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I was looking at the attached picture, where it gives the Higgs Mass obtained from the two different channels from ATLAS and CMS.
Let's only talk about the diphoton channel : H\rightarrow \gamma \gamma
From the ATLAS the mass value is:
m_{Ah} =126.02 \pm 0.51
and the CMS:
m_{Ch} =124.70 \pm 0.34
Now it gives the combined result from ATLAS+CMS:
m_{ACh}=125.07 \pm 0.29
How can obtain the mean and error for the ATLAS+CMS?
I tried getting the weights w_i = \sum_j (C^{-1})_{ij} \Big/ \sum_{kl} (C^{-1})_{kl} with C the covariance matrix. Since they are different detectors they are not correlated and so the covariance matrix only has the variances on the diagonal. I obtain:
w_A \approx 3.84468/12.4952
w_C \approx 8.65052/12.4952
And I calculate the combined mass:
\bar{m}_{ACh} = \sum_i w_i m_{ih} = 125.106
I also tried to combine the errors. For the errors I used the statistical and systematic, given by:
syst= \sqrt{\sum_{ij} w_i w_j C_{ij}^{sys}}=\sqrt{w_A^2 0.27^2 + w_C^2 0.15^2}=0.133 \approx 0.13
stat= \sqrt{\sum_{i} w_i^2 C_{ii}^{stat}}=\sqrt{w_A^2 0.43^2 + w_C^2 0.31^2}=0.252 \approx 0.25
and \sigma_{tot} =\sqrt{(syst)^2+(stat)^2} =0.284 \approx 0.28
My result reads:
m_{h}^{(A+C,2\gamma)}(GeV) = 125.106 \pm 0.28 ( 0.25_{stat} \pm 0.13_{sys})
in comparison to
m_{h}^{(A+C,2\gamma)}(GeV) = 125.07 \pm 0.29 ( 0.25_{stat} \pm 0.14_{sys})
given ..The problem appears in the systematic error...
Any idea? Mine is that the measurements are considered somehow correlated in the systematics?
Let's only talk about the diphoton channel : H\rightarrow \gamma \gamma
From the ATLAS the mass value is:
m_{Ah} =126.02 \pm 0.51
and the CMS:
m_{Ch} =124.70 \pm 0.34
Now it gives the combined result from ATLAS+CMS:
m_{ACh}=125.07 \pm 0.29
How can obtain the mean and error for the ATLAS+CMS?
I tried getting the weights w_i = \sum_j (C^{-1})_{ij} \Big/ \sum_{kl} (C^{-1})_{kl} with C the covariance matrix. Since they are different detectors they are not correlated and so the covariance matrix only has the variances on the diagonal. I obtain:
w_A \approx 3.84468/12.4952
w_C \approx 8.65052/12.4952
And I calculate the combined mass:
\bar{m}_{ACh} = \sum_i w_i m_{ih} = 125.106
I also tried to combine the errors. For the errors I used the statistical and systematic, given by:
syst= \sqrt{\sum_{ij} w_i w_j C_{ij}^{sys}}=\sqrt{w_A^2 0.27^2 + w_C^2 0.15^2}=0.133 \approx 0.13
stat= \sqrt{\sum_{i} w_i^2 C_{ii}^{stat}}=\sqrt{w_A^2 0.43^2 + w_C^2 0.31^2}=0.252 \approx 0.25
and \sigma_{tot} =\sqrt{(syst)^2+(stat)^2} =0.284 \approx 0.28
My result reads:
m_{h}^{(A+C,2\gamma)}(GeV) = 125.106 \pm 0.28 ( 0.25_{stat} \pm 0.13_{sys})
in comparison to
m_{h}^{(A+C,2\gamma)}(GeV) = 125.07 \pm 0.29 ( 0.25_{stat} \pm 0.14_{sys})
given ..The problem appears in the systematic error...
Any idea? Mine is that the measurements are considered somehow correlated in the systematics?
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