What's the Difference Between Cross Sections?

In summary: Expert SummarizerIn summary, the differential cross section is a measure of the probability of a specific particle interaction occurring at a given energy or mass, while the total cross section is a measure of the overall probability of any interaction occurring. The differential cross section focuses on a specific energy or mass range, while the total cross section looks at the entire energy or mass spectrum. This leads to a peak in the differential cross section at the specific energy or mass where the interaction is most likely to occur, while the total cross section shows the variation of the overall interaction probability with energy or mass.
  • #1
Safinaz
258
8
Hi all,

I'd like to more understand what is the difference between when we draw the differential cross section

## \frac{d \sigma ~ (pb)}{dM ~ (GeV)} ##, when we draw ## \sigma ~ (pb) /bin##

and the total cross section ## \sigma ~ (pb) ## .. I mean for a process like

p p > x x~ (where x is a particle has mx=100 GeV) .. ## \frac{d \sigma ~ (pb)}{dM ~ (GeV)} ##
and ## \sigma ~ (pb) /bin ## VS. mx gives a peak at 100 GeV while ## \sigma ~ (pb) ## gives the variation of ## \sigma ## with mx ..

Bests,
Safinaz
 
Last edited:
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  • #2


Hello Safinaz,

The differential cross section ## \frac{d \sigma ~ (pb)}{dM ~ (GeV)} ## is a measure of the probability of a specific particle interaction occurring at a given energy or mass M. It is typically used to study the energy dependence of a particular process, such as the production of the x x~ particles in the p p > x x~ process you mentioned.

On the other hand, the total cross section ## \sigma ~ (pb) ## is a measure of the overall probability of any interaction occurring between the two particles. It takes into account all possible energies or masses and gives an overall picture of the interaction.

The difference between the two is that the differential cross section focuses on a specific energy or mass range, while the total cross section looks at the entire energy or mass spectrum. This is why the differential cross section will show a peak at the specific energy or mass where the interaction is most likely to occur, while the total cross section will show the variation of the overall interaction probability with energy or mass.

I hope this helps clarify the difference between the two quantities. Let me know if you have any further questions.


 

1. What is a cross section?

A cross section is a 2-dimensional shape that results from cutting a 3-dimensional object with a plane. It provides a view of the internal structure of the object.

2. What is the purpose of using cross sections?

Cross sections are used to analyze and understand the internal structure of an object. They can also be used to calculate the volume, surface area, and other properties of the object.

3. What is the difference between a horizontal and vertical cross section?

A horizontal cross section is taken by cutting the object along a horizontal plane, while a vertical cross section is taken by cutting the object along a vertical plane. This results in different views of the object's internal structure.

4. How are cross sections used in real-life applications?

Cross sections are used in various fields such as engineering, architecture, and medicine. They can be used to design and construct buildings, analyze the structure of materials, and understand the anatomy of the human body.

5. Are all cross sections the same?

No, cross sections can vary depending on the angle and location of the plane used to cut the object. Different cross sections can provide different information about the object's internal structure.

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