Exploring the Topological Cross Section in Experimental Quantum Physics

[cfar]

Hello,

I've found in some of the articles on experimental quantum physics the term "Topological cross section"
Now I'm trying to understand what is it and in particular what the difference between topological and differential cross section?

Thanks in advance for suggestions on any reading materials.

 

[Bill_K]

I believe it means the total cross section for reactions with n outgoing lines.

 

[cfar]

I believe it means the total cross section for reactions with n outgoing lines.

I'm not sure if I understand you right. Can you please give me a relationship between total cross section and topological cross section.

 

[Bill_K]

From what I gather, the total cross section σ is the sum over n of the topological cross sections σ_n. Again, σ_n is the total cross section (i.e. integrated over angles) of all reactions with n outgoing lines. It looks like they count only visible (charged) lines and/or just the ones that exceed a given momentum.

 

[andrien]

May be it is just another word used,because in drawing feynman diagrams one use only those diagrams which are topologically different.

 

[Bill_K]

May be it is just another word used,because in drawing feynman diagrams one use only those diagrams which are topologically different.

Every Feynman diagram is topologically different. And every process comes from an infinite number of different Feynman diagrams.

 

[andrien]

: Every Feynman diagram is topologically different.

in drawing feynman diagrams one use only those diagrams which are topologically different.

Do you find contradication between these two statements?

 

[cfar]

From what I gather, the total cross section σ is the sum over n of the topological cross sections σ_n. Again, σ_n is the total cross section (i.e. integrated over angles) of all reactions with n outgoing lines. It looks like they count only visible (charged) lines and/or just the ones that exceed a given momentum.

Well, your guess about counting only charged particles I can understand, but counting only ones that exceed any given momentum can't be true. In this case the value of this cross section would greatly depend on which momentum they will take.

 

[cfar]

May be it is just another word used,because in drawing feynman diagrams one use only those diagrams which are topologically different.

I think it's not that simple. "digitool.library.mcgill.ca/thesisfile74351.pdf" I found the following definition of this term:

The term topological cross section means that the cross section is not corrected for any production of possible meson resonances that might be produced in an intermediate stage before we observe the final six (four) pions.

Thought I didn't understand it yet.