What's the Difference Between Cross Sections?

[Safinaz]

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

 

[AndyW]

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.