Consequences of chirally enhanced explanations of $(g-2)_\mu$ for $h\to \mu\mu$ and $Z\to \mu\mu$

With the long-standing tension between experiment and Standard-Model (SM) prediction in the anomalous magnetic moment of the muon $a_\mu$ recently reaffirmed by the Fermilab experiment, the crucial question becomes which other observables could be sensitive to the underlying physics beyond the SM to which $a_\mu$ may be pointing. While from the effective field theory (EFT) point of view no direct correlations exist, this changes in specific new physics models. In particular, in the case of explanations involving heavy new particles above the electroweak (EW) scale with chiral enhancement, which are preferred to evade exclusion limits from direct searches, correlations with other observables sensitive to EW symmetry breaking are expected. Such scenarios can be classified according to the $SU(2)_L$ representations and the hypercharges of the new particles. We match the resulting class of models with heavy new scalars and fermions onto SMEFT and study the resulting correlations with $h\to\mu\mu$ and $Z\to\mu\mu$ decays, where, via $SU(2)_L$ symmetry, the latter process is related to $Z\to\nu\nu$ and modified $W$-$\mu$-$\nu$ couplings.