Bhabha Scattering: Relative Sign Difference & Fermi Statistics

[guestspeaker]

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...

 

[daschaich]

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.

 

[guestspeaker]

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?

 

[daschaich]

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.

 

[guestspeaker]

okay okay :) I was hoping for something immediately obvious from just the diagrams (like the -1 for fermion loop etc.)

 

[daschaich]

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.

 

[ansgar]

the relative minus sign comes from the fact that you must reorder your fermion operators relative the different diagrams when you make the contraction.