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‎Common/Tools/Multiplicity/README.md‎

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# Multiplicity/centrality tools in O2/O2Physics
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# Multiplicity/centrality tools in O2/O2Physics
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This directory serves to aggregate all files necessary for multiplicity
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and centrality calibration going from pp to Pb-Pb. It offers functionality
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to perform simple slicing in percentiles, such as what is done in
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proton-proton collisions, as well as the Glauber + analytical NBD fitter
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used to perform anchoring and hadronic event distribution estimates in
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nucleus-nucleus collisions.
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This directory serves to aggregate all files necessary for multiplicity
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and centrality calibration going from pp to Pb-Pb. It offers functionality
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to perform simple slicing in percentiles, such as what is done in
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proton-proton collisions, as well as the Glauber + analytical NBD fitter
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used to perform anchoring and hadronic event distribution estimates in
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nucleus-nucleus collisions.
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## Files
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* `README.md` this readme
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* `CMakeLists.txt` definition of source files that need compiling
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* `multCalibrator.cxx/h` a class to do percentile slicing of a given histogram. Used for all systems.
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* `multMCCalibrator.cxx/h` a class to perform data-to-mc matching of average Nch.
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* `multGlauberNBDFitter.cxx/h` a class to do glauber fits.
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* `multModule.h` a class to perform calculations of multiplicity and centrality tables for analysis. Meant to be used inside the main core service wagon 'multcenttable'.
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* `multCalibrator.cxx/h` a class to do percentile slicing of a given histogram. Used for all systems.
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* `multMCCalibrator.cxx/h` a class to perform data-to-mc matching of average Nch.
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* `multGlauberNBDFitter.cxx/h` a class to do glauber fits.
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* `multModule.h` a class to perform calculations of multiplicity and centrality tables for analysis. Meant to be used inside the main core service wagon 'multcenttable'.
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‎Common/Tools/Multiplicity/macros/README.md‎

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# Example multiplicity calibration macros
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You will find some example macros in this directory that will allow for the calculation of a glauber fit and the corresponding calibration histograms.
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You will find some example macros in this directory that will allow for the calculation of a glauber fit and the corresponding calibration histograms.
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A simplified description of the procedure necessary to generate a
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Glauber + NBD fit to a certain histogram is described below.
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A simplified description of the procedure necessary to generate a
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Glauber + NBD fit to a certain histogram is described below.
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## Performing a Glauber + NBD fit
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### First step: calculation of Glauber MC sample
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### First step: calculation of Glauber MC sample
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The Glauber + NBD model assumes that the multiplicity / amplitude
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distribution that one intends to fit can be described as coming
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from a certain number N_{ancestor} of particle-emitting sources called 'ancestors'. Each ancestor is assumed to produce particles
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according to a negative binominal distribution. Further,
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the number of ancestors is assumed to be related to the basic
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glauber quantities N_{part} and N_{coll} via the formula:
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distribution that one intends to fit can be described as coming
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from a certain number N_{ancestor} of particle-emitting sources called 'ancestors'. Each ancestor is assumed to produce particles
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according to a negative binominal distribution. Further,
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the number of ancestors is assumed to be related to the basic
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glauber quantities N_{part} and N_{coll} via the formula:
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N_{ancestor} = f * N_{part} + (1-f) N_{coll}
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N_{ancestor} = f * N_{part} + (1-f) N_{coll}
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Usually, the value f is fixed at 0.8, and thus the range of
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N_{ancestors} is typically 0-700 in Pb-Pb collisions.
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N_{ancestors} is typically 0-700 in Pb-Pb collisions.
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In order to allow for Glauber + NBD fitting, the correlation of
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(N_{part}, N_{coll}) needs to be known. For that purpose,
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a tree of Glauber MC needs to be generated using TGlauberMC using the relevant nuclei, which also involves choosing an appropriate nuclear profile.
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In order to allow for Glauber + NBD fitting, the correlation of
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(N_{part}, N_{coll}) needs to be known. For that purpose,
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a tree of Glauber MC needs to be generated using TGlauberMC using the relevant nuclei, which also involves choosing an appropriate nuclear profile.
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Once TGlauberMC has been used to produce a tree with N_{part} and
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N_{coll} values, their correlation needs to be saved to a 2D histogram that serves as input to the Glauber + NBD fitter used in
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O2/O2Physics. This is done using the macro called `saveCorrelation.C` contained in this directory, which produces a file named `baseHistos.root`. The file `saveCorrelation.C` serves as
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Once TGlauberMC has been used to produce a tree with N_{part} and
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N_{coll} values, their correlation needs to be saved to a 2D histogram that serves as input to the Glauber + NBD fitter used in
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O2/O2Physics. This is done using the macro called `saveCorrelation.C` contained in this directory, which produces a file named `baseHistos.root`. The file `saveCorrelation.C` serves as
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an example for the Pb-Pb case and minor adaptation may be needed
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in case other nuclei are to be used.
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in case other nuclei are to be used.
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### Second step: execution of Glauber + NBD fitter
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### Second step: execution of Glauber + NBD fitter
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The fitting procedure is done via the macro ``. Because
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the numerical fitting utilizes a convolution of a N_{ancestor}
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distribution and NBD distributions, it will not be as fast
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The fitting procedure is done via the macro ``. Because
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the numerical fitting utilizes a convolution of a N_{ancestor}
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distribution and NBD distributions, it will not be as fast
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as typical one-dimensional fits: typical times of 10-100 seconds
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are not unusual. The macro will produce an output file
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that contains:
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are not unusual. The macro will produce an output file
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that contains:
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* the original fitted histogram
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* the actual glauber fit distribution, plotted all the way
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to zero multiplicity
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* the original fitted histogram
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* the actual glauber fit distribution, plotted all the way
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to zero multiplicity
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This output can then be used to extract percentiles.
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This output can then be used to extract percentiles.
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### Third step: calculation of percentile boundaries
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### Third step: calculation of percentile boundaries
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Once both the data and glauber fit distributions are known,
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Once both the data and glauber fit distributions are known,
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the next step is to create a 'stitched' data/glauber distribution in
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which the distribution at low multiplicities follows
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the glauber fit and the distribution at higher multiplicities
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follows the data. The multiplicity value in which the switch from
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glauber to data takes place is called 'anchor point'.
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which the distribution at low multiplicities follows
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the glauber fit and the distribution at higher multiplicities
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follows the data. The multiplicity value in which the switch from
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glauber to data takes place is called 'anchor point'.
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Because of the fact that this 'stitching' procedure may need to be tuned and the actual glauber fit is slow, the stitching is done
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in a separate macro called `runCalibration.C`. It is provided
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Because of the fact that this 'stitching' procedure may need to be tuned and the actual glauber fit is slow, the stitching is done
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in a separate macro called `runCalibration.C`. It is provided
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in this directory as well and it is the third and last step in calculating percentile boundaries. The macro will printout some
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key boundaries as well as save an output file with the calibration.
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key boundaries as well as save an output file with the calibration.
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*Bonus*: at the stage in which the glauber fit has been done
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*Bonus*: at the stage in which the glauber fit has been done
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and all information is available, a de-convolution process
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can be used to calculate the average N_{part} and N_{coll}
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in centrality slices. This functionality is also provided
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can be used to calculate the average N_{part} and N_{coll}
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in centrality slices. This functionality is also provided
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in O2Physics as part of the `multGlauberNBDFitter` and the
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`runCalibration.C` macro can optionally also perform that
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deconvolution. *Warning*: this procedure might take a mooment.
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`runCalibration.C` macro can optionally also perform that
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deconvolution. *Warning*: this procedure might take a mooment.

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