A model of spontaneous CP breaking at low scale

We introduce a CP symmetric model where masses of fermions are given by dimensional-5 operators, and CP is spontaneously broken at TeV scale. The unique feature of the model is that new CP symmetric gauge sector coexists with new CP symmetric fermions simultaneously at TeV scale. An ultraviolet completion of the model is also proposed. It is observed that the fine-tuning of the SM Higgs boson mass in this model is softened in a relatively small amount approximately up to 6 TeV. Other interesting consequences are presence of a possible dark matter candidate whose mass may be bounded from above by the SM Higgs mass. The model may also provide an explanation of recently observed flavour anomalies.