Physics Results: FSQ13002
Multidimensional analysis of BoseEinstein correlations in pp collisions at 2.76 and 7 TeV
Abstract
Twoparticle, quantumstatistical (BoseEinstein) correlations are measured in multidimensional projections of the pair relative momentum. The measurement extends previously performed onedimensional studies to two and threedimensions for the 7 TeV data, and presents for the first time for the 2.76 TeV data collected in 2013 at the CERN LHC. The measurements are performed at both energies for different intervals of the pair average momentum and for increasing charged particle multiplicitiy. The fit parameters corresponding to the estimated lengths of homogeneity and chaoticity parameters are presented.
Results
Figure 1 
Caption 


1D single ratios as a function of for data and Monte Carlo (Pythia 6  Z2 tune) samples corresponding to pp collisions at 2.76 TeV are shown on the left, and the corresponding double ratio superimposed by the exponential fit, on the right. 
Summary of One Dimensional BEC Results
Figure 2 
Caption 


Results of the exponential fits to the double ratios in different and bins are shown for pp collisions at 2.76 TeV and for the present analysis with full sample at 7 TeV. The left plot shows the values obtained for the intercept parameter, , and the right one, the corresponding values for the invariant radius fit parameter, . The statistical uncertainties are indicated by error bars (which in some cases are smaller than the marker's size), whereas the systematic ones are indicated by empty (2.76 TeV data) or shaded boxes (7 TeV data). 
Figure 3 
Caption 

Fit parameter is shown as a function of the charged particle multiplicity, for pp collisions at 2.76 TeV and for the the present analysis at 7 TeV. As seen in the plot, the new results increase proportionally to , showing a similar dependence on the charged multiplicity as the ones previously obtained at both 0.9 and 7 TeV in Ref. [1], also shown in the plot. The inner error bars represent the statistical uncertainties (which in some cases are smaller than the marker's size) and the outer error bars the statistical and systematic uncertainties added in quadrature. 
Figure 4 
Caption 



The anticorrelation region is highlighted by zooming the correlation axis in each plot. Two fit functions are shown as compared to the data points: the exponential and the model. 



The anticorrelation’s depth, , is quantified in the plot on the bottom by the difference of the baseline function, C(1 + q), and the model fit function calculated at the minimum. The inner error bars represent the statistical uncertainties (which in some cases are smaller than the marker's size) and the outer error bars the statistical and systematic uncertainties added in quadrature. The results are shown for pp collisions at 2.76 TeV and for the present analysis at 7 TeV, together with those from Ref. [1], corresponding to pp collisions at both 0.9 and 7 TeV. 
Summary of Two Dimensional BEC Results
Figure 5 
Caption 


Double ratios in the LCMS corresponding to results integrated in all and bins are shown in the left panel as a function of ; the plot on the top refers to the data from pp collisions at 2.76 TeV and the one on the bottom, to the 7 TeV data. 


The right panel shows the corresponding 1D projections of the single and double ratios in terms of (for < 0.05 GeV) and (for < 0.05 GeV). The Gaussian, the exponential and the Levy (with a = 1) fit functions are shown superimposed to the data points. 
Figure 6 
Caption 


The radius parameters obtained with the stretched exponential (Levytype with a = 1) fit function are shown for pp collisions at 2.76 and 7 TeV in the CM frame (top) and in the LCMS (bottom), as a function of and for different bins. The statistical uncertainties are indicated by error bars (which in some cases are smaller than the marker's size), and the systematic ones are indicated by empty (at 2.76 TeV) or shaded boxes (at 7 TeV). 


Figure 7 
Caption 


The intercept parameter obtained with the stretched exponential fit function is shown as a function of and in different bins of , for pp collisions at both 2.76 and 7 TeV in the CM frame (left) and in the LCMS (right). The statistical uncertainties are indicated by error bars (which in some cases are smaller than the marker's size), whereas the systematic ones are indicated by empty (at 2.76 TeV) or shaded boxes (at 7 TeV). 
Figure 8 
Caption 


Results obtained in the LCMS for the 2D double ratios with zoomed axes, as a function of () for four charged multiplicity bins, , increasing from top left to bottom right. The 1D projections in (for GeV) and (for GeV) are shown sidebyside to the corresponding 2D double ratios. 


Summary of Three Dimensional BEC Results
Figure 9 
Caption 

Results for the 3D double ratios obtained in the LCMS are shown, the upper panel corresponding to the 2D projections in , , , , and , integrated in and , with < 0.05 GeV, < 0.005 GeV and < 0.005 GeV, respectively. 

The middle panel shows the 1D projections in terms of the relative momentum components , , and of the single ratios of data and Monte Carlo, and the lower panel shows the 1D projections of the corresponding double ratios. The Gaussian, the exponential and the Levy (with index of stability a=1) fit functions are shown superimposed to the data points. 
Figure 12 
Caption 


Results corresponding to the intercept parameter in the CM frame and in the LCMS are shown as a function of (integrated in ), for pp collisions at 7 TeV, and for fits to the double ratios with three different functions. The statistical uncertainties are indicated by error bars (which in some cases are smaller than the marker's size), whereas the systematic ones are indicated by shaded boxes. 
Figure 13 
Caption 


Results corresponding to the intercept parameter in the CM frame and in the LCMS are shown as a function of (integrated in ), for pp collisions at 7 TeV, and for fits to the double ratios with three different functions. In this case, the values of shown in the plots were corrected for efficiency and acceptance. The statistical uncertainties are indicated by error bars (which in some cases are smaller than the marker's size), whereas the systematic ones are indicated by the shaded boxes. 
Figure 14 
Caption 

Results for the 3D double ratios obtained in the LCMS are shown, the upper panel corresponding to the 2D projections in (, ), (, ), and (), integrated in and , with < 0.05 GeV, < 0.005 GeV and < 0.005 GeV, respectively. 

The bottom panel shows 1D projections of the same data, with the complementary two variables constrained to be within the first bin (i.e., < 0.05 GeV). 
Comparison of Two and Three Dimensional BEC Results (Supplementary Figures)
Figure 15 
Caption 


Comparison of the fit radius parameters (left) and (right), obtained with the stretched exponential function in the CM frame and in the LCMS, respectively, is shown. These results for the 2D (in ) fit to the double ratios in pp collisions at 2.76 and 7 TeV, and for the 3D (in , ) ones in pp collisions at 7 TeV, are presented as a function of (integrated in ). In this case, the values of were corrected for efficiency and acceptance. The statistical uncertainties are indicated by error bars (which in some cases are smaller than the marker's size), whereas the systematic ones are indicated by the shaded boxes. 
Ref. [1]: CMS Collaboration, “Measurement of BoseEinstein Correlations in pp collisions at
0.9 and 7 TeV”, JHEP 05 (2011) 029, doi:10.1007/JHEP05(2011)029.