Why Electron & Neutrino Form Doublet in Electroweak Model

In summary: For massless particles, this means a Lagrangian with a global SU(2) symmetry. However, for this symmetry to act on particles with the same spacetime properties, the only option is to combine the left electron and neutrino spinors into a doublet. This is supported by the fact that singlets are uncharged and do not fit into the SU(2) representation. Therefore, the left electron and neutrino spinors are combined into a doublet in the Weinberg-Salam model. In summary, the left electron and neutrino spinors are combined into a doublet in the Weinberg-Salam model in order to maintain both Lorentz and gauge invariance in the Lagrangian.
  • #1
ericthebee
4
0
Hello, I've unfortunately a trivial question, but one I couldn't answer by reading my references.
In the Weinberg-Salam model, why do we take the left electron and neutrino spinors to form a doublet?
I'd like a "physical" answer, if possible, and a more formal one, which I think is based on the SU(2) representations.
My teacher's notes start with writing down a Lagrangian for massless electron and neutrino, and then he literally says "...we must now determine the internal symmetries of the Lagrangian. It's obvious that an internal symmetry must act on particles which have the same space-time properties. The only possibility is then to put together the electron and the neutrino (left parts) in a doublet". Perhaps I'm just too stupid, but it's unintelligible to me.

Thanks everyone :).
 
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  • #2
You have two particles, so your choices are one doublet or two singlets. Since singlets are uncharged, that eliminates two singlets as a possibility.
 
  • #3
Technically, you could have had them in singlets (anomaly cancelation aside, having them in singlets would mean also putting the quarks in singlets and then there would be no fermions charged under SU(2)). However, this is not what we observe in Nature.

The general idea is to build a Lagrangian which is both Lorentz and gauge invariant.
 

FAQ: Why Electron & Neutrino Form Doublet in Electroweak Model

Why do electrons and neutrinos form a doublet in the electroweak model?

The electroweak model is a theory that unifies the electromagnetic and weak nuclear forces. In this model, the fundamental particles are organized into families or generations. The first generation includes the electron and its associated neutrino, while the second and third generations include heavier particles with similar properties. The reason for this organization is still not fully understood, but it is believed to be a consequence of the symmetries and interactions between these particles and the forces they experience.

How does the doublet structure of electrons and neutrinos relate to the weak nuclear force?

In the electroweak model, the weak nuclear force is carried by particles called W and Z bosons. These particles interact with particles in the electron-neutrino doublet, causing them to change into each other. This process is known as weak isospin and is responsible for the weak nuclear force, which is much weaker than the electromagnetic force. The doublet structure of electrons and neutrinos is essential for this interaction to occur and is a key aspect of the electroweak model.

What evidence supports the idea of electrons and neutrinos forming a doublet?

The existence of the electron-neutrino doublet is supported by many experiments and observations. For example, the weak interaction between electrons and neutrinos has been observed in particle accelerators, where they can be created and measured. Additionally, neutrinos have been detected coming from nuclear reactions, providing evidence for their existence and interactions with electrons. The mathematical predictions of the electroweak model, which include the doublet structure, have also been verified through various experiments.

Can the doublet structure of electrons and neutrinos be explained by other theories?

The electroweak model is currently the most successful theory for explaining the properties of particles and their interactions. Other theories, such as grand unified theories, may also provide explanations for the doublet structure of electrons and neutrinos. However, these theories are still being tested and refined, and the electroweak model remains the most widely accepted and supported theory for this phenomenon.

How does the doublet structure of electrons and neutrinos impact our understanding of the universe?

The doublet structure of electrons and neutrinos is a fundamental aspect of the electroweak model, which is a key component of the Standard Model of particle physics. The Standard Model provides a framework for understanding the fundamental particles and forces that make up our universe. By understanding the doublet structure, we gain a deeper understanding of the symmetries and interactions that govern the behavior of particles and the forces that act on them. This knowledge is crucial for advancing our understanding of the universe and exploring the mysteries of the subatomic world.

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