How to calculate yields from the cross section?

[phypar]

I have a result for the differential cross section [tex]d\sigma/d\eta dP_T^2[/tex], but I want to obtain the corresponding differential yields [tex]dN/d\eta dP_T^2[/tex]. How to relate yields to cross section?

 

[dukwon]

Cross section has units of area, and yield is dimensionless, so you need to multiply by some quantitiy that has units of inverse area.
This would be the number of particles to pass through a unit area, otherwise known as "integrated luminosity"
\begin{equation}
L = \int \mathcal{L}\;\text{d}t
\end{equation}
where ##\mathcal{L}## is luminosity (more properly called "flux" outside of particle physics), which is the number of particles passing through a unit area per unit time.
Yield is simply determined from
\begin{equation}
N = L\sigma
\end{equation}