Light scalar beyond the Higgs mixing limit

TL;DR

This work introduces and studies a general flavor-aligned light scalar $φ$ with potential sub-GeV masses, focusing on how its diagonal couplings to SM fermions can differ from Higgs-proportional expectations. It builds a two-tier EFT framework (SMEFT$_φ$ above the EW scale and WET$_φ$ at hadronic scales) to connect UV completions to low-energy meson processes, and derives meson decay amplitudes for $K o πφ$ and $η^{(′)} o πφ$ within chiral perturbation theory, including partial $ ext{O}(p^4)$ effects. By exploring UV realizations—2HDM with a light singlet, a dark-sector dilaton, and vector-like quarks with a light scalar—the paper shows how flavor-aligned couplings arise and evolve through loop effects and penguin diagrams. Phenomenologically, kaon decays and $ ext{η}$/$ ext{η′}$ transitions constrain the low-energy couplings and UV parameters, with distinct patterns depending on whether $φ$ decays to photons or invisibly. Overall, the work highlights the unique signatures of a general flavor-aligned scalar and outlines avenues for further exploration in heavier mesons and cosmological contexts.

Abstract

We explore the possibility that the interactions of a light scalar singlet, which mixes with the Standard Model~(SM) Higgs, also receive other UV contributions of comparable size. We focus, in particular, on the flavor aligned limit, where couplings of the light scalar to the SM are almost flavor diagonal, but not necessarily proportional to the Higgs Yukawa couplings. The phenomenology of such a general flavor aligned light scalar differs from both the Higgs-mixed scalar, as well as from a general axion-like particle. We explore this for light scalar masses below a few hundred MeV, such that they can be produced in kaon decays, and in decays of $η$ and $η'$ mesons, and the transitions described using chiral perturbation theory. We then derive constraints on the light scalar interactions, assuming that light scalar decays are either just into photons or are invisible. We also discuss several UV examples of such light scalar models: a two-Higgs doublet model extended by a light scalar, a light dilaton from the dark sector, and a SM extended by heavy vector-like quarks and a light scalar. For the latter we also performed matching onto low energy theory at one-loop.

Figures (5)

• Figure 1: One-loop penguin diagrams for $s\to d\phi$ transition in the VLQ model, assuming couplings of the SM fermions to only up-type VLQ $SU(2)_L$ singlets.
• Figure 2: One-loop penguin diagrams for $s\to d\phi$ transition in the VLQ model, assuming couplings of the SM fermions to only down-type VLQ $SU(2)_L$ singlets.
• Figure 3: The 95$\%$ CL upper bounds on $\phi$ couplings to pseudoscalar mesons, assuming $\phi\to\gamma\gamma$ dominance. (Left) Upper bounds on model-independent $K_I$ and $K_8$ couplings, where the other parameters are profiled over, from $\eta^{(\prime)}$ decays, and on $\kappa_W-K_\Theta$, $\kappa_u^\phi-\kappa^\phi_{s+d}/2$, $\kappa^\phi_{s-d}$ and the penguin contributions $|\kappa^\phi_{sd,ds}|$ from the NA62 search for $K^+\to\pi^+\phi$. Only one parameter is switched on at a time. (Right) Model-dependent upper bounds on $\kappa^\phi_u$, $\kappa^\phi_c$, $\kappa^\phi_t$ and $\kappa^\phi\equiv\kappa^\phi_u=\kappa^\phi_d=\kappa^\phi_s$ in the $u$--only, $c$--only, $t$--only and $uds$ benchmark models with VLQs, respectively. Note that the limits for the $c,t$--only benchmark models are the same for $m_\phi\lesssim 200\,$MeV.
• Figure 4: Same as \ref{['fig:KIK8KThetaWUzeta']}, but assuming $\phi\to\,$invisible dominance.
• Figure 5: One-loop diagrams contributing to scalar FCNC in the down-type VLQ model of Section \ref{['sec:UV']} (left) and the SM (right). Arrows indicate the hypercharge flow.