Flavour-Changing Neutral Current Top Decays in the Three Higgs Doublet Model

TL;DR

The paper addresses the question of whether top-quark flavour-changing neutral current (FCNC) decays can be enhanced in a democratic Three Higgs Doublet Model (3HDM) with a $Z_3$-symmetric scalar potential and Natural Flavour Conservation. It develops the scalar and Yukawa sectors, identifies three alignment hierarchies (regular, medial, inverted), and computes one-loop FCNC amplitudes for $t \to q X$ using a full loop-level framework. Through extensive parameter scans under vacuum stability, perturbativity, unitarity, electroweak precision (S,T,U), Higgs signal-strength, and $B\to X_s\gamma$ constraints, the study finds that loop-induced top FCNCs can be significantly enhanced relative to the SM, especially in the medial hierarchy where light non-SM scalars boost $t \to qH_1$ rates up to $\mathcal{O}(0.1)$ in theory-only regions, though experimental data push most channels down to $\mathcal{O}(10^{-13}-10^{-9})$. The inverted hierarchy remains phenomenologically disfavoured when all constraints are applied, while the regular hierarchy yields smaller but potentially observable BRs, highlighting rare top decays as a promising probe of extended scalar sectors and guiding future HL-LHC searches for non-SM Higgs final states. Overall, the work demonstrates that top FCNC decays offer a powerful window into the structure and mass spectrum of multi-Higgs-doublet models.

Abstract

We study flavour-changing neutral current decays of the top quark in the democratic Three Higgs Doublet Model featuring a $Z_3$-symmetric scalar potential and Natural Flavour Conservation. In this framework, while such processes are absent at tree-level, the extended scalar sector induces new one-loop contributions to rare top decays. We compute the branching ratios for processes of the form $t \to q X$ (with $q = u, c$ and $X$ denoting a boson of the model), and explore the viable regions of the parameter space under theoretical consistency conditions and current experimental constraints. Several alignment-limit scenarios corresponding to different hierarchies among the CP-even Higgs states are analysed, and we find that the predicted branching ratios can significantly exceed their Standard Model expectations while remaining consistent with existing limits. In particular, we identify scenarios with light non-standard scalars that can lead to rates within the projected sensitivity of the High-Luminosity LHC. Our results therefore highlight rare top decays as a promising probe of the extended scalar sector of the Three Higgs Doublet Model.

Figures (4)

• Figure 1: Feynman diagrams contributing to the $t\to c\gamma$ process in the SM (top row) and in the 3HDM (bottom rows).
• Figure 2: Predicted branching ratios for top FCNC decays in the regular hierarchy scenario. Results are shown for scenarios consistent with theoretical requirements ('T', cyan) and additionally satisfying the imposed experimental constraints ('T+E', green). The upper panel represents the full scan, while the lower panel provides numerical values for the maxima and minima for each decay channel.
• Figure 3: Predicted branching ratios for top FCNC decays in the medial hierarchy scenario. Results are shown for scenarios consistent with theoretical requirements ('T', cyan) and additionally satisfying the imposed experimental constraints ('T+E', green). The upper panel represents the full scan, while the lower panel provides numerical values for the maxima and minima for each decay channel.
• Figure 4: Predicted branching ratios for top FCNC decays in the inverted hierarchy scenario. Results are shown for scenarios consistent with theoretical requirements ('T', cyan) with the the upper panel representing the full scan and the lower panel providing the associated numerical values for the maxima and minima for each decay channel.