# Why Tri-Bimaximal ?

1. Jan 17, 2007

### mjsd

Why "Tri-Bimaximal"?

$$\displaymath{U_{PMNS}=\begin{pmatrix} \sqrt{2/3}& 1/\sqrt{3}& 0\\ -1/\sqrt{6}& 1/\sqrt{3}& 1/\sqrt{2}\\ 1/\sqrt{6}& -1/\sqrt{3}& 1/\sqrt{2}\end{pmatrix}}$$

This matrix implies $$\theta_{13}=0, \sin \theta_{12} = 1/\sqrt{3}$$ (ie. not maximal mixing) and $$\theta_{23}=\pi/4$$ (ie. maximal mixing)

OK, to my question, WHY do we call this matrix "Tri-Bimaximal"? How does this name come about? Two large mixing angles and the $$1/\sqrt{3}$$?

2. Jan 17, 2007

### Accidently

The "bi-maximal mixing" is from the third column -- that means the third mass eigenstate is a maximal mixing state of muon neutrino and tauon neutrino flavor eigenstates.

Whereas the "tri-maximal mixing" can be seen from the second column -- the second mass eigenstate is a full mixing of all the three flavor eigenstates (each of them occupies 1/3)

3. Jan 17, 2007

### mjsd

oh well, physicists have weird names for things...but I knew this one has good meaning (for someone told me before, but I forgot). Thanks.

4. Jan 18, 2007

### arivero

Someone (CarlB?) had a history about a referee rejecting a paper on grounds of the absurdity of using such name, tribimaximal, in the title or abstract of a paper.

5. Jan 18, 2007

### mjsd

perhaps those guys (like me before) didn't quite know the meaning of tribimaximal when they are using them (although I am very well aware of all the properties of the mixing matrix, I didn't know tri-bimaximal really means tri-maximal and bi-maximal)? May be there are ppl out there who really hate the term tri-bimaximal.

6. Jan 18, 2007

### CarlB

Actually, it wasn't a referee rejecting it, just a particle theorist who wouldn't read past the title of the Koide paper that said "tribimaximal".

The sociologists have studied how physicists read physics papers and it turns out that very few papers that are "read" actually are considered at all beyond a very shallow level. The mathematics is usually too difficult to allow people to spend the time to read much.

See the paper Does understanding physical science need deep mathematical knowledge? at this site: