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Hi, I'm looking at the unitarity constraints for the Two-Higgs Doublet Model and I'm trying to follow what they do in the attached article, which can also be found here: https://arxiv.org/pdf/hep-ph/0312374v1.pdf.

However I do not know how to get the scattering matrices in eq. (7). They say that it is an easy calculation that can be done for each set of states given in eq. (4) and (5) using the potential given in eq. (1) and using the relations given in eq. (3) and (6).

I do not know how I should use eq. (3) and (6). It would be very nice if someone could give me hints for how to do this.

However I do not know how to get the scattering matrices in eq. (7). They say that it is an easy calculation that can be done for each set of states given in eq. (4) and (5) using the potential given in eq. (1) and using the relations given in eq. (3) and (6).

I do not know how I should use eq. (3) and (6). It would be very nice if someone could give me hints for how to do this.