Tree-level unitarity constraints in Two-Higgs Doublet Model

[mr. bean]

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.

 

[AndyW]

Hi there,

I'm glad to see that you are interested in the Two-Higgs Doublet Model and are trying to understand the unitarity constraints. The article you have attached is a great resource for understanding this topic. Let me try to provide some guidance for calculating the scattering matrices in eq. (7).

Firstly, it is important to note that eq. (7) represents the scattering amplitudes between states in the Two-Higgs Doublet Model. These states are defined in eq. (4) and (5) as the physical Higgs bosons (H, h, A, and H+), the Goldstone bosons (G+, G-), and the would-be Goldstone bosons (G0, G'0). These states are related to the two Higgs doublets (Φ1 and Φ2) through the relations given in eq. (3) and (6).

To calculate the scattering matrices, you can use the Feynman rules for the Two-Higgs Doublet Model, which are derived from the potential given in eq. (1). These rules will allow you to calculate the Feynman diagrams for the scattering processes and then use the relations in eq. (3) and (6) to express the scattering amplitudes in terms of the states in eq. (4) and (5).

For example, to calculate the scattering amplitude for the process H+G- → H+G-, you would first use the Feynman rules to draw the relevant Feynman diagram. Then, using the relations in eq. (3) and (6), you can express the H+ and G- states in terms of the Higgs doublets Φ1 and Φ2. Finally, you can use the Feynman rules to calculate the scattering amplitude for the process in terms of the Higgs doublets, and then use the relations in eq. (3) and (6) again to express the amplitude in terms of the physical states in eq. (4) and (5).

I hope this helps you understand how to use eq. (3) and (6) to calculate the scattering matrices in eq. (7). It may take some practice and patience, but with the help of the Feynman rules and the relations in eq. (3) and (6), you should be able to calculate the scattering amplitudes for all the processes listed in eq. (7).