Abstract

We evaluate the impact of theoretical uncertainties on the measured energy of hadronic jets. The analysis is performed using events with a Z boson and a single jet observed in pp collisions at ps = 1.96 TeV in 4.62 fb^-1 of data from the Collider Detector at Fermilab (CDF). The jets are measured using the CDF non-compensating sampling calorimeters which have a non-linear response to single particles. The transverse momenta (p_T) of the jet and the boson should balance each other due to momentum conservation in the plane transverse to the direction of the p and p beams. We evaluate the dependence of the measured p_T-balance on theoretical uncertainties associated with initial and final state radiation, choice of renormalization and factorization scales, parton distribution functions, jet-parton matching, calculations of matrix elements, and parton showering. We find that the uncertainty caused by parton showering at large angles is largest. We conclude that special actions have to be taken to achieve an uncertainty on the jet energy scale of even 3% in an experiment with a non-linear hadronic calorimeter such as those at CDF and at the LHC, a possible limitation on discovery potential in signatures containing jets.

Statement of the problem in setting the jet energy scale

The discovery potential of the LHC will strongly depend on the accuracy of Standard Model (SM) predictions, as any new physics has to be clearly separated from SM phenomena. In this paper we study the precision of modeling of the QCD jets that are produced in the majority of SM events. The uncertainties of the jet-related predictions directly impact the measurement of jet energies (jet energy scale, JES), missing transverse momentum, and, consequently, the discovery potential for supersymmetry and many other models of physics beyond the SM. This is especially important for experiments which use non-compensating calorimeters such as CMS, ATLAS, and CDF. The impact on the discovery potential depends on the detector technology, jet clustering, and event selection.

It has been a common practice to relate a clustered jet energy, measured in a calorimeter, to energy of the particle jet or the parent parton. The relation is performed by correcting the measured jet energy for instrumental effects, and fragmentation and radiation effects. Some of the corrections can not be extracted from data so that one relies on the accuracy of the SM predictions. Some of the uncertainties on the predictions are estimated by varying parameters of the ingredient models. However, the ingredient models do not work well across the whole phase-space of transverse momentum and separation of jets; one has to estimate the uncertainties due to the limited coverage of the phase space separately. The latter set of uncertainties can be estimated by comparing predictions to data. In the end, the total uncertainty on the jet energy corrections can be disentangled into individual components, which need to be combined into the total uncertainty.

We take events with a Z boson and a jet observed in ppbar collisions at $\sqrt{s}$ = 1.96 TeV in 4.62 fb^-1 of data from CDF as a precision SM process to test the measured jet energy using p_T-balance, p_T(jet)/p_T(Z). The Z bosons are observed as clearly-identified pairs of electrons or muons. The transverse momentum of the bosons is also well-measured making them an ideal instrument for the analysis. We find that the observed p_T-balance is different from that given by the predictions. The overall discrepancy between the observed and the predicted balances was previously used to estimate the uncertainty on the JES at CDF}. In this paper we investigate the sources of uncertainties contributing to the observed discrepancy and the precision of the SM predictions for hadronic jets. Finally, we compare the total of the uncertainties and the observed discrepancy to check the completeness of the investigation.

The JES at CDF is determined independently of the p_T-balance using the measured single particle response in the calorimeters. The in-cone parton showering (PS) has been extensively studied and is in a good agreement with the predictions. We rely on the predicted energy of the leading (highest in p_T) jet to study the p_T-balance in Z-jet events.

Additional improvements in the description of SM QCD processes are required to improve the discovery potential of the LHC experiments. Having the large-angle FSR as one of the largest sources of discrepancy dictates a need for higher-order corrections to the parton showering or a parton-jet matching scheme which would cover the problematic region.

Event selection

• Triggered on high-p_T electrons and muons (p_T > 18 GeV)
• A Z-boson is identified as a pair of oppositely charged electrons or muons. The invarian mass of the lepton pair is required to be within 80 to 100 GeV/c².
• Jets are clustered using cone algorithm. The minimum energy of a cluster is 3 GeV. Cone radius can be 0.4, 0.7, or 1.0
• Jets can not overlap with photons or electrons.
• Minimum pT of the leading jet is 8 GeV; the sub-leading jet is always softer than the threshold.
• The leading jet is back-to-back to the Z-boson, Δφ(jet1-Z) > 3.0 rad.
• The leading jet has to be in the central region of the calorimeter, 0.2 < |η_det.(jet1)| < 0.8.
  

