- #1

- 5

- 1

- TL;DR Summary
- How to plot a normalized differential cross section from histogram with number of events/bin.

Hello,

I know that this question might be a bit silly but I am confused about plotting a normalized differential cross section. Suppose that I have a histogram with the x-axis representing some observable X and the y-axis the number of events per bin. I want the y-axis to show the normalized cross section, i.e., $$\frac{1}{\sigma}\frac{d\sigma}{dX}$$

First question: To obtain the differential cross section ##\frac{d\sigma}{dX}## I use ##N=\sigma L##, so ##\frac{\Delta N}{L\Delta X} = \frac{\Delta\sigma}{\Delta X}##, where ##\Delta N## is the number of events per bin, ##\Delta X## is the bin width, and L the integrated luminosity. Is this approach correct? If so, should I scale the full histogram by a factor of ##\frac{1}{L \Delta X}## or should I scale each bin by this factor?

Second question: I have to divide by the total cross section, i.e., multiply by ##\frac{L}{N}##, where N is the total number of events (the integral of the histogram). Is this right? If so, the luminosity will just cancel out, how the bin error can be scaled to the given luminosity then?

I hope these questions make sense. Thanks in advance.

I know that this question might be a bit silly but I am confused about plotting a normalized differential cross section. Suppose that I have a histogram with the x-axis representing some observable X and the y-axis the number of events per bin. I want the y-axis to show the normalized cross section, i.e., $$\frac{1}{\sigma}\frac{d\sigma}{dX}$$

First question: To obtain the differential cross section ##\frac{d\sigma}{dX}## I use ##N=\sigma L##, so ##\frac{\Delta N}{L\Delta X} = \frac{\Delta\sigma}{\Delta X}##, where ##\Delta N## is the number of events per bin, ##\Delta X## is the bin width, and L the integrated luminosity. Is this approach correct? If so, should I scale the full histogram by a factor of ##\frac{1}{L \Delta X}## or should I scale each bin by this factor?

Second question: I have to divide by the total cross section, i.e., multiply by ##\frac{L}{N}##, where N is the total number of events (the integral of the histogram). Is this right? If so, the luminosity will just cancel out, how the bin error can be scaled to the given luminosity then?

I hope these questions make sense. Thanks in advance.