Search for exotic decays of the Higgs boson to a pair of new light bosons in the $\mu \mu bb$ final state at $\sqrt{s}=13~\mathrm{TeV}$ with the full Run 2 dataset

A search for exotic decays of the $125\,\mathrm{GeV}$ Higgs boson is performed in a final state with two muons and two jets identified as originated from b quarks. The considered process is the Higgs decay to a pair of new light bosons, $\mathrm{a_1}$, one decaying to a pair of muons and the other to a pair of b quarks. The mass of the exotic boson, $m_{a_{1}}$, is assumed to be above $15~\mathrm{GeV}$ and below $m_{H}/2$. A data sample corresponding to an integrated luminosity of $138~\mathrm{fb}^{-1}$ recorded with the CMS detector is exploited where no statistically significant excess is observed over the standard model backgrounds. Upper limits at the $95\%$ confidence level are set on the branching fraction $Br(H\rightarrow a_{1} a_{1} \rightarrow \mu^{+} \mu^{-} b \bar b)$; they are found to be in the range $(0.17-3.3)\times 10^{{\rm -4}}$ depending on the $m_{a_{1}}$ values. $$\textit{This document has been revised with respect to the version dated November 8, 2022.}$$