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---+ Multidimensional HBT analysis

Multidimensional HBT analysis is often used to study dimensions of the system formed in high energy collisions along different directions. This twiki gathers the multidimensional HBT results obtained by modifying Padova's code for including different projections of the pair relative momenta. Previous 1-dimensional results can be found [[http://cms.cern.ch/iCMS/analysisadmin/cadi?ancode=QCD-10-003][here (0.9 and 2.36 !TeV)]] and [[http://cms.cern.ch/iCMS/analysisadmin/cadi?ancode=QCD-10-023][here (0.9 and 7 !TeV)]].

---++ Datasets

The current analysis uses the same dataset used by Padova in the 1-dimensional study:

   * *7 !TeV data* [[https://cmsweb.cern.ch/das/request?input=dataset%3D%2FMinimumBias%2FCommissioning10-Apr20ReReco-v1%2FRECO&instance=cms_dbs_caf_analysis_01][April 20th (data)]]     3_5_7     GR_R_35X_V7A::All
   * *7 !TeV MC* [[https://cmsweb.cern.ch/das/request?view=list&limit=10&instance=cms_dbs_prod_global&input=%2FMinBias_TuneZ2_7TeV-pythia6%2FFall10-START38_V12-v1%2FGEN-SIM-RECO][/MinBias_TuneZ2_7TeV-pythia6/Fall10-START38_V12-v1/GEN-SIM-RECO]]
   * *900 !GeV data* [[https://cmsweb.cern.ch/das/request?view=list&limit=10&instance=cms_dbs_prod_global&input=dataset+dataset%3D*Commissioning10-May6th*][May 6th data]] (3_5_8patch3     GR_R_35X_V8B::All)
   * *900 !GeV MC* [[https://cmsweb.cern.ch/das/request?view=list&limit=10&instance=cms_dbs_prod_global&input=%2FMinBias_TuneZ2_900GeV-pythia6%2FSummer10-START36_V10A-v1%2FGEN-SIM-RECO+][/MinBias_TuneZ2_900GeV-pythia6/Summer10-START36_V10A-v1/GEN-SIM-RECO]] CMSSW_3_6_2

The full statistics corresponds to 2.7M events from data and 1.5M events from MC (Pythia6-Z2). All plots in this twiki made use of full statistics.

---++ How to run the code

%TWISTY{id="" mod="div" showlink="Show details&nbsp;" hidelink="Hide details&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

The code that produces multidimensional HBT results is located at Padova:

=@gate.pd.infn.it --> @t2-ui-05.pd.infn.it=

in the following directories:

=/home/lagana/WorkOn= and
=/lustre/cmswork/lagana/7TeV=

To run the code, simply =make= at =/home/lagana/WorkOn= and run the macros =./run_program_data.sh= and =./run_program_MC.sh= at =/lustre/cmswork/lagana/7TeV=.

The newer macros to produce histograms are at =/home/lagana/7TeV/BecTree=. These macros uses a tree with the following structure to make histograms:

<verbatim>
typedef struct
{
   float qinv;
   float qt;
   float qout;
   float qlong;
   float qside;
   float coulomb_same_signal;
   int   ch1ch2;//charge product
   float kT;
   int   Nch;
} hbt_tree_entry;
</verbatim>

The usage of TTree instead of !THnSparse is due to problems with memory allocation for !THnSparse in the 5-dimensional case (qO vs. qL vs. qS vs. kT vs. Nch).

%ENDTWISTY%

---++ Additional plots & studies

   * Single ratios of data and MC with (++) pairs and (--) pairs considered separately, using !SameEvent/!MixedEvent pairs
   * Double ratio of the above single ratio plots
   * Check normalization issue of plots by extending the plotting region up to 5 !GeV/c in both qL and qT
   * Data and Monte Carlo Quality Plots
      * Pseudorapity
      * Phi
      * pT
      * Multiplicity
      * dxy
      * ndof
   * PID (dE/dx): comparision with current results using the adopted cuts but no PID. 
   * We might want to perform the analysis in the LCMS reference frame.


---++ qT vs. qL results

This section shows several correlation functions in the transverse and longitudinal component of the 3-momentum difference (qT and qL) obtained in the center-of-mass reference frame. Multiplicity (Nch) and momentum average (kT) studies are presented. Two different ways of combining tracks for constructing the reference sample have been used: event mixing with similar track multiplicity per eta region, and opposite charged tracks from same event. The following legend specifies the combinations used:

   * *SE* = Same Event
   * *ME* = Mixed Event
   * *AS* = All Signs (charges) = [(++),(--),(+-)]
   * *SS* = Same Sign (charge)
   * *OS* = Opposite Sign (charge)

Unless other stated, single and double ratio histograms in (qT,qL) were normalized up to 2 !GeV/c. 

