We study a dark matter model with one singlet complex scalar and two Higgs doublets. The scalar potential respects a softly broken global symmetry, which makes the imaginary part of the singlet become a pseudo-Nambu-Goldstone boson acting as a dark matter candidate. The pseudo-Nambu-Goldstone nature of the boson leads to the vanishing of its tree-level scattering amplitude off nucleons at zero momentum transfer. Therefore, although the interaction strength could be sufficient large to yield a viable relic abundance via thermal mechanism, direct detection is incapable of probing this candidate. We further investigate the constraints from Higgs measurements, relic abundance observation, and indirect detection. *

We investigate the potential stochastic gravitational waves from first-order electroweak phase transitions in a model with pseudo-Nambu-Goldstone dark matter and two Higgs doublets. The dark matter candidate can naturally evade direct detection bounds, and can achieve the observed relic abundance via the thermal mechanism. Three scalar fields in the model obtain vacuum expectation values, related to phase transitions at the early Universe. We search for the parameter points that can cause first-order phase transitions, taking into account the existed experimental constraints. The resulting gravitational wave spectra are further evaluated. Some parameter points are found to induce strong gravitational wave signals, which have the opportunity to be detected in future space-based interferometer experiments LISA, Taiji, and TianQin.

A minimal model of spontaneous CP violation based on two-Higgs-doublet and two-Higgs-singlet fields is constructed. The model has a Peccei-Quinn-type U(1) symmetry which breaks at lo8-10" GeV energy scale. Physical CP violation arises from scalar-pseudoscalar mixings. A relatively large electric dipole moment for charged leptons and small 1 E'/E are predicted.In spontaneous T-violation (STV) models,' CP is assumed to be a good symmetry prior to symmetry breakdown and hence BQcD is taken to be zero from the outset.

Using the photon spectrum of a high energy charged parton, we investigate the 𝐽/𝜓 production via the two photon interaction mechanism in ultra-peripheral pp collisions. It is shown that the contributions from the direct electromagnetic and the corresponding fragmentation processes are meaningful for the 𝐽/𝜓 productions in ultra-peripheral pp collisions at LHC energy.