Bhabha Scattering: Relative Sign Difference & Fermi Statistics

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Discussion Overview

The discussion revolves around the relative sign difference in the diagrams for Bhabha scattering, particularly focusing on the role of Fermi statistics and Wick contractions in understanding this phenomenon. The scope includes theoretical reasoning and technical explanations related to particle physics diagrams.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the relative sign difference in Bhabha scattering diagrams and suggests that Fermi statistics may influence this but is unclear on how.
  • Another participant recommends consulting Peskin and Schroeder for a similar example in Yukawa theory, indicating that careful work through Wick contractions is necessary.
  • A participant notes that the example in Peskin and Schroeder involves t- and u-channel diagrams, questioning if a similar heuristic argument can be applied to the s- and t-channel diagrams of Bhabha scattering without using Wick contractions.
  • Another participant emphasizes the importance of Wick contractions for understanding the diagrams and mentions that checking the signs of the Bhabha diagrams is a straightforward calculation.
  • One participant expresses a desire for an obvious explanation from the diagrams alone, referencing the (-1) factor associated with fermion loops.
  • A later reply mentions that the relative minus sign arises from the need to reorder fermion operators when making contractions between different diagrams.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the explanation for the relative sign difference, with multiple viewpoints and approaches being discussed. The discussion remains unresolved regarding the clarity of the heuristic arguments and the necessity of Wick contractions.

Contextual Notes

The discussion highlights the dependence on specific calculations and the interpretation of Fermi statistics, as well as the potential limitations of understanding the diagrams in isolation without reference to established Feynman rules.

guestspeaker
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I cannot figure out why there is a relative sign difference between the two diagrams for bhabha scattering. Fermi statistics is at play here but I don't see how that affects the relative sign between 2 different diagrams...
 
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Work through the Wick contractions carefully. If you have a copy of Peskin and Schroeder handy, in section 4.7 they do exactly this for an example in Yukawa theory that is similar to Bhabha scattering.
 
The example in P&S is with t- and u-channel diagrams, for which the negative sign can come from a "heuristic" argument of antisymmetrization of the final states.

But for Bhabha scattering, the diagrams are s- and t-channel... is there a similar heuristic argument without resorting to the Wick contractions?
 
I thought you wanted to understand where the heuristic argument involving Fermi statistics came from. The diagrams are simply shorthand for the processes, including the Wick contractions; "resorting" to the latter is necessary to understand the former.

Besides, it's a pretty trivial calculation; it took me three lines to check the signs of the Bhabha diagrams, and should only have taken two.
 
okay okay :) I was hoping for something immediately obvious from just the diagrams (like the -1 for fermion loop etc.)
 
guestspeaker said:
okay okay :) I was hoping for something immediately obvious from just the diagrams (like the -1 for fermion loop etc.)

I was wondering whether to mention the fermion loop, because its (-1) factor also comes from anticommuting the fermion operators to untangle the contractions! It's not something that I can derive from the diagram in isolation (without reference to the Feynman rules), it's just so trivial a calculation that it's easy to remember how it goes.PS. Where are my manners? Welcome to Physics Forums! Hope you stick around.
 
the relative minus sign comes from the fact that you must reorder your fermion operators relative the different diagrams when you make the contraction.
 

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