- #1
ChrisVer
Gold Member
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suppose you have 2 bins each with cross section [itex] \sigma_1, \sigma_2[/itex]...
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?
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?