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 proton-proton collisions at a center-of-mass energy of 7 TeV with the CMS detector at the LHC. Data corresponding to an integrated luminosity of 36 $pb^{-1}$ have been analysed. A next-to-leading order perturbative QCD calculation is compared to the measurements and shows an overall satisfactory agreement. A discrepancy is observed for regions of the phase space populated by photons radiated at small relative angle.

Introduction

The differential cross section has been measured as a function of the diphoton invariant mass, $m_{\gamma\gamma}$, the azimuthal angle between the two photons, $\Delta\varphi_{\gamma\gamma}$, the transverse momentum of the photon pair, $p_{T,\gamma\gamma}$ $=\sqrt{{p_{T,\gamma_{1}}}^{2}+{p_{T,\gamma_{2}}}^{2}+2\,p_{T,\gamma_{1}}p_{T_,\gamma_{2}}\cos\Delta\varphi_{\gamma\gamma}}$, where $p_{T,\gamma_{1}}$ and $p_{T,\gamma_{2}}$ are the transverse momenta of the two photons, and the cosine of the angle between the two photons in the Collins-Soper reference frame [1], $\cos\vartheta^{*}=\tanh(\frac{\Delta y_{\gamma\gamma}}{2})$, Δ$ y_{\gamma\gamma} $ being the difference between the two photon rapidities. In addition the integrated cross section has been measured. All measurements refer to a kinematic acceptance requiring at least one isolated photon with $E_T$ > 23 GeV and a second isolated photon with $E_T$ > 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 $\mathcal{I}$ 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 minimum-ionizing particles such that its distribution for the background can be steadily obtained from a data-driven method, the impinging-track 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 QCD-10-035 (Tarball)

Approved Plots and tables from QCD-10-035 (click for pdf)

Included in the draft paper

Figure 1 Description
DFit_Proj_g1_diphoMass_7_EBEB_log DFit_Proj_g2_diphoMass_7_EBEB_log Example of the projections of the two-dimensional fit of the two photon ECAL isolation variables, in the interval 100 GeV < $m_{\gamma\gamma}$ < 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 $\pm$ 13.
Figure 2 Description
diphot_xsec_m_all
(a)
diphot_xsec_m_all_ratio
(b)
Measured cross section of diphoton production as a function of the invariant mass of the photon pair (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| < 1.44 or 1.57 <|η| <2.5. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.
Figure 3 Description
diphot_xsec_m_eb
(a)
diphot_xsec_m_eb_ratio
(b)
Measured cross section of diphoton production as a function of the invariant mass of the photon pair (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| <1.44. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.
Figure 4 Description
diphot_xsec_pt_all
(a)
diphot_xsec_pt_all_ratio
(b)
Measured cross section of diphoton production as a function of the transverse momentum of the photon pair (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| < 1.44 or 1.57 <|η| <2.5. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.
Figure 5 Description
diphot_xsec_pt_eb
(a)
diphot_xsec_pt_eb_ratio
(b)
Measured cross section of diphoton production as a function of the transverse momentum of the photon pair (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| < 1.44. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.
Figure 6 Description
diphot_xsec_dphi_all
(a)
diphot_xsec_dphi_all_ratio
(b)
Measured cross section of diphoton production as a function of the azimuthal angle between the two photons (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| < 1.44 or 1.57 < |η| < 2.5. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.
Figure 7 Description
diphot_xsec_dphi_eb
(a)
diphot_xsec_dphi_eb_ratio
(b)
Measured cross section of diphoton production as a function of the azimuthal angle between the two photons (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| < 1.44. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.
Figure 8 Description
diphot_xsec_costheta_all
(a)
diphot_xsec_costheta_all_ratio
(b)
Measured cross section of diphoton production as a function of the absolute value of the cosine of the polar angle between the two photons in the Collins-Soper reference frame and of the photon pair (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| < 1.44 or 1.57 < |η| <2.5. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.
Figure 9 Description
diphot_xsec_costheta_eb
(a)
diphot_xsec_costheta_eb_ratio
(b)
Measured cross section of diphoton production as a function of the absolute value of the cosine of the polar angle between the two photons in the Collins-Soper reference frame and of the photon pair (a) and bin-by-bin comparison with the theory (b) for photons within the pseudorapidity region |η| < 1.44. The total systematic uncertainties are represented by the shaded area, the different contributions are added in quadrature sequentially.

Integrated cross-section
integrated_xsec Measured cross-section integrated in the region indicated in the introduction. The region 1.44 < |η| <1.57 is excluded.