---+++ Nch and kT integrated

  *1.* 2D distributions of *number of pairs in (qT,qL)*  corresponding to: Signal (Same Event, Same Sign),  Background_Mix (Mixed Event, All Signs)  and Background_Opp  (Same Event, Opposite Sign) %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *    Top: Lego plots of  (*SE,SS*), (*ME,AS*) and (*SE,OS*)  

   *    Bottom: Superimposed surface plots of (*SE,SS*) and (*ME,AS*)  [left and middle],  and (*SE,SS*), (*SE,OS*)  [right plot] <br />
     <img src="%ATTACHURLPATH%/No-of-pairs-in-qTqL.png" alt="No-of-pairs-in-qTqL.png" width='1258' height='662' />
 
<!--   <img src="%ATTACHURLPATH%/2d-signal-and-backgr.png" alt="2d-signal-and-backgr.png" width='789' height='678' />

     <img src="%ATTACHURLPATH%/2d-signal-and-backgr.png" alt="2d-signal-and-backgr.png" width='789' height='678' /> 
-->

<!--   
   *b.*    Signal (same event, same sign)  &  background (same event, opposite sign) [qTqL-signal-and-backgr-same-and-opp-charge.png]: <br />
     <img src="%ATTACHURLPATH%/qTqL-signal-and-backgr-same-and-opp-charge.png" alt="qTqL-signal-and-backgr-same-and-opp-charge.png" width='383' height='631' />
-->

%ENDTWISTY%

  *2.* 1D distributions of *number of pairs*  along qT for first qL bin (left) and along qL for first qT bin  (right) %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.*    (*SE,SS*) and (*ME,AS*): <br />
     <img src="%ATTACHURLPATH%/2d-signal-and-backgr-projections.png" alt="2d-signal-and-backgr-projections.png" width='1171' height='608' />

   *b.*    (*SE,SS*) and (*SE,OS*): <br />
     <img src="%ATTACHURLPATH%/qTqL-signal-and-backgr-same-and-opp-charge-projections.png" alt="qTqL-signal-and-backgr-same-and-opp-charge-projections.png" width='1180' height='600' />

%ENDTWISTY%

  *3.* 2D single ratios  (*SE,SS*)/(*ME,AS*) in (qT,qL): Data and MC  %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.*    2D single ratios: <br />
     <img src="%ATTACHURLPATH%/qTqL-data-mc-single-ratios_v3.png" alt="qTqL-data-mc-single-ratios_v3.png" width='999' height='572' />

   *b.*    2D single ratios with error bars: <br />
     <img src="%ATTACHURLPATH%/qTqL-data-mc-single-ratios_v3err.png" alt="qTqL-data-mc-single-ratios_v3err.png" width='999' height='572' />

%ENDTWISTY%

  *4.* 2D double ratios Data[(*SE,SS*)/(*ME,AS*)]/MC[(*SE,SS*)/(*ME,AS*)] in (qT,qL):  %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.* 2D double ratios:  [   *2.7M data/1.5M MC evts*;   *chi2/ndf = 6542/1596* ] <br />
     <img src="%ATTACHURLPATH%/qTqL-double-ratio_v3.png" alt="qTqL-double-ratio_v3.png" width='596' height='572' />

   *b.* 2D double ratios with error bars: <br />
     <img src="%ATTACHURLPATH%/qTqL-double-ratio_v3err.png" alt="qTqL-double-ratio_v3err.png" width='596' height='572' />

   *c.*    2D double ratio in (qT,qL): <br />
     <img src="%ATTACHURLPATH%/2d-double-ratio-with-2d-fit_v3.png" alt="2d-double-ratio-with-2d-fit_v3.png" width='596' height='572' />

%ENDTWISTY%

  *5.* Fitted functions to the 2D double ratios Data[(*SE,SS*)/(*ME,AS*)]/MC[(*SE,SS*)/(*ME,AS*)] in (qT,qL) %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.* 2D double ratio in (qT,qL) with Gaussian fit (and normalization) in the range (qT,qL)<2 !GeV/c: [   *2.7M data/1.5M MC evts*;   *chi2/ndf = 6542/1596* ]

   <img src="%ATTACHURLPATH%/2d-double-ratio-with-2d-fit.png" alt="2d-double-ratio-with-2d-fit.png" width='596' height='572' />

   *b.*     2D double ratio in (qT,qL) with Gaussian fit (and normalization) in the range (qT,qL)<5 !GeV/c:

   <img src="%ATTACHURLPATH%/2d-double-ratio-with-2d-fit_v4.png" alt="2d-double-ratio-with-2d-fit_v4.png" width='596' height='572' />

