tree-level in the 2HDM, and compares these to the effects of the full contributions generated at one-loop. Note that the EFT expansion is only formally consistent if $c_{\beta -\alpha }$ is small (i.e., close to the alignment limit, $c_{\beta -\alpha }=0$).