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

• thoms2543
In summary, the neutrino mass eigenstate couple to the group of SU(2) doublet if we intentionally not impose any flavor symmetry on it.
thoms2543
can the neutrino mass eigenstate couple to the group of SU(2) doublet?if we intentionally not impose any flavor symmetry on it.

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

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!

what i mean is can we write

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

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

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.

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...

## 1. Can neutrino mass eigenstate couple to the group of SU(2)?

Yes, neutrino mass eigenstates can couple to the group of SU(2). Neutrinos are known to interact weakly, and the weak interaction is described by the SU(2) group. Therefore, neutrinos can couple to this group through weak interactions.

## 2. How does the coupling of neutrino mass eigenstates to SU(2) affect their properties?

The coupling of neutrino mass eigenstates to the SU(2) group does not affect their properties significantly. Neutrinos are still considered to be electrically neutral, and their mass, spin, and lepton number remain unchanged. However, the coupling does play a role in neutrino oscillations, which is the phenomenon of neutrinos changing from one mass eigenstate to another as they travel.

## 3. Can the coupling of neutrino mass eigenstates to SU(2) be measured experimentally?

Yes, the coupling of neutrino mass eigenstates to SU(2) can be measured experimentally. In fact, many experiments have been conducted to study the interactions of neutrinos with the SU(2) group. These experiments include neutrino oscillation experiments, which have provided strong evidence for the existence of neutrino mass and their coupling to the SU(2) group.

## 4. Is the coupling of neutrino mass eigenstates to SU(2) the same for all three types of neutrinos?

Yes, the coupling of neutrino mass eigenstates to the SU(2) group is the same for all three types of neutrinos. Neutrinos are classified into three types: electron neutrinos, muon neutrinos, and tau neutrinos. Despite their different masses, all three types of neutrinos interact weakly and therefore couple to the SU(2) group in the same way.

## 5. How does the coupling of neutrino mass eigenstates to SU(2) contribute to our understanding of the Standard Model?

The coupling of neutrino mass eigenstates to the SU(2) group is an important aspect of the Standard Model, which is the current best theory to explain the fundamental particles and their interactions. By studying the interactions of neutrinos with the SU(2) group, scientists can gain a better understanding of the weak interaction and its role in the universe. Additionally, the measurement of the coupling of neutrino mass eigenstates to SU(2) provides valuable information for testing and improving the Standard Model.

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