Measurement of the Cross Section for Prompt Diphoton Production with 5.4 fb -1 of CDF Run II Data.

Ray Culbertson, Sasha Pronko and Costas Vellidis (Fermilab)  [Contact]

Abstract [Link to public note]

A measurement is reported of the cross section of prompt photon pair production in proton-antiproton collisions at a total CM energy of 1.96 TeV using 5.36 fb ^-1 of data collected with the CDF IIb detector at the Fermilab Tevatron collider. The cross section is presented as a function of kinematic variables sensitive to the reaction mechanism. The data are compared with three pertinent model calculations, at leading order, fixed next-to-leading order, and P_T-resummed matched to next-to-leading order in the strong coupling at the hard scattering. The comparison shows that none of the models adequately describes all aspects of the data.

Introduction

The diphoton final state is a signature of many Standard Model (SM) and possible new physics processes, such as low mass Higgs bosons, graviton states in extra dimensions, and super-symmetric states. However, all these yet unobserved processes are difficult to search because they are associated with a strong incoherent background of electromagnetic radiation from the quarks of the colliding proton-(anti)proton beams. Since the radiation occurs in the complicated environment of "hot" hadronic matter produced by the colliding beams, it is not easy to predict its rate and kinematic dependences in a Quantum ChromoDynamics (QCD) theoretical framework which takes into account the strong interactions between the colliding partons. High precision measurements of the diphoton production cross section, differential in kinematic variables sensitive to various terms of the production mechanism, are essential to constrain QCD calculations and models of the proton structure, and eventually to support searches of unobserved particles.

Event Selection and Background Subtraction

The data used in this measurement were collected with the CDF IIb detector between February 2002 and June 2009 using a diphoton trigger that requires two EM clusters, each of E_T > 12 GeV, with CES χ ² < 20 and fiducial to the CEM calorimeter, which implies a range of -1 < y < 1 in the rapidity of each photon. To enhance the purity of the diphoton sample, two main cuts are applied: (i) On the transverse energy E_T > 17 GeV for the first photon in the event and E_T > 15 GeV for the second photon; (ii) on the calorimeter isolation energy of each photon, in a cone of radius R=0.4 around the photon direction in the η - φ space, to be at most 2 GeV with a very mild increase of this cutoff with increasing photon E_T. The isolation cut implies that the angular separation of the two photons in the event is Δ R>0.4.

The background of photons created within hadronic jets is subtracted with a statistical procedure, which properly takes into account the full correlations between the two photons in each event, using the track isolation for the first time. This is defined as the scalar sum of the transverse momenta of all tracks originating from the primary vertex of the event and lying within the photon isolation cone. In contrast with the calorimeter isolation, the track isolation does not depend (i) on the multiple interactions between different pairs of colliding hadrons, due to the primary vertex requirement, and (ii) on the energy leakage from the calorimeter cluster. It also provides better resolution in the low E_T range, where the background is most significant. It can thus be used to separate signal and background photons with less systematic uncertainty than other methods. The systematic uncertainty in the signal fraction achieved with the track isolation method is of the order of 15-20%. The method is tested by measuring a fraction consistent with 100% in a signal Monte Carlo sample and consistent with 0% purity in a background Monte Carlo sample.

Corrections and Normalization

The cross section differential in a kinematic variable, averaged over a bin of the variable, is determined by dividing the number of signal events in the bin by the trigger efficiency, the diphoton selection efficiency, the integrated luminosity and the bin size. The diphoton trigger efficiency is derived from data. It is consistent with 100% over all of the kinematic range with a flat uncertainty of 3%. The selection efficiency is determined from data and Monte Carlo with an iterative method, based first on the Monte Carlo and then using the data to reweigh the Monte Carlo events and obtain a better representation of the true diphoton distribution. It is corrected for the "underlying event", by a constant factor of 0.88 per event, and for luminosity dependence. The uncertainty in the selection efficiency, coming from the luminosity dependence correction, grows linearly from 1.8% for E_T < 40 GeV to 3% at E_T = 80 GeV and remains constant above this point. A flat 6% uncertainty (3% per photon) comes from the underlying event correction. Finally, a 6% constant uncertainty comes from the Tevatron integrated luminosity.

The Z ⁰ → e ⁺e ^- sample is used for calibration by applying "diphoton-like" event selection, i.e. allowing for a track associated with each one of the two prompt electromagnetic objects in the event. The electromagnetic energy scale in data and Monte Carlo is corrected by tuning the Z ⁰ mass peak to the world average and an uncertainty from this correction is estimated to grow linearly from 0 at E_T < 40 GeV up to 1.5% at E_T = 80 GeV and remain constant above this point. All systematic uncertainties in the cross section measurement are added in quadrature. As a final cross check, the Z ⁰ → e ⁺e ^- cross section is measured in the range between 65 and 115 GeV/c ² of the e ⁺e ^- mass using the diphoton-like event selection and all of the corrections and normalizations applied to the diphoton cross section. The result of (256 ± 3) pb is in good agreement with the known value of 254 pb.

