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Combinations of measurements: obtain mean and errors

  1. Jul 16, 2015 #1

    ChrisVer

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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 : [itex]H\rightarrow \gamma \gamma[/itex]
    From the ATLAS the mass value is:
    [itex]m_{Ah} =126.02 \pm 0.51[/itex]
    and the CMS:
    [itex]m_{Ch} =124.70 \pm 0.34[/itex]

    Now it gives the combined result from ATLAS+CMS:
    [itex]m_{ACh}=125.07 \pm 0.29[/itex]

    How can obtain the mean and error for the ATLAS+CMS?

    I tried getting the weights [itex]w_i = \sum_j (C^{-1})_{ij} \Big/ \sum_{kl} (C^{-1})_{kl}[/itex] with [itex]C[/itex] 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:
    [itex]w_A \approx 3.84468/12.4952[/itex]
    [itex]w_C \approx 8.65052/12.4952[/itex]
    And I calculate the combined mass:
    [itex]\bar{m}_{ACh} = \sum_i w_i m_{ih} = 125.106[/itex]
    I also tried to combine the errors. For the errors I used the statistical and systematic, given by:
    [itex]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[/itex]
    [itex]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[/itex]
    and [itex] \sigma_{tot} =\sqrt{(syst)^2+(stat)^2} =0.284 \approx 0.28[/itex]

    My result reads:
    [itex]m_{h}^{(A+C,2\gamma)}(GeV) = 125.106 \pm 0.28 ( 0.25_{stat} \pm 0.13_{sys})[/itex]
    in comparison to
    [itex]m_{h}^{(A+C,2\gamma)}(GeV) = 125.07 \pm 0.29 ( 0.25_{stat} \pm 0.14_{sys})[/itex]
    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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    Last edited: Jul 16, 2015
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  3. Jul 16, 2015 #2

    Orodruin

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    I strongly suspect they are using a more sophisticated statistical analysis than simply assuming everything is Gaussian ...
     
  4. Jul 16, 2015 #3

    ChrisVer

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    I don't know, I have seen several times giving the results from experiment A, experiment B etc... and then giving the A+B+... total result in similar figures.
    So I'm trying to understand how they get the total result.
     
  5. Jul 16, 2015 #4

    Orodruin

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    Of course you have, things are often very close to Gaussian. If this was all there was to combining ATLAS and CMS data, we would not need to wait for a combined analysis, anyone with a pocket calculator could do it.
     
  6. Jul 16, 2015 #5

    mathman

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    A guess: they had data to more significant figures (for the errors) than presented.
     
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