Scalar singlets under the Standard Model gauge group appear naturally in many well-motivated New Physics scenarios, such as the composite Higgs models. Unlike the Higgs boson in the Standard Model, they can induce large flavour-changing neutral currents (FCNCs) in the top sector. We investigate systematically the effects of a light scalar singlet S with top-quark FCNC couplings, by including the low-energy constraints from the Bs → μ+μ− decay, the muon anomalous magnetic moment (g − 2)μ and the neutron Electric Dipole Moment (EDM). We also perform a detailed Monte-Carlo simulation of the channel pp → tS + j with S → μ+μ− and S → \( b\overline{b} \) , and investigate the LHC sensitivity to the tcS couplings. It is found that the scalar singlet S can induce scalar-type contributions to the Bs → μ+μ− decay, which do not suffer from the helicity suppression and contain a large CKM factor \( {V}_{cs}^{\ast }{V}_{tb} \) . As a result, constraints on the tcS couplings from the measured branching ratio \( \mathcal{B} \) (Bs → μ+μ−) are quite stringent, being even stronger than the expected LHC sensitivity in some parameter spaces. Besides the CP-conserving tcS couplings, we have also considered the case of CP-violating tcS couplings, with \( {y}_{R,L}^{ct}=\left|{y}_{R,L}^{ct}\right|{e}^{i{\theta}_{R,L}} \) . It is found that the CP observables \( {\mathcal{A}}_{\Delta {\varGamma}_s}^{\mu \mu} \) and \( {\mathcal{S}}_{\mu \mu} \) of the Bs → μ+μ− decay are sensitive to the phase θR, while the neutron EDM can provide bounds on the phase difference θL − θR. Therefore, they are complementary to each other in probing the CP phases of the tcS couplings.