   * *Table* : This is the fit parameters for the double ratio in the extended region up to 5 !GeV/c.
<verbatim>
========================= levy =============================
 FCN=67184.8 FROM MIGRAD    STATUS=CONVERGED     211 CALLS         212 TOTAL
                     EDM=1.07999e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  A            9.96406e-01   9.63276e-05   1.17919e-05   1.88398e-01
   2  lambda       6.01941e-01   1.36403e-02   4.62944e-04   1.62719e-02
   3  rT           7.62178e-01   1.01102e-02   7.27200e-04   2.68371e-02
   4  rL           1.30967e+00   1.93013e-02   7.65773e-04   2.05645e-02
   5  alpha        1.29732e+00   1.89508e-02   1.14568e-03   2.66247e-02
========================= gauss =============================
 FCN=67943.6 FROM MIGRAD    STATUS=CONVERGED     167 CALLS         168 TOTAL
                     EDM=1.5424e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  N            9.96641e-01   9.53700e-05   1.18611e-05   1.55992e-01
   2  lambda       3.74079e-01   4.29788e-03   2.94035e-04  -1.30118e-02
   3  rT           6.48435e-01   6.45172e-03   6.06889e-04   8.92616e-02
   4  rL           1.00638e+00   7.18590e-03   5.87569e-04   7.21473e-03
========================= gauss2 =============================
 FCN=67927.1 FROM MIGRAD    STATUS=CONVERGED    1296 CALLS        1297 TOTAL
                     EDM=5.15976e-08    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  A            9.97339e-01   1.96392e-04   1.18680e-05  -2.93886e-01
   2  lambda       3.75592e-01   4.34080e-03   2.96579e-04  -1.89226e-02
   3  rT           6.52515e-01   6.58415e-03   6.12730e-04   3.22711e-02
   4  rL           1.01225e+00   7.37662e-03   5.92636e-04   4.11233e-02
   5  delta       -6.59857e-05   1.62301e-05   1.00264e-06   2.58126e+00
</verbatim>

   *c.* 2D double ratio in (qT,qL) with exponential fit (and normalization) in the range (qT,qL)<2 !GeV/c:

   <img src="%ATTACHURLPATH%/2d-double-ratio-with-2d-fit_exp.png" alt="2d-double-ratio-with-2d-fit_exp.png" width='800' height='800' />

   *d.* 2D double ratio in (qT,qL) with Levy-type fit (and normalization) in the range (qT,qL)<2 !GeV/c:

   <img src="%ATTACHURLPATH%/qTqL-dratio-levy.png" alt="qTqL-dratio-levy.png" width='596' height='572' />

<!--
   *e.* 2D double ratio in (qT,qL) [normalization upt to (qT,qL) = 5 !GeV/c]:
     <img src="%ATTACHURLPATH%/2d-double-ratio-with-2d-fit_v3.png" alt="2d-double-ratio-with-2d-fit_v3.png" width='596' height='572' />
-->

%ENDTWISTY%

  *6.* 1D projections along qT (first qL bin) and along qL (first qT bin) %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   [ *chi2/ndf = 6542/1596 (from 2d fit)* ]

   *a.* 1D double double Data[(*SE,SS*)/(*ME,AS*)]/MC[(*SE,SS*)/(*ME,AS*)] versus qL for first bin in qT: <br />
     <img src="%ATTACHURLPATH%/first-bin-qL-with-2d-fit_v2.png" alt="first-bin-qL-with-2d-fit_v2.png" width='1265' height='558' />

   *b.* 1D double double Data[(*SE,SS*)/(*ME,AS*)]/MC[(*SE,SS*)/(*ME,AS*)] versus qT for first bin in qL: <br />
     <img src="%ATTACHURLPATH%/first-bin-qT-with-2d-fit_v2.png" alt="first-bin-qT-with-2d-fit_v2.png" width='1265' height='558' />

   *c.* Single and double ratio projections up to 5 !GeV: <br />
     <img src="%ATTACHURLPATH%/qTqL_single_and_double_ratio_projections.png" alt="qTqL_single_and_double_ratio_projections.png" width='796' height='772' />

%ENDTWISTY%

  *7.* 2D single ratios and double ratio in (qT,qL) with Background_Opp (SE, OS): %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   * 2D single ratios (*SE,SS*)/(*SE,OS*) for data (left) and MC (middle), and double ratio Data[(*SE,SS*)/(*SE,OS*)]/MC[(*SE,SS*)/(*SE,OS*)] (right): <br />
     <img src="%ATTACHURLPATH%/qTqL-data-mc-same-and-opp-charge-ratios.png" alt="qTqL-data-mc-same-and-opp-charge-ratios.png" width='1646' height='598' />

%ENDTWISTY%

  *8.* 2D single ratios and double ratio in (qT,qL) for opposite sign as signal, with Background_Mix (*ME,AS*): %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   * 2D single ratios (*SE,OS*)/(*ME,OS*) in (qT,qL) for data (left) and MC (middle), and double ratio Data[(*SE,OS*)/(*ME,OS*)]/MC[(*SE,PS*)/(*SE,OS*)] (right)
     <img src="%ATTACHURLPATH%/2d-opp-charge-single-and-double-ratios.png" alt="2d-opp-charge-single-and-double-ratios.png" width='1277' height='494' />

