Echoes of Veltman criteria on the next-two-Higgs-doublet model

TL;DR

This paper explores the Next-Two-Higgs Doublet Model's potential to address the naturalness problem by analyzing quadratic divergences and their compatibility with current experimental data, revealing insights into the Higgs spectrum and parameter space.

Contribution

It provides a detailed calculation of quadratic divergences in the N2HDM and assesses their implications for naturalness and model parameters in light of recent LHC data.

Findings

Quadratic divergences for the three CP-even Higgs bosons are small but may require fine-tuning.

The model's parameter space and Higgs spectrum are significantly affected by divergence control.

The Higgs singlet-doublet admixture influences the model's naturalness and experimental compatibility.

Abstract

We investigate how the Next-Two-Higgs Doublet Model extension (N2HDM) should look if we are to address the naturalness problem using dimensional regularization. In such a model, new Higgs states are predicted, namely: three CP-even $h_{1,2,3}$, one CP-odd $A$, and a pair of charged Higgs boson $H^\pm$. Our calculations of the overall quadratic divergences have been performed with full consistency with the latest data from the Large Hadron Collider (LHC) concerning the observed 125 GeV Higgs boson, alongside precision electroweak data tests and lower mass limits on charged Higgs boson. It is shown that the quadratically divergent quantum corrections $\delta_i$ (i=1,2,3) for the three CP-even Higgs bosons are controllably small, though hidden fine-tuning might still be required. This reveals a significant impact on the model parameter space, Higgs spectrum mass, and notably the singlet-doublet admixture.