bhabha scattering

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

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.