Sunset / sunrise diagrams in 2D

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SUMMARY

The discussion focuses on the calculation of the complete amplitude for a 2D sunrise diagram involving integrals with different masses. The specific integral in question is $$ \int d^2k d^2l \frac{1}{(k^2-m_1^2)(l^2-m_2^2)((p-k-l)^2-m_3^2)} $$, where p represents the external momentum. The complexity arises when dealing with generic masses, particularly when some masses are equal and others are zero. The context is related to phi four theory in 2D, indicating a specific theoretical framework for the calculations.

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  • Understanding of quantum field theory, specifically phi four theory.
  • Familiarity with multi-dimensional integrals and their applications in physics.
  • Knowledge of mass parameters in particle physics and their implications in diagrams.
  • Proficiency in mathematical techniques for evaluating integrals involving singularities.
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  • Research techniques for evaluating multi-dimensional integrals in quantum field theory.
  • Study the implications of mass variations in Feynman diagrams, particularly in phi four theory.
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The discussion is beneficial for theoretical physicists, graduate students in quantum field theory, and researchers focusing on particle interactions and Feynman diagrams.

nidnus
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Hi,

Can anyone point me to a reference where the complete amplitude for a sunrise diagram in 2D with generally different masses is written down. That is, I want the value of the following integral

$$ \int d^2k d^2l \frac{1}{(k^2-m_1^2)(l^2-m_2^2)((p-k-l)^2-m_3^2)}

$$

where p is the external momentum. For equal masses the answer is simple while it seem to be more complicated for generic masses. I'm especially interested in the case where some of the masses are equal and others are zero.

Thanks
 
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What theory is it?
 
Doesn't really matter. The integral is as stated above. If you want to you can think about it as phi four theory in 2D.
 

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