%ENDTWISTY%

  *9.* 2D single ratio Data[(*SE,SS*)]/MC[(*SE,SS*)] in (qT,qL) %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%
<!--
   * qTqL_data_over_mc_same_charge.png: <br />
-->
     <img src="%ATTACHURLPATH%/qTqL_data_over_mc_same_charge.png" alt="qTqL_data_over_mc_same_charge.png" width='596' height='572' />

%ENDTWISTY%

---+++ Nch study

  *10.* 2D single ratios (*SE,SS*)/(*ME,AS*) in (qT,qL) for Data and MC in 3 Nch bins: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.* 2D single ratios for Data and MC in 3 Nch bins:
     <img src="%ATTACHURLPATH%/2d-data-and-mc-single-ratio-Nch_v3.png" alt="2d-data-and-mc-single-ratio-Nch_v3.png" width='1171' height='681' />

   *b.*  2D single ratios with error bars for Data and MC in 3 Nch bins:
     <img src="%ATTACHURLPATH%/2d-data-and-mc-single-ratio-Nch_err.png" alt="2d-data-and-mc-single-ratio-Nch_err.png" width='1171' height='681' />

%ENDTWISTY%

  *11.* 2D double ratios Data[(*SE,SS*)/(*ME,AS*)]/MC[(*SE,SS*)/(*ME,AS*)] in (qT,qL) in 3 Nch bins: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

  [ *chi2/ndf (Nch1) = 3661/1596*;   *chi2/ndf (Nch2) = 4940/1596*;   *chi2/ndf (Nch3) = 4665/1596* ] 

   *a.*    2D double ratios  in 3 Nch bins: 
     <img src="%ATTACHURLPATH%/2d-double-ratio-Nch_v3.png" alt="2d-double-ratio-Nch_v3.png" width='1338' height='534' />

   *b.*    2D double ratios with error bars  in 3 Nch bins:
     <img src="%ATTACHURLPATH%/2d-double-ratio-Nch_v3err.png" alt="2d-double-ratio-Nch_v3err.png" width='1338' height='534' />

%ENDTWISTY%

<!--  ATTENTION! THIS IS COMMENTED OUT!
  *12.* qTqL "opposite charge double ratios" divided in multiplicity bins %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   * 2d-opp-charge-double-ratios_Nch.png: <br />
     <img src="%ATTACHURLPATH%/2d-opp-charge-double-ratios_Nch.png" alt="2d-opp-charge-double-ratios_Nch.png" width='1084' height='445' />

%ENDTWISTY%

<!--  ATTENTION! THIS IS COMMENTED OUT!
  *13.* [To be completed]  qTqL data/mc (same charge) divided in Nch bins %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *

%ENDTWISTY%


---+++ kT study

  *12.* 2D single ratios (*SE,SS*)/(*ME,AS*) for Data and MC in 3 kT bins: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.* 2D single ratios for Data (top) and MC (bottom) in 3 kT bins:
     <img src="%ATTACHURLPATH%/2d-data-mc-single-ratio-kT_v3.png" alt="2d-data-mc-single-ratio-kT_v3.png" width='1359' height='899' />

   *b.* 2d-data-mc-single-ratio-kT_v3err.png: <br />
     <img src="%ATTACHURLPATH%/2d-data-mc-single-ratio-kT_v3err.png" alt="2d-data-mc-single-ratio-kT_v3err.png" width='1359' height='899' />

%ENDTWISTY%

  *13.* 2D double ratios Data[(*SE,SS*)/(*ME,AS*)]/MC[(*SE,SS*)/(*ME,AS*)] in (qT,qL) in 3 kT bins: 
qTqL double ratio divided in kT bins %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.* 2D double ratios in (qT,qL) in 3 kT bins:
     <img src="%ATTACHURLPATH%/2d-double-ratio-kT_v3.png" alt="2d-double-ratio-kT_v3.png" width='1739' height='736' />

   *b.* 2D double ratios with error bars  in 3 kT bins:
     <img src="%ATTACHURLPATH%/2d-double-ratio-kT_v3err.png" alt="2d-double-ratio-kT_v3err.png" width='1739' height='736' />

%ENDTWISTY%

  *14.* 2D single ratios in (qT,qL) with Background_Opp (SE, OS) for Data and MC in 3 kT bins: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *a.* 2D single ratios (*SE,SS*)/(*SE,OS*) for data (top) and MC (bottom) in (qT,qL) in 3 kT bins:
     <img src="%ATTACHURLPATH%/2d-opp-charge-single-ratios_kT_v3.png" alt="2d-opp-charge-single-ratios_kT_v3.png" width='1593' height='990' />

