The $h \to 4 \ell$ spectrum at low $m_{34}$: Standard Model vs. light New Physics

We analyze $h\to 4\ell$ decays in the kinematical region where the dilepton pair of low invariant mass ($m_{34}$) is not far from QCD resonances ($\Psi$ and $\Upsilon$ states). On the one hand, we present precise predictions of the spectrum within the Standard Model, taking into account non-perturbative QCD effects. On the other hand, we illustrate the sensitivity of this spectrum to New Physics models predicting the existence of new exotic light states. In particular, we show that parameter regions of models relevant to explain the $(g-2)_\mu$ anomaly could be probed in the future by means of $h\to 4\ell$ decays.