Theoretical Calculations

• The Pythia program, using a Leading-Order (LO) matrix element to calculate the cross section, which additionally features realistic representation of the physics events, by hadronizing the final state partons, and includes parameterizations of real gluon radiation before and/or after the hard scattering, of secondary parton interactions within the colliding hadrons and of multiple interactions between different hadrons in the colliding beams (all these parameterizations forming together the so-called ''underlying event''). Pythia was run so as to generate inclusive photon+X events, where X is a photon or a jet, with a diphoton filter. Therefore, events with one photon from Intial- (ISR) of Final-State Radiation (FSR) were included, together with the events where both photons come from the hard scattering. This simulation effectively resums the cross section for photon and gluon emission from the initial and final state quarks.
• The Diphox program, using a fixed Next-to-Leading (NLO) matrix element to calculate the cross section, which explicitly includes photon fragmentation, i.e. processes where a quark loses almost all of its energy to the photon detected in the event, in such a way that one or both photons in the event may come from fragmentation.
• The P_T-resummed NLO ResBos program where the cross section is resummed to all orders for soft initial-state gluon emission at low diphoton transverse momentum, and then it is smoothly matched to the NLO prediction at high diphoton transverse momentum and adjusted so as to approximately account for fragmentation.

All calculations are done by Monte Carlo event generation and are subject to the experimental kinematic and isolation cuts. The predictions are therefore appropriately averaged over the experimental phase space for each kinematic bin in the differential cross section histograms. NLO theoretical uncertainties are estimated for the choice of the mass scale, by varying it by a factor of 2 up and a factor of 2 down relative to the default scale μ = M_{γ γ} /2 in Diphox and μ = M_{γ γ} in ResBos, and for the parton distribution functions (PDF) of the proton, which are the CTEQ6M set in both Diphox and ResBos, by varying the event weights within the 90% level uncertainties of the 20 CTEQ6M eigenvectors. The two uncertainties are added in quadrature. The predictions of ResBos are restricted to the diphoton mass range from 2m_b = 9 GeV/c ² to 2m_t = 350 GeV/c ², where m_b and m_t are the masses of the bottom and top quarks, respectively.

Results

Total cross sections in pb:

• Data: 12.470 ± 0.205_(stat) ± 3.735_(syst)
• ResBos: 11.306
• Diphox: 10.577
• Pythia: 9.185

The figures below show the differential cross section as a function of various kinematic variables in comparison with the three models. The left plots show the absolute spectra. The next to left show the relative deviations between the data and the models, separately shown for each model, together with the model uncertainties. The next to right plots show the event selection efficiency before and after reweighing the Monte Carlo to the data. The right plots show the breakdown of the systematic uncertainties. The shaded area around each data point is the total systematic uncertainty of the measurement in the corresponding bin.

From left to right: The cross section as a function of the diphoton mass without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton mass for large photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton mass for small photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton mass for diphoton transverse momentum larger than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton mass for diphoton transverse momentum smaller than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton transverse momentum without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton transverse momentum for large photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton transverse momentum for small photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton transverse momentum for diphoton transverse momentum larger than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton transverse momentum for diphoton transverse momentum smaller than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the diphoton rapidity without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon azimuths without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon azimuths for diphoton transverse momentum larger than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon azimuths for diphoton transverse momentum smaller than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon pseudo-rapidities without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon pseudo-rapidities for large photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon pseudo-rapidities for small photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon pseudo-rapidities for diphoton transverse momentum larger than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the difference of the two photon pseudo-rapidities for diphoton transverse momentum smaller than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the distance of the two photon cones without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the distance of the two photon cones for diphoton transverse momentum larger than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the distance of the two photon cones for diphoton transverse momentum smaller than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the logarithm of the diphoton trasnverse momentum over mass ratio without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the logarithm of the diphoton trasnverse momentum over mass ratio for diphoton transverse momentum smaller than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the half difference of the two photon rapidities without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the half difference of the two photon rapidities for diphoton transverse momentum larger than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the half difference of the two photon rapidities for diphoton transverse momentum smaller than the diphoton mass; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the half sum of the two photon rapidities without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the ratio of low to high photon transverse momentum without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the ratio of low to high photon transverse momentum for large photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the ratio of low to high photon transverse momentum for small photon-photon azimuthal distance; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the cosine of the polar angle in the Collins-Soper frame without cut; relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the pseudo-rapidity of each photon (two entries per event); relative deviations between data and theory; event selection efficiency; systematics breakdown.

From left to right: The cross section as a function of the transverse momentum of each photon (two entries per event); relative deviations between data and theory; event selection efficiency; systematics breakdown.