   *b.* 2d-opp-charge-single-ratios_kT_v3err.png: <br />
     <img src="%ATTACHURLPATH%/2d-opp-charge-single-ratios_kT_v3err.png" alt="2d-opp-charge-single-ratios_kT_v3err.png" width='1593' height='990' />

%ENDTWISTY%

  *15.* 2D double ratio with Background_Opp (SE, OS) in 3 kT bins: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   * 2D double ratios Data[(*SE,SS*)/(*SE,OS*)]/MC[(*SE,SS*)/(*SE,OS*)] in (qT,qL) in 3 kT bins:
     <img src="%ATTACHURLPATH%/2d-opp-charge-double-ratios_kT_v3.png" alt="2d-opp-charge-double-ratios_kT_v3.png" width='1739' height='718' />

   * 2d-opp-charge-double-ratios_kT_v3err.png: <br />
     <img src="%ATTACHURLPATH%/2d-opp-charge-double-ratios_kT_v3err.png" alt="2d-opp-charge-double-ratios_kT_v3err.png" width='1739' height='718' />

%ENDTWISTY%

---++ qOut vs. qLong vs. qSid results

This section shows the correlation function obtained for the three independent components of the momentum difference: q_out, q_long and q_side. As statistics is still low for this study, no Nch nor kT study have been performed yet.

---+++ Nch and kT integrated

  *16.* 2D single ratios (*SE,SS*)/(*ME,AS*) in (qO,qL) [first qS bin], in (qS,qO) [first qL bin], and in (qS,qL) [first qO bin]:  %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

       Back view:   

   *a.*    2D single ratios in (qO,qL) [first qS bin] (left), in (qS,qO) [first qL bin] (middle), and in (qS,qL) [first qO bin] (right) for Data (top) and MC (bottom):  
     <img src="%ATTACHURLPATH%/3d-3x2d-data-and-mcsingle-ratios_twisted.png" alt="3d-3x2d-data-and-mcsingle-ratios_twisted.png" width='1562' height='985' />

   *b.*    2D single ratios with error bars in (qL,qO) [first qS bin] (left), in (qS,qO) [first qL bin] (middle), and in (qL,qS) [first qO bin] (right) for Data (top) and MC (bottom):
     <img src="%ATTACHURLPATH%/3d-3x2d-data-and-mcsingle-ratios_err.png" alt="3d-3x2d-data-and-mcsingle-ratios_err.png" width='1562' height='990' />

       Front view: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *c.*    2D single ratios in (qO,qL) [first qS bin] (left), in (qS,qO) [first qL bin] (middle), and in (qS,qL) [first qO bin] (right) for Data (top) and MC (bottom):    
     <img src="%ATTACHURLPATH%/3d-3x2d-data-and-mcsingle-ratios.png" alt="3d-3x2d-data-and-mcsingle-ratios.png" width='1562' height='985' />
%ENDTWISTY%

%ENDTWISTY%

  *17.* 2D double ratios Data[(*SE,SS*)/(*ME,AS*)]/MC[(*SE,SS*)/(*ME,AS*)] in (qO,qL) [first qS bin], in (qS,qO) [first qL bin], and in (qS,qL) [first qO bin]:   %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

       Back view:   

   *a.*    2D double ratios in (qO,qL) [first qS bin] (left), in (qO,qS) [first qL bin] (middle), and in (qL,qS) [first qO bin] (right):  
3d-3x2d-double-ratio_v3.png: <br />
     <img src="%ATTACHURLPATH%/3d-3x2d-double-ratio_v3.png" alt="3d-3x2d-double-ratio_v3.png" width='1739' height='718' />

   *b.*    2D double ratios with error bars in (qO,qL) [first qS bin] (left), in (qO,qS) [first qL bin] (middle), and in (qL,qS) [first qO bin] (right): 
3d-3x2d-double-ratio_v3_err.png: <br />
     <img src="%ATTACHURLPATH%/3d-3x2d-double-ratio_v3_err.png" alt="3d-3x2d-double-ratio_v3_err.png" width='1739' height='718' />

       Front view: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *c.*    2D double ratios in (qO,qL) [first qS bin] (left), in (qO,qS) [first qL bin] (middle), and in (qL,qS) [first qO bin] (right): 
3d-3x2d-double-ratio_v2.png: <br />
     <img src="%ATTACHURLPATH%/3d-3x2d-double-ratio_v2.png" alt="3d-3x2d-double-ratio_v2.png" width='1739' height='688' />
%ENDTWISTY%

%ENDTWISTY%

  *18.* 1D single and double ratios (*SE,SS*)/(*ME,AS*) along qO [first qS & qL bins], along qL [first qO & qS bins], and along qS [first qO & qL bins] for Data and MC: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

