suppose you have 2 bins each with cross section [itex] \sigma_1, \sigma_2[/itex]...(adsbygoogle = window.adsbygoogle || []).push({});

if you combine those bins, is it a logical assumption to say that the cross section will also be added?

I suppose from the equality of the luminosity one can get:

[itex] \frac{1}{2}[ N_1 / \sigma_1 + N_2 /\sigma_2] = N_{1+2}/ \sigma_{1+2}[/itex]

Obviously [itex] N_{1+2} = N_1 + N_2 [/itex] (the entries of the 2 bins is equal to the sum of the entries of each bin)

However by that I obtain:

[itex]\frac{N_1}{\sigma_1} + \frac{N_2}{\sigma_2} =2 \frac{N_1 + N_2}{\sigma_{1+2}}[/itex]

[itex] \sigma_{1+2} = \frac{2 \sigma_1 \sigma_2 (N_1 + N_2)}{N_1 \sigma_2 + N_2 \sigma_1}[/itex]

Isn't this result irrational?

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# A Cross sections of bins and combination

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