A Light Higgs at the LHC and the B-Anomalies

After the Higgs discovery, the LHC has been looking for new resonances, decaying into pairs of Standard Model (SM) particles. Recently, the CMS experiment observed an excess in the di-photon channel, with a di-photon invariant mass of about 96~GeV. This mass range is similar to the one of an excess observed in the search for the associated production of Higgs bosons with the $Z$ neutral gauge boson at LEP, with the Higgs bosons decaying to bottom quark pairs. On the other hand, the LHCb experiment observed a discrepancy with respect to the SM expectations of the ratio of the decay of $B$-mesons to $K$-mesons and a pair of leptons, $R_{K^{(*)}} = BR(B \to K^{(*)} \mu^+\mu^-)/BR(B\to K^{(*)} e^+e^-)$. This observation provides a hint of the violation of lepton-flavor universality in the charged lepton sector and may be explained by the existence of a vector boson originating form a $U(1)_{L_\mu - L_\tau}$ symmetry and heavy quarks that mix with the left-handed down quarks. Since the coupling to heavy quarks could lead to sizable Higgs di-photon rates in the gluon fusion channel, in this article we propose a common origin of these anomalies identifying a Higgs associated with the breakdown of the $U(1)_{L_\mu - L_\tau}$ symmetry and at the same time responsible to the quark mixing, with the one observed at the LHC. We also discuss the constraints on the identification of the same Higgs with the one associated with the bottom quark pair excess observed at LEP.