# Two doublets and a triplet

1. Jun 3, 2012

### majon

Updated: I was reading a paper discussing a Higgs triplet under SU(2)L. In addition to the usual Higgs doublet. Both are written as:

$$D = \begin{pmatrix} x \\ y \end{pmatrix}$$
$$T = \begin{pmatrix} X \\ Y \\ z \end{pmatrix}$$

Now, at some point, the author says the lagrangian contains a term like,

$$D D T^{\dagger}$$

$$\sim c \begin{pmatrix} x \\ y \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} \begin{pmatrix} X & Y & z \end{pmatrix}$$

In the paper, c is a factor that doesn't carry any group index.

I have a naive question:

How can: (2 ×1) (2 ×1) (1×3) be an allowed term? Also, this reminded me of something I heard and didn't understand, which is that two doublets can produce a triplet. But I don't see how.

Please note that I encounter group theory very little in my studies, hence I find myself constantly confused about some of its techniques.

Last edited: Jun 3, 2012