Properties of quark and gluon jets

Properties of a hadronic jet depend on the tree-level parton initiating it. A jet initiated by a gluon has higher multiplicity of stable hadrons than a jet of the same energy initiated by a light quark. The difference in the observed particle multiplicities is due to the different color charges of a quark and a gluon. Similarly gluon jets produce a softer spectrum of stable hadrons than quark jets.

Quark and gluon jets of the same momentum deposit different amounts of energy in a non-compensating sampling calorimeter due the non-linear response of the calorimeter to charged hadrons. On average quark jets produce more energy that gluon jets of the same true momentum. To illustrate that we show p_T-balance for quark and gluon jets in figures below. In this study we rely on the PYTHIA predictions for quark and gluon jets and on the well-tuned single particle response.

The average pT-balance as a function of pT(Z) is on the left. The ratio of predicted and measured distributions in \pt-balance is on the left. The jets are clustered using cone radii of 0.4, 0.7, and 1.0.

We perform a direct test of the quark-gluon composition of the observed jets by using the number of tracks observed within the jet cone. The number of tracks is different for quark and gluon jets as shown below. Overall, the observed events are in a good agreement with the SM predictions (PYTHIA).

The average number of tracks within a jet cone as a function of pT(Z) is on the left. The ratio of the predicted number of tracks to the measured number in data versus pT(Z) is on the right. The yellow band represents a 3% uncertainty on the predicted tracking efficiency.

Kinematical properties of Z+jet events and quark/gluon composition of the leading jet both depend on the PDF's and the matrix elements. Therefore, the kinematic properties probe indirectly the quark/gluon composition. The SM predictions are studied using the distributions of sum and difference of rapidities of a Z boson and the leading jet, |y(Z)+η(jet1)| and |y(Z)-η(jet1)|, respectively figures below. We require p_T(Z) > 15 GeV/c. We observe good agreement between data and the predictions (both ALPGEN and PYTHIA).

The rapidity distributions for the Z+jet system. The jet clustering is performed with cone radii of 0.4, 0.7, and 1.0

Characteristics of out-of-cone radiation

An understanding of the energy flow outside of the leading jet's cone is essential for interpreting the measurement of p_T-balance in Z-jet events. Raw calorimeter energy summed in annuli outside of the jet cone requires a sophisticated treatment since the calorimeter response is especially non-linear for the softer particles. Also, the energy is sensitive to the pile-up of additional pp interactions and the underlying event.

Instead of using the out-of-cone energy directly, we exploit correlations between p_T-balance and properties of the sub-leading jet (e.g. p_T(jet2), Δφ(jet1-jet2), etc.). Multiple in-time pp interactions produce jets which are unrelated to the leading jet recoiling against the Z-boson. The presence of multiple interactions in an event diminishes the correlation between the \pt-balance and the properties of the sub-leading jet. In this section we require all events to have exactly one primary vertex to avoid the events with overlapping pp interactions.

We measure the dependence of the p_T-balance on difference in φ-angle between the leading jet (jet1) and the sub-leading one (jet2), Δφ(jet1-jet2), for events with p_T(Z) > 25 GeV/c (see figures below). The correlation depends on the jet cone size. The data is inconsistent with the predictions for jets with cone of 0.4. This inconsistency indicates that the data has more large-angle radiation than the predictions.

The rapidity distributions for the Z+jet system. The jet clustering is performed with cone radii of 0.4, 0.7, and 1.0

Conclusions and results

We estimate the sensitivity of the predicted p_T-balance on parton showering, tree-level matrix elements, parton distribution functions, parton-jet matching procedure, renormalization and factorization scales, multiple ppbar interactions, and calorimeter response of single stable particles. The contribution from each source of uncertainty is presented in the table below. The uncertainty caused by mis-modeling of the parton shower at large angles is found to be the largest. The sum of the uncertainties is consistent with the discrepancy between data and predictions in the p_T-balance. The remaining uncertainties (e.g. modeling of Underlying Event, calorimeter stability, etc) are significantly smaller than the discrepancy and we omit them.

The discovery potential of the LHC experiments (ATLAS and CMS) crucially depends on the accuracy of measurements involving hadronic jets with jet and di-jet spectra, the calculation of mis-E_T, top quark mass, background estimates for BSM searches being prominent examples. The contribution from the each source of uncertainty may vary depending on event selection and detector setup of a given experiment. However, in all cases the accuracy of jet energy measurements can be dramatically improved by developing new models for parton showering, which can describe FSR at large angles, or jet-parton matching schemes.