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# System prepended metadata

title: Multiplicity Smearing

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# Multiplicity Smearing

+ ### The original concept: 
    > Let me follow the original one first, where they try to smear the gen lvl multiplicity to the reco lvl distribution.

    1. Given a certain response matrix, will have the gen lvl mult ($x$) smear to the corresponded reco lvl distribution ($N(y)|_{x}$)
    ![](https://i.imgur.com/qRQ9iDB.png)
    2. So the concept is actually like a convolutional operation: $\delta(x) \to f(y)|_{x}$ ($f(y)|_{x}$: normalized $N(y)|_{x}$), for instance:
    for $N_{trk}^{gen}=8$, after the operation, will become a smeared distribution
    ![](https://i.imgur.com/CQzaeCj.png)
    3. This can make the smeared gen ntrk distribution look like reco's:
    ![](https://i.imgur.com/ZUHm9Kh.png)
    4. This will not ensure the event-to-event matching btw reco, gen mult, since when doing the smearing as point 2 suggests, it is a random-sampling process.
    ![](https://i.imgur.com/1vUA7PE.png)

+ ### Conclusion: 
    It seems to me that this is an operation only applicable on gen level, where we do want smeared/randomized the gen distribution

+ ### Detailed results: 
    https://drive.google.com/drive/folders/1pOr61WhGcglmqP3o5HyS1sCPbaoezMpk?usp=sharing