Higgs decay to Z and Z* at LHC

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What is the Z* and why it has different mass from Z ?
Goodmornig.I would like to explain me What is the Z* at higgs decay and why it has different mass from Z ?
 
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What is measured experimentally is 4 muons (2 positive & 2 negative).
Then you make a cut on your data to only keep events which has a muon pair (positive and negative) with an invariant mass = mZ (+/- some threshold due to Z-width and experimental uncertainty).
After that, plot the invariant mass of the 4 muons, you should see a peak centered around mH (which we now know is ≈ 125 GeV).
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Just one more flavor. If mH > 2mZ we would have the same signal 4 muons. But then one could make one more cut, namely that you would have two pair of muons with invariant mass = mZ
 
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Still the WW* Branching ratio is much higher for mH = 125 GeV
which is a much harder signal to measure, since the W decay is more "messy" than Z decays.
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