Normalization, reweighting, and the scale factor:

[mborn]

Hi all,

I am about to begin my studies as an experimentalist and I keep hearing about these terms when someone represents his data as histograms.
Can some one here, please, give me a clear explanation about their meanings.
My background is theory and you can use as much mathematics as you can!

Thanks a lot in advance,

~mborn

 

[Rajini]

normalization: generally this term comes in spectrum...after getting a experimental spectrum one often normalize it...experimental spectrum and normalized spectrum are same but with different y-axis value..for e.g., area of a exp. spectrum is different from normalized spectrum..usually a normalized one's area is often 1 or some value.
reweighting..:similar to normalization..it depends on experiment.
scale factor: usually multiplying either x- or y-axis by a constant.
hope this help

 

[mborn]

To make things eaiser, let's say you are in a a particle physics experiment that is trying to discover a particle.
Now, for normalization, how can we make the area under the histogram equal one?
Can you elaborate more on reweighting? What is the difference between reweighting (to Monte Carlo) and normalization?

~mborn

 

[Rajini]

Hi,
normalization(actually this is a general technique used everywhere not only for particle physics):
think..we have a exp. spectrum $$\int I(E)\;{\rm d}E=X$$
now we will normalize that spectrum such that area under the spectrum is 1.
So what ppl. usually do is
$$\int I_{\rm norm}(E)\;{\rm d}E=\frac{1}{X}\int I(E)\;{\rm d}E=1$$
This is how a normalization done.[but i am not completely sure..i assume others from this forum may correct us in case of error.]
Now i can give a example for weighing (i don't know exactly what is reweighing?).
in this integral:
$$\int \frac {I(E)}{E}\;{\rm d}E$$
$$I(E)$$ is weighed by a factor of $$(1/E)$$
hope it may help..

 

[mborn]

Thank you Rajini,

So, I am OK now with normalization! Still I hope someone here will explain reweighting for us.
As far as I know, reweighting is to divide the number of events in each bin of a histogram by the total number of events. If this is true, then why do we need to do reweighting?

~mborn