Fit results on TH3 histogram:
<verbatim>
(gaussian)
 FCN=102698 FROM MIGRAD    STATUS=CONVERGED     215 CALLS         216 TOTAL
                     EDM=6.66544e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  A            9.94606e-01   1.19551e-04   1.79773e-05   4.44709e+00
   2  #lambda      3.59709e-01   4.19717e-03   3.42560e-04   3.09150e-01
   3  r_{out}      1.00776e+00   8.44181e-03   1.02888e-03   1.80669e-02
   4  r_{long}     6.25623e-01   6.29383e-03   7.16620e-04  -1.02031e-01
   5  r_{side}     9.22774e-01   1.09497e-02   1.28068e-03  -2.58040e-02
chi2/ndf=102698/63995

(exponential)
 FCN=102371 FROM MIGRAD    STATUS=CONVERGED     214 CALLS         215 TOTAL
                     EDM=5.3958e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  A            9.93962e-01   1.22222e-04   1.79370e-05   1.32247e+00
   2  #lambda      8.62423e-01   1.16002e-02   8.10546e-04  -8.73707e-03
   3  r_{out}      1.47726e+00   1.46637e-02   1.63201e-03   3.61240e-02
   4  r_{long}     8.62767e-01   1.01834e-02   1.05780e-03   6.84615e-02
   5  r_{side}     1.18971e+00   1.69778e-02   1.76234e-03   2.30381e-02
chi2/ndf=102371/63995
</verbatim>

   *a.* Normalized up to 5 !GeV/c and zoomed up to 2 !GeV/c 
   * 3d-3x1d-single-and-double-ratios_v2.png: <br />
     <img src="%ATTACHURLPATH%/3d-3x1d-single-and-double-ratios_v2.png" alt="3d-3x1d-single-and-double-ratios_v2.png" width='546' height='709' />

   *b.* Normalized and shown up to 5 !GeV/c %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%
   * 3d-3x1d-single-and-double-ratios.png: <br />
     <img src="%ATTACHURLPATH%/3d-3x1d-single-and-double-ratios.png" alt="3d-3x1d-single-and-double-ratios.png" width='546' height='709' />
%ENDTWISTY%

%ENDTWISTY%

---+++ Nch study

Statistics is to low for dividing in Nch bins.

  *19.* [To be completed]  qOqLqS double ratio vs. multiplicity
%TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *

%ENDTWISTY%

---+++ kT study

Statistics is to low for dividing in kT bins.

  *20.* [To be completed]  qOqLqS double ratio vs. kT
%TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   *

%ENDTWISTY%

---++ Comments

Leave here any comment you would like to make.

   * (Caio) Do we understand the increasing value of r_T with increasing kT in bullet 13? It should decrease, as r_L (and r_inv in the q-invariant analysis).

---++ Comparison: Approved/published plots versus plots remade from Trees

This section shows the comparison between the plots I generated after modifying Padova code with the plots of the PAS (Phisics Analysis Summary) in [[http://cms.cern.ch/iCMS/jsp/analysis/admin/analysismanagement.jsp?ancode=QCD-10-023][this link]].

  *A.* Double ratio comparison %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   * qinv_dratio_padova_comparison_v2.png: <br />
     <img src="%ATTACHURLPATH%/qinv_dratio_padova_comparison_v2.png" alt="qinv_dratio_padova_comparison_v2.png" width='980' height='648' />

*Normalization up to 5 !GeV* %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%
   * Double_ratio-2GeV-5GeV.png: <br />
     <img src="%ATTACHURLPATH%/Double_ratio-2GeV-5GeV.png" alt="Double_ratio-2GeV-5GeV.png" width='1260' height='571' />
%ENDTWISTY%

%ENDTWISTY%

  *B.* Double ratio for increasing number of events in the sample: %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%
   * qinv_dif-events_v1.png: <br />
     <img src="%ATTACHURLPATH%/qinv_dif-events_v1.png" alt="qinv_dif-events_v1.png" width='1010' height='634' />
%ENDTWISTY%

  *C.* Mixing/opposite charge/data over mc %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%
   * qinv-backgr-comparison_v3.png: <br />
     <img src="%ATTACHURLPATH%/qinv-backgr-comparison_v3.png" alt="qinv-backgr-comparison_v3.png" width='800' height='1000' />
%ENDTWISTY%

  *D.* qinv data/MC same charge %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%
   * qinv-data-over-mc-same-charge.png: <br />
     <img src="%ATTACHURLPATH%/qinv-data-over-mc-same-charge.png" alt="qinv-data-over-mc-same-charge.png" width='596' height='572' />
%ENDTWISTY%

  *E.* qinv same charge/opp charge %TWISTY{id="" mod="div" showlink="Show plot&nbsp;" hidelink="Hide plot&nbsp;" remember="off" showimgright="%ICONURLPATH{toggleopen-small}%" hideimgright="%ICONURLPATH{toggleclose-small}%" start="hide" }%

   * qinv-same-over-opposite-charge.png: <br />
     <img src="%ATTACHURLPATH%/qinv-same-over-opposite-charge.png" alt="qinv-same-over-opposite-charge.png" width='1054' height='559' />

%ENDTWISTY%

---++ Code logbook

This section lists the modifications I made in Padova code. All modifications can be found with the tag =Caio= inside each file at =Padova:/home/lagana/WorkOn=.

