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Using a geometric description of 2HDM, the CP-odd invariants are classified into three independent sectors: scalar potential, Yukawa interaction, and CKM matrix. We calculate the effective thermal potential of 2HDM in a basis invariant way and show that the CP phases in the CKM matrix cannot leak to the effective potential at all orders. In the 2HDM with a softly broken Z₂ symmetry, the leading thermal correction to the effective potential tends to restore the CP symmetry at high temperatures.
Cao et al. (Fri,) studied this question.
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