Can neutrino mass eigenstate couple to the group of SU(2)

[thoms2543]

can the neutrino mass eigenstate couple to the group of SU(2) doublet?if we intentionally not impose any flavor symmetry on it.

$$\left(\begin{array}{c}\nu_{1}\\e\end{array}\right)$$

 

[kuon]

sorry, I don't understand the question very well, what do you mean with the neutrino mass eigenstate coupling to the SU(2) doublet?

Which doublet? coupling? The flavor symmetry is broken by the Yukawa terms, what do you mean not imposing?

All I can tell you is this, I hope it helps:

1. In the SM the fermions get the mass from the Yukawa terms.
2. In the SM the neutrinos are massless so there's no need of a right handed neutrino.
3. Neutrino masses can be given (since they have been found experimentally). In that case (if you think of the neutrino as a Dirac particle), you just need to add a right handed neutrino, and you'll get a Yukawa just like the one for the quarks. Diagonalize the Yukawa matrix as for the quarks and you'll have your mass terms for the neutrinos.

Also the neutrino mass eigenstate right and left are together also in a term where they interact with the Higgs. After changing the basis from interacting to mass you can also look at the kinetic terms of the leptons to see which couplins there are for the neutrinos with the gauge W and Z gauge bosons.

That's all!

 

[thoms2543]

what i mean is can we write

$$\left(\begin{array}{c}\nu_{1}\\e\end{array}\right)$$

instead of
$$\left(\begin{array}{c}\nu_{e}\\e\end{array}\right)$$

 

[Parlyne]

No. We can't. $\nu_e$ can be written as a linear superposition of the mass states; but, the doublet structure is fundamental to the structure of the SU(2) couplings. If you replaced the standard doublet in the manner you suggest, you would change the way that weak interactions work. In particular, you would eliminate neutrino oscillations.

 

[thoms2543]

i try it that way in the lepton charge current. the result is i get the charge current exactly like quark current which is flavor changing if i write the mass eigenstate in the superposition of flavor eigenstate...i don't know i am correct to do that way...