   * *%GREEN%EventMixer.c%ENDCOLOR%*
      * *line 4* inserted =using namespace ROOT::Math;=
      * *line 6* tree declaration
<verbatim>
typedef struct
{
   float qinv;
   float qt;
   float qout;
   float qlong;
   float qside;
   float coulomb_same_signal;
   int   ch1ch2;//charge product
   float kT;
   int   Nch;
} hbt_tree_entry;
hbt_tree_entry signal_tree_entry;//must be global
hbt_tree_entry backgr_tree_entry;//must be global
</verbatim>
      * *line 103* created new histograms =qTqL_SignalHisto_yesCoulomb = new !TH2D("qTqL_SignalYesCoulomb", "qTqL_SignalYesCoulomb", 40, 0., 2., 40, 0., 2.);=
      * *line 114-122* create N-Dim histograms (analog =hqschVsKtVsNch->Fill(TMath::Abs(psum1.Pt())/2.,GTVector.size(),q,CoulombW(q));=)
<verbatim>
    //===========================================================
    // 4D histograms (Caio)
    //===========================================================
    //                 {qT, qL, kT,  Nch}
    Int_t bins[4] =    {40, 40, 100, 150};
    Double_t xmin[4] = {0., 0., 0.,  0.};
    Double_t xmax[4] = {2., 2., 5.,  150.};
    qTqL_kT_Nch_SignalHisto_yesCoulomb = new THnSparseF("qTqL_kT_Nch_SignalHisto_yesCoulomb", "...", 4, bins, xmin, xmax);
    qTqL_kT_Nch_SignalHisto_noCoulomb  = new THnSparseF("qTqL_kT_Nch_SignalHisto_noCoulomb", "...", 4, bins, xmin, xmax);
    //===========================================================
    // 5D histograms (Caio)
    //===========================================================
    //                               {qO, qL, qS, kT,  Nch}
    Int_t qOqLqS_kT_Nch_bins[5] =    {40, 40, 40, 100, 150};
    Double_t qOqLqS_kT_Nch_xmin[5] = {0., 0., 0., 0.,  0.};
    Double_t qOqLqS_kT_Nch_xmax[5] = {.8, .8, .8, 5.,  150.};
    qOqLqS_kT_Nch_SignalHisto_yesCoulomb = new THnSparseF("qOqLqS_kT_Nch_SignalHisto_yesCoulomb", ..., 5, qOqLqS_kT_Nch_bins, qOqLqS_kT_Nch_xmin, qOqLqS_kT_Nch_xmax);
    qOqLqS_kT_Nch_SignalHisto_noCoulomb  = new THnSparseF("qOqLqS_kT_Nch_SignalHisto_noCoulomb",..., 5, qOqLqS_kT_Nch_bins, qOqLqS_kT_Nch_xmin, qOqLqS_kT_Nch_xmax);
    qOqLqS_kT_Nch_RefHisto               = new THnSparseF("qOqLqS_kT_Nch_RefHisto", "qOqLqS_kT_Nch_RefHisto", 5, qOqLqS_kT_Nch_bins, qOqLqS_kT_Nch_xmin, qOqLqS_kT_Nch_xmax);
</verbatim>
      * *line 154* and *251* write new histograms to file =qTqL_ReferenceHisto->Write();=
      * *line 156* tree creation
<verbatim>
    //===========================================================
    // HBT trees
    //===========================================================
    hbt_signal_tree = new TTree("hbt-signal-tree", "hbt-signal-tree");
    hbt_backgr_tree = new TTree("hbt-backgr-tree", "hbt-backgr-tree");
    //
    hbt_signal_tree->Branch("signal-pairs", &signal_tree_entry, "qinv/F:qt/F:qout/F:qlong/F:qside/F:coulomb_ss/F:ch1ch2/I:kT/F:Nch/I");
    hbt_backgr_tree->Branch("backgr-pairs", &backgr_tree_entry, "qinv/F:qt/F:qout/F:qlong/F:qside/F:coulomb_ss/F:ch1ch2/I:kT/F:Nch/I");
</verbatim>
      * *line 251* and *154* Sumw2 in new histograms =qTqL_SignalHisto_yesCoulomb->Sumw2();=
      * *line 288* delete new histograms =delete qTqL_SignalHisto_yesCoulomb;=
      * *line 494* and *637* declared 3D vectors =XYZVector k1, ...=
      * *line 537* and *654* fill new histograms =qTqL_SignalHisto_yesCoulomb->Fill(sqrt(qT.Mag2()), sqrt(qlon.Mag2()), !CoulombW(q));= (analog =hqdch->Fill(q,CoulombWpm(q))=)
      * *line 574-577* fill 4D histograms
<verbatim>