Table 1 Description
table_sys_summary 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
table_xsec_m_gamgam Differential cross section as a function of the variable $m_{\gamma\gamma}$ with statistical (stat.) and systematic uncertainties (sys.).
Table 3 Description
table_xsec_pt_gamgam Differential cross section as a function of the variable $p_{T,\gamma\gamma}$ with statistical (stat.) and systematic uncertainties (sys.).
Table 4 Description
table_xsec_dphi_gamgam Differential cross section as a function of the variable $\Delta\phi$ with statistical (stat.) and systematic uncertainties (sys.).
Table 5 Description
table_xsec_cos_theta_star Differential cross section as a function of the variable $\cos\vartheta^*$ with statistical (stat.) and systematic uncertainties (sys.).

Additional approved material for conferences

Figure A Description
w_rc_valid
(a)
Validation of the signal probability density function (PDF) extraction on electrons and positrons from W decays. The sPlot technique [2] is used to extract the PDF of the ECAL isolation variable $\mathcal{I}$ 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
z_rc_valid
(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 electron-positron pair. The distribution of the ECAL isolation variable $\mathcal{I}$ is compared to the distribution with the random cone method used in the analysis.
Figure C Description
rc_simu_valid
(a)
rc_simu_valid_ee
(b)
Validation of the signal probability density function (PDF) extraction on the simulation. The actual PDF of the ECAL isolation variable $\mathcal{I}$ 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
impinging_track_valid
(a)
impinging_track_valid_ee
(b)
Validation of the background probability density function (PDF) extraction. The PDF of the ECAL isolation variable $\mathcal{I}$ is obtained with the impinging-track 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 $\mathcal{I}$ 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 one-impinging-track events. The two distributions, the corrected one obtained from two-impinging-track events and the one from the one-impinging-track events are compared for the barrel (a) and the endcap (b) and show a good agreement.
Figure E Description
pdfs_eb
(a)
pdfs_ee
(b)
Probability density function (PDF) of the ECAL isolation variable $\mathcal{I}$ for the background, obtained with the impinging-track method, in red, and for the signal, obtained with the random-cone method, in blue. The PDFs are shown separately for the barrel (a) and the endcap (b).
Figure F Description
pdf_reweighting The probability density function (PDF) of the ECAL isolation variable $\mathcal{I}$ has a moderate dependence on the photon candidate transverse energy $E_T$, on its pseudorapidity η, and on the pile-up conditions. The events of the sample used to extract the PDF for the signal and the background, using respectively the random cone and the impinging-track methods, are weighted to mimic the distributions of $E_T$, η, and of the number of primary vertices. The figure illustrates this reweighting technique by comparing the $E_T$ distributions before and after the reweighting to the one of the diphoton candidate sample.
Figure G Description
dy_m Drell-Yan contamination to the $m_{\gamma\gamma}$ distribution of the signal yield. The Drell-Yan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield.
Figure H Description
dy_pt Drell-Yan contamination to $p_{T,\gamma\gamma}$ distribution of the signal yield. The Drell-Yan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield.
Figure I Description
dy_dphi Drell-Yan contamination to $\Delta\varphi_{\gamma\gamma}$ distribution of the signal yield. The Drell-Yan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield.
Figure J Description
dy_costhetas Drell-Yan contamination to $\cos \theta^{*}$ distribution of the signal yield. The Drell-Yan spectrum has been estimated with the simulation using the NLO generator POWEG and has been subtracted from the signal yield.
Figure K Description
uncert_m_eb uncert_m_ee The different contributions to the uncertainties of the $m_{\gamma\gamma}$ spectrum measurements.
Figure L Description
uncert_pt_eb uncert_pt_ee The different contributions to the uncertainties of the $p_{T,\gamma\gamma}$ spectrum measurements.
Figure M Description
uncert_dphi_eb uncert_dphi_ee The different contributions to the uncertainties of the $\Delta\varphi_{\gamma\gamma}$ spectrum measurements.
Figure N Description
uncert_costhethas_eb uncert_costhetas_ee The different contributions to the uncertainties of the $\cos \theta^{*}$ spectrum measurements.


[1] J. C. Collins and D. E. Soper, "Angular distribution of dileptons in high-energy hadron collisions", Phys. Rev. D 16 (Oct, 1977) 2219?2225, doi:10.1103/PhysRevD.16.2219.

[2] M. Pivk and F. R. Le Diberder, "sPlot: a statistical tool to unfold data distributions", Nucl. 668 Instrum. Meth. A555 (2005) 356-369, arXiv:physics/0402083.


PhilippeGras 20-Jul-2011 Page is now approved. Removed warning.
PhilippeGras 19-Jul-2011 DY contamination legend
PhilippeGras 17-Jul-2011 First version of the text
SuzanneGascon 14-Jul-2011
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