Phenomenology of a very light scalar (100 MeV < mh < 10 GeV) mixing with the SM Higgs

In this paper we investigate the phenomenology of a very light scalar, h, with mass 100 MeV < m(h) < 10 GeV, mixing with the SM Higgs. As a benchmark model we take the real singlet scalar extension of the SM. We point out apparently unresolved uncertainties in the branching ratios and lifetime of h in a crucial region of parameter space for LHC phenomenology. Bounds from LEP, meson decays and fixed target experiments are reviewed. We also examine prospects at the LHC. For m(h) less than or similar to m(B) the dominant production mechanism is via meson decay; our main result is the calculation of the differential pT spectrum of h scalars originating from B mesons and the subsequent prediction of upto thousands of moderate (triggerable) pT displaced dimuons possibly hiding in the existing dataset at ATLAS/CMS or at LHCb. We also demonstrate that the subdominant Vh production channel has the best sensitivity for m(h) greater than or similar to m(B) and that future bounds in this region could conceivably compete with those of LEP.