# How to construct effective interaction vertex?

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In literatures, I often come across interactions like the $D^*D\gamma$ vertex:
$$\mathcal{L}_{D^*D\gamma}(x)=\frac{e}{4} \epsilon^{\mu \nu \alpha \beta} F_{\mu \nu}(x)\left({g_1} D^{*-}_{\alpha \beta}(x)D^+(x)+g_2 \bar{D}^{*0}_{\alpha\beta}(x)D^0{x}\right)+h.c.$$
where $D^{(*)}$ stands for $D^{(*)}$meson.

I can only check that each term respect parity, however why the relative sign between $g_1$ and $g_2$ are positive? Is it just a convention?

The above formula is about pseudo-scalar vector (massless) vector or $PVV$interaction.
As to construct $VVV, VPV$ or other fancy interactions, I have no idea.
I've searched on the web and the textbook, but they are not focused on this.

So how to construct interactions like this from scratch?

I'll be very appreciated if someone could tell me any books or references on this topic.

asked Feb 29, 2016

Normally the idea of "matching" in EFT is to write down all possible interactions that respect the symmetry, organized by operator dimensions. Then calculate the scattering amplitudes as a function of coupling constants, then match them with experiments or the UV theory results, then you can determine the values of the coupling constants.

@JiaYiyang Yes, I know the general constrains of the symmetry. However, I can't be 100 percent sure about the terms I wrote down, so I really want a textbook or papers who has a through treatment on this topic. For example, the interaction of massive $V$ in $VVP$ vertex will be different from a massless vector particle; gauge symmetry will play a important role.

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