Tree-level diagram Moller scattering

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Homework Help Overview

The discussion revolves around Moller scattering of electrons, specifically the tree-level diagrams that can be derived from a given Lagrangian for spinless electrons and photons. The participants are exploring the implications of the Lagrangian and the types of diagrams that can be drawn for the process $$e^-e^- \to e^-e^-$$.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the interaction terms in the Lagrangian and question the number of tree-level diagrams that can be constructed. There is a focus on identifying the t and u channels and the possibility of an s-channel diagram. Some participants express uncertainty about whether a third diagram exists and whether the notation for the electrons is appropriate given the context.

Discussion Status

The discussion is active, with participants presenting differing views on the existence of an s-channel diagram. Some suggest that the original question may contain an error, while others defend the possibility of such a diagram based on the properties of the particles involved. There is an ongoing examination of the implications of the Lagrangian and the nature of the particles.

Contextual Notes

Participants note that the Lagrangian only includes the field for the electron without its antiparticle, leading to questions about the nature of the electron in this context. There is a recognition that the notation used may be misleading, given the assumptions about particle properties.

kelly0303
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Homework Statement


If the electron and photon were spinless, in the non-relativistic limit we can write the Lagrangian as: $$L=-\frac{1}{2}\phi_e(\Box+m_e^2)\phi_e-\frac{1}{2}A_0\Box A_0+em_eA_0\phi_e\phi_e$$ For Moller scattering $$e^-e^- \to e^-e^- $$ Draw the three tree level diagrams following from the Lagrangian.

Homework Equations

The Attempt at a Solution


So the interaction part must couple 2 electrons with a photon. 2 tree level diagrams are normal scattering (like in QED) in t and u channel. What is the 3rd one? Is there another vertex I am missing from the Lagrangian? Thank you!
 
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kelly0303 said:

Homework Statement


If the electron and photon were spinless, in the non-relativistic limit we can write the Lagrangian as: $$L=-\frac{1}{2}\phi_e(\Box+m_e^2)\phi_e-\frac{1}{2}A_0\Box A_0+em_eA_0\phi_e\phi_e$$ For Moller scattering $$e^-e^- \to e^-e^- $$ Draw the three tree level diagrams following from the Lagrangian.

Homework Equations

The Attempt at a Solution


So the interaction part must couple 2 electrons with a photon. 2 tree level diagrams are normal scattering (like in QED) in t and u channel. What is the 3rd one? Is there another vertex I am missing from the Lagrangian? Thank you!
There is no third diagram, indeed. It seems to be a mistake in the question (they probably were thinking of ##e^-e^+ \to e^+ e^-##).
 
I don't see why you can't have an s-channel diagram. The problem is just asking for the scattering between scalars right? There's no e^+ particle.
 
king vitamin said:
I don't see why you can't have an s-channel diagram. The problem is just asking for the scattering between scalars right? There's no e^+ particle.
A scalar can still be charged. If the scalar electron is charged, there cannot be an s-channel for the process ##e^-e^- \to e^-e^-##.

But now I notice that the Lagrangian contains only ##\phi_e##, not ##\phi_e^*## so it seems that you are correct and I was wrong, and that their electron is its own antiparticle (in which case the notation ##e^-## is terribly misleading).
 

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