Do the muon and charm quark couple to the Higgs with SM strength?
This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.
In plain words
The Higgs has been seen decaying to the heavy third-generation fermions, but its decays to the muon and to the charm quark (second-generation particles) are rare and only hinted at. Confirming them would show that the Higgs gives mass the same way across generations.
Precise statement
Measure the coupling modifiers $\kappa_{\mu}$ and $\kappa_c$ relative to the SM. ATLAS Run 2 plus Run 3 $H \to \mu\mu$ gives $3.4\sigma$ ($2.5\sigma$ expected) with signal strength $1.4 \pm 0.4$ (Phys. Rev. Lett. 135, 231802, 2025), CMS Run 2 gives $3.0\sigma$; the best direct charm bound is $\left|\kappa_c\right| < 4.2$ at 95 percent CL (ATLAS VH, JHEP 04 (2025) 075). An answer is a $\ge 5\sigma$ observation of $H \to \mu\mu$ with $\kappa_{\mu}$ to $\sim 10\%$, and a $\kappa_c$ measurement that separates 1 from 0.
What would settle it
HL-LHC $H \to \mu \mu$ and $H \to c\ \mathrm{cbar}$ analyses, followed by percent-level $\mathrm{BR}(H \to c\ \mathrm{cbar})$ and $\operatorname{BR}(H \to \mu \mu)$ measurements at a Higgs factory.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Evidence-level $H \to \mu\mu$ from ATLAS (2025) and CMS (2020); $H \to c\,\mathrm{cbar}$ not observed, with limits about 11 times the SM rate as of 2025.
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