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A search for a long-lived scalar particle $\chi$ is performed, looking forthe decay ${B^+ \to K^+ \chi}$ with ${\chi \to \mu^+\mu^-}$ in $pp$ collisiondata corresponding to an integrated luminosity of $3\, {\rm fb}^{-1}$,collected by the LHCb experiment at centre-of-mass energies of $\sqrt{s}=7$ and8$\,$TeV. This new scalar particle, predicted by Hidden Sector models, isassumed to have a narrow width. The signal would manifest itself as an excessin the dimuon invariant mass distribution over the Standard Model background.No significant excess is observed in the accessible ranges of mass ${250 <m(\chi) < 4700\,\rm MeV/c^2}$ and lifetime ${0.1 < \tau(\chi) < 1000\,\rm ps}$.Upper limits on the branching fraction $\mathcal{B}(B^+ \to K^+ \chi(\mu^+\mu^-))$ at 95% confidence level are set as a function of $m(\chi)$ and$\tau(\chi)$, varying between $2\times10^{-10}$ and $10^{-7}$. These are themost stringent limits to date. The limits are interpreted in the context of amodel with a light inflaton particle.

Search for long-lived scalar particles in $B^+ \to K^+ \chi (\mu^+\mu^-)$ decays