Measurement of the Production Cross Section of Pairs of Isolated Photons in pp collisions at √ s = 7 TeV
The integrated and differential cross sections of the production of pairs of
isolated photons have been measured in protonproton collisions at a
centerofmass energy of 7 TeV with the CMS detector at the LHC. Data
corresponding to an integrated luminosity of 36 have been
analysed. A nexttoleading order perturbative QCD calculation is compared to
the measurements. A discrepancy is observed for regions of the phase space where the
two photons have an azimuthal angle difference approximately less than 2.8.
Introduction
The differential cross section has been measured as a function of the diphoton
invariant mass, , the azimuthal angle between the two
photons, , the transverse momentum of the photon
pair,
,
where and are the transverse momenta
of the two photons, and ,
Δ being the difference
between the two photon rapidities. At lowest order in QCD,
is the centerofmass scattering angle for the
and
processes.
In addition the integrated cross section has
been measured. All measurements refer to a kinematic acceptance requiring at
least one isolated photon with > 23 GeV and a second
isolated photon with > 20 GeV, separated by
R = 0.45 within the pseudorapidity η < 2.5,
excluding the transition region between the barrel and endcap calorimeters,
1.44 <η <1.57. The isolation criterion requires the sum
of the transverse momenta of all the particles within a cone of
R < 0.4 around the photon to be less than 5 GeV.
An isolation variable based on the energy in the electromagnetic
calorimeter (ECAL) has been used to statistically estimate the fraction of diphoton
events among the selected candidates. This variable has been constructed to
minimise the dependence on the energy deposited by minimumionizing particles
such that its distribution for the background can be steadily obtained from a datadriven
method, the impingingtrack method. This method consists of selecting a pure
background sample by requiring one charged particle impinging the isolation
area and of the correction of the charged particle footprint.
Approved Plots from QCD10035 (Tarball)
Approved Plots and tables from QCD10035 (click for pdf)
Included in the draft paper
Figure 1 
Description 


Example of the projections of the twodimensional fit of the two photon ECAL isolation variables, in the interval 100 GeV < < 140 GeV for the region η< 1.44. The continuous blue line represents the sum of the signal and the background contributions whereas the dashed red line represents the background contribution only. In this interval, with 149 selected candidates, the number of signal events has been determined to be 81 13. 
Figure 2 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of the invariant mass of the photon pair (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η < 1.44 or 1.57 <η <2.5. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Figure 3 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of the invariant mass of the photon pair (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η <1.44. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Figure 4 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of the transverse momentum of the photon pair (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η < 1.44 or 1.57 <η <2.5. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Figure 5 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of the transverse momentum of the photon pair (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η < 1.44. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Figure 6 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of the azimuthal angle between the two photons (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η < 1.44 or 1.57 < η < 2.5. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Figure 7 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of the azimuthal angle between the two photons (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η < 1.44. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Figure 8 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of = (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η < 1.44 or 1.57 < η <2.5. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Figure 9 
Description 
(a) 
(b) 
Measured cross section of diphoton production as a function of = (a) and binbybin comparison with the theory (b) for photons within the pseudorapidity region η < 1.44. In both plots, the inner and outer error bars on each point show the statistical and total experimental uncertainties. The 4% uncertainty on the integrated luminosity is not included in the error bars. The dotted line and shaded region represent the systematic uncertainties on the theoretical prediction from the theoretical scales and the PDFs, respectively. 
Integrated crosssection 

Measured crosssection integrated in the region indicated in the introduction. The region 1.44 < η <1.57 is excluded. 
Table 1 
Description 

Summary of the systematic uncertainties. In this table are listed the different sources of systematic uncertainties on the measured cross section with their respective contribution. 
Table 2 
Description 

Differential cross section as a function of the variable with statistical (stat.) and systematic uncertainties (syst.). 
Table 3 
Description 

Differential cross section as a function of the variable with statistical (stat.) and systematic uncertainties (syst.). 
Table 4 
Description 

Differential cross section as a function of the variable with statistical (stat.) and systematic uncertainties (syst.). 
Table 5 
Description 

Differential cross section as a function of the variable  with statistical (stat.) and systematic uncertainties (syst.). 
Additional approved material for conferences
Figure A 
Description 
(a) 
Validation of the signal probability density function (PDF) extraction on electrons and positrons from W decays. The sPlot technique [1] is used to extract the PDF of the ECAL isolation variable for the electrons and positrons. It is compared with the PDF estimated with the random cone method used in the analysis. The bottom plots show the ratio of the two distributions. 
Figure B 
Description 
(a) 
Validation of the signal probability density function (PDF) extraction on electrons and positrons from Z decays. A pure sample of electrons and positrons is obtained by applying a mass constraint on electronpositron pair. The distribution of the ECAL isolation variable is compared to the distribution with the random cone method used in the analysis. 
Figure C 
Description 
(a) 
(b) 
Validation of the signal probability density function (PDF) extraction on the simulation. The actual PDF of the ECAL isolation variable and the one extraced with the random cone method are compared for the barrel (a) and the endcap (b) and show a good agreement. 
Figure D 
Description 
(a) 
(b) 
Validation of the background probability density function (PDF) extraction. The PDF of the ECAL isolation variable is obtained with the impingingtrack method, which was developed for this analysis. The method uses a pure background sample selected by requiring one charged particle impinging the ECAL isolation region (called "impinging track"), whose footprint is corrected in order to retrieve the PDF of the ECAL isolation variable of events with no impinging track. The validation consists of requiring a second impinging track and apply the same correction on one of the tracks to retrieve the PDF for oneimpingingtrack events. The two distributions, the corrected one obtained from twoimpingingtrack events and the one from the oneimpingingtrack events are compared for the barrel (a) and the endcap (b) and show a good agreement. 
Figure E 
Description 
(a) 
(b) 
Probability density function (PDF) of the ECAL isolation variable for the background, obtained with the impingingtrack method, in red, and for the signal, obtained with the randomcone method, in blue. The PDFs are shown separately for the barrel (a) and the endcap (b). 
Figure F 
Description 

The probability density function (PDF) of the ECAL isolation variable has a moderate dependence on the photon candidate transverse energy , on its pseudorapidity η, and on the pileup conditions. The events of the sample used to extract the PDF for the signal and the background, using respectively the random cone and the impingingtrack methods, are weighted to mimic the distributions of , η, and of the number of primary vertices. The figure illustrates this reweighting technique by comparing the distributions before and after the reweighting to the one of the diphoton candidate sample. 
Figure G 
Description 

DrellYan contamination to the distribution of the signal yield. The DrellYan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield. 
Figure H 
Description 

DrellYan contamination to distribution of the signal yield. The DrellYan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield. 
Figure I 
Description 

DrellYan contamination to distribution of the signal yield. The DrellYan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield. 
Figure J 
Description 

DrellYan contamination to distribution of the signal yield. The DrellYan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield. 
Figure K 
Description 


The different contributions to the uncertainties of the spectrum measurements. 
Figure L 
Description 


The different contributions to the uncertainties of the spectrum measurements. 
Figure M 
Description 


The different contributions to the uncertainties of the spectrum measurements. 
Figure N 
Description 


The different contributions to the uncertainties of the spectrum measurements. 
[1] M. Pivk and F. R. Le Diberder, "sPlot: a statistical tool to unfold data distributions", Nucl. 668 Instrum. Meth. A555 (2005) 356369, arXiv:physics/0402083.
Link to paper on arXiv