Question about a cross section from PDG

[ChrisVer]

Hi everyone, I was wondering, is the cross section at Eq 50.25 in
http://pdg.lbl.gov/2017/reviews/rpp2017-rev-cross-section-formulae.pdf
correct?

Because I see a term in the denominator with [itex]\frac{1}{s\Gamma}[/itex] whereas in several other references, the propagator term in the matrix element comes with [itex]\frac{1}{M \Gamma}[/itex].
[eg. eq29 here http://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20150205.11.pdf and I can give a further list]
Thanks.

 

[mfb]

I'm a bit surprised to the the center of mass energy there, but note that the two expressions are very similar for ##\Gamma \ll M##: The right term is only relevant if ##\sqrt s \approx M##.

 

[ChrisVer]

Yup. Since I've found instances where the additional part in the propagator (added to [itex]s-m^2 [/itex] ) is written as a function of [itex]s[/itex]: [itex] \Pi(s)[/itex], and through choosing a renormalization scheme they can set it as : [itex] \gamma(s = M^2 ) = M [/itex] , which basically translates to what you've written about the right term.

Additionally I've found that the propagator can be written as: [itex]D(s) = \frac{1}{s-m^2 + i \sqrt{s} \Gamma} [/itex] (after summing up several Feynman diagrams)... as shown on slide7 here: https://www.stfc.ac.uk/files/lecture-7/

Finding multiple different instances for the same thing is confusing indeed...