        Double_t qTqL_kT_Nch_entry[4] = {sqrt(qT.Mag2()), sqrt(qlon.Mag2()), TMath::Abs(psum1.Pt())/2., GTVector.size()};
        qTqL_kT_Nch_SignalHisto_yesCoulomb->Fill(qTqL_kT_Nch_entry, CoulombW(q));
        qTqL_kT_Nch_SignalHisto_noCoulomb->Fill(qTqL_kT_Nch_entry);
</verbatim>
      * *line 585* =qlon.SetCoordinates(0, 0, q3D.Z());= and =qout = qT.Dot(KT.Unit())*KT.Unit();= and =qsid = qT - qout;=
      * *line 598* hbt_tree_entry filling
   <verbatim>
        // qinv, qt, qout, qlong, qside, kT, Nch  -- Tree (Caio)======================
        signal_tree_entry.qinv   = q;
        signal_tree_entry.qt     = sqrt(qT.Mag2());
        signal_tree_entry.qout   = sqrt(qout.Mag2());
        signal_tree_entry.qlong  = sqrt(qlon.Mag2());
        signal_tree_entry.qside  = sqrt(qsid.Mag2());
        signal_tree_entry.coulomb_same_signal = CoulombW(q);
        signal_tree_entry.ch1ch2 = GTCharge[ev1] * GTCharge[rev1];
        signal_tree_entry.kT     = TMath::Abs(psum1.Pt())/2.;
        signal_tree_entry.Nch    = GTVector.size();
        hbt_signal_tree->Fill();
        //============================================================================
   </verbatim>
      * *line 608* 5D entry =Double_t qOqLqS_kT_Nch_entry[5] = {sqrt(qout.Mag2()), sqrt(qlon.Mag2()), sqrt(qsid.Mag2()), TMath::Abs(psum1.Pt())/2., GTVector.size()};=
      * *line 609* 5D fill =qOqLqS_kT_Nch_SignalHisto_yesCoulomb->Fill(qOqLqS_kT_Nch_entry, !CoulombW(q));=
      * *line 719* 5D reference histos filling
<verbatim>
    //4D reference histos (Caio)==========
    Double_t qTqL_kT_Nch_entry[4] = {sqrt(qT.Mag2()), sqrt(qlon.Mag2()), TMath::Abs(psum2.Pt())/2., SizeEv1};
    qTqL_kT_Nch_RefHisto->Fill(qTqL_kT_Nch_entry);
    // qO vs. qS vs. qL vs. kT vs. Nch (Caio)=====================================
    Double_t qOqLqS_kT_Nch_entry[5] = {sqrt(qout.Mag2()), sqrt(qlon.Mag2()), sqrt(qsid.Mag2()), TMath::Abs(psum2.Pt())/2., SizeEv1};
    qOqLqS_kT_Nch_RefHisto->Fill(qOqLqS_kT_Nch_entry);
    //====================================
</verbatim>
   * *%GREEN%EventMixer.h%ENDCOLOR%*
      * *line 4* inserted =#include "Math/Vector3D.h"=
      * *line 5* inserted =#include "THnSparse.h"=
      * *line 132* declared new histograms =TH2D* qTqL_SignalHisto_yesCoulomb;=
      * *line 140* 4D histograms =THnSparseF* qTqL_kT_Nch_SignalHisto_yesCoulomb;=
   * *%GREEN%EtaSegMix.c%ENDCOLOR%*
      * *line 51* replaced =pow(10,10)= by =std::pow(10.,10.)= because of incompatibility with =#include "Math/Vector3D.h"=
      * *line 60* replaced =pow(10,maxnbins - mm)= by =std::pow(10.,(double)(maxnbins - mm))= because of incompatibility with =#include "Math/Vector3D.h"=
   * *%GREEN%EtaSegRotatedMix.c%ENDCOLOR%*
      * *line 56* replaced =pow(10,10)= by =std::pow(10.,10.)= because of incompatibility with =#include "Math/Vector3D.h"=
      * *line 100* replaced =pow(10,maxnbins - mm)= by =std::pow(10.,(double)(maxnbins - mm))= because of incompatibility with =#include "Math/Vector3D.h"=
   * *%GREEN%/home/lagana/7TeV/Bec2d%ENDCOLOR%*
      * New directory with the following macros to produce data and MC single ratio and double ratio
         * produceDataSingleRatio.C
         * produceMcSingleRatio.C
         * produceDoubleRatio.C
         * run2dPlots.sh
      * The output files are =2d-data-results.root=, =2d-mc-results.root= and =2d-double-ratio.root=
   * *%GREEN%/home/lagana/7TeV/Bec3d%ENDCOLOR%*
      * New directory to produce qOqLqS results

-- Main.CaioLagana - 05 Apr 2012

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