Probing color coherence effects in pp collisions at sqrt(s) = 7 TeV

A study of color coherence effects in pp collisions at a center-of-mass energy of 7 TeV is presented. The data used in the analysis were collected in 2010 with the CMS detector at the LHC and correspond to an integrated luminosity of 36 pb−1. Events are selected that contain at least three jets and where the two jets with the largest transverse momentum exhibit a back-to-back topology. The measured angular correlation between the secondand third-leading jet is shown to be sensitive to color coherence effects, and is compared to the predictions of Monte Carlo models with various implementations of color coherence. None of the models describe the data satisfactorily. Published in the European Physical Journal C as doi:10.1140/epjc/s10052-014-2901-8. c © 2014 CERN for the benefit of the CMS Collaboration. CC-BY-3.0 license ∗See Appendix A for the list of collaboration members ar X iv :1 31 1. 58 15 v2 [ he pex ] 1 2 Ju n 20 14


n Table 1.The
PYTHIA [21] (version 6.422) event generator uses leading-order (LO) matrix elements to generate the 2 → 2 hard process in perturbative QCD (pQCD) and the parton shower (PS) model to simulate higher-order processes [22][23][24].The PS model gives a good description of parton emission when the emitted partons are close in phase space.Events are generated with the Z2 tune for the underlying event.This Z2 tune is identical to the Z1 tune described in Ref. [25], except that Z2 uses the CTEQ6L1 [26] parton distribution functions (PDFs) of the proton in which the parton showers are ordered in p T .The hadronization is simulated using the Lund string model [27,28].The older D6T tune [29][30][31], where parton showers are ordered in Q 2 , is consi ered for comparison.The D6T tune was designed to describe the lower-energy results of UA5 and CDF.The color coherence effects are implemented in PYTHIA 6 by means of an angular ordering algorithm where the effects can be switched on and off via the steering parameters MSTP(67) and MSTJ(50), which control the initial-state and the final-state showers, respectively.
p

Measurement of the normalized β distribution and systematic uncertainties

The PYTHIA 8 [32] (version 8.145) event generator, used with tune 4C [33], orders the parton showers in p T and models the underlying event using the multiple-parton interaction model rom PYTHIA 6 including initial-and final-state QCD radiation.The color coherence effects are implemented in a similar manner as for the p T -ordered showers in PYTHIA 6.

The HERWIG++ [11,34] (version 2.4.2) event generator takes LO matrix elements and simulates parton showers using the coherent branching algorithm with angular ordering of showers.The cluster hadronization model [35] is used in the formation of hadrons from the quarks and gluons produced in the parton s ower.The underlying event is simulated using the eikonal multiple partonic scattering model [36].The color coherence effects are implemented by the angular ordering of emissions in the parton shower using the coherent branching algorithm [37].

The MADGRAPH 4 [38] (version 2.24) event generator is interfaced with PYTHIA 6 for the parton showering and the hadronization using the D6T tune and uses ixed-order matrix element calculations for the multiparton topologies.From two to four partons are considered in the final state.The color coherence for the hard jets at leading order co amplitudes in the model.The k T MLM matching scheme [39] applied with a matching parameter of 60 GeV avoids double-counting between the partons from MADGRAPH and the PS.


Measurement of the normalized β distribution and systematic uncertainties

The measurement of the β distribution is performed in two regions defined by the pseudorapidity of the second jet: the central region |η 2 | ≤ 0.8 and the forward region 0.8 < |η 2 | ≤ 2.5.

The angular correlation effects considered in this analysis appear to have a reduced sensitivity to th transverse momentum of the leading jet p T1 .Consequently different p T1 bins are merged into one single bin.

The β distribution in a given η 2 region is obtained as a sum of the events weighted by the luminosity collected by the trigger used in the associated p T1 bin.In case of MC samples the β distribution is obtained by summing together the events weighted by their generation level weight in a given η 2 region.The normalized β distribution is then obtained by dividing the weighted number of events in a given bin of β by the total weighted number of events in the given η 2 region.

In order to correct for the smearing effects induced by the detector resolution, an unfolding procedure is performed using the response matrices obtained from MC event generators.For this purpose the events generated with the MC programs ( YTHIA 6, PYTHIA 8, MADGRAPH + PYTHIA 6, and HERWIG++) are processed through a full CMS detector simulation package based on GEANT 4 [40].

Particle-level jets are built from the four-vectors of the MC generated particles with hadronization, but without detector effects.These jets are obtained using the same jet al orithm as for the reconstructed events.The resolutions in ∆η 23 and ∆φ 23 are found to be of the order of 0.005 to 0.01, depending on the transverse momentum and pseudorapidity of the jets.

An iterative Bayesian unfold in the RooUnfold package [42] is used to derive the unfolding corrections to the measured β distributions from the detector effects.The response matrix used to unfold the data is built using HERWIG++.The impact of the unfolding on the normalized distributions is typically of t e order of 1%.

Most of the systematic effects cancel out in the normaliz d β distribution, but the residual influence of several sources of systematic uncertainty has been considered:

• The jet

nergy scale uncer
ainty is evaluated varying the jet response by 2.5-5%, depending on the η and p T of the jets [43].The impact of this source of systematic uncertainties is below 1%.

• The jet energy and angular resolutions are accounted for by varying them by ±10% [44] and rebuilding the response matrices for the unfolding accordingly.The observed impact from both sources is in the range of 0.4-0.6%.

• The uncertainty due to the unfolding procedure is estimated by the dependence of the response matrix on the choice of MC generator, Alternative response matrices are built using alternative generators: PYTHIA 6, PYTHIA 8 and MADGRAPH + PYTHIA 6.

The observed effect is of the order of 0.5%.

The measurement

found to be ins
nsitive to the number of pileup interactions within statistical fluctuations.In the data corresponding to this analysis the average number of pileup events per bunch crossing was around two.The total systematic uncertainties for each bin are about 2%, and a list of the major uncertainties is summarized in Table 3.Each systematic source was found to be fully correlated between β and η 2 bins [43,44].However, the various systematic sources are uncorrelated among themselves.


Results

The unfolded β distributions are shown in Fig. 4 together with the predictions from the various MC models for the central (|η 2 | ≤ 0.8) and forward (0.8 < |η 2 | ≤ 2.5) regions.The values of the unfolded β distributions and their uncertainties are presented in Tables 4 and 5.

The ratios of the various MC predictions to the measured β distributions are shown in Fig. 5.

The data exhibit a clear enhancement of events compared to the PYTHIA and MADGRAPH generators near the event plane (β = 0) and a suppression in the transverse plane (β = π/2).The χ 2 comparisons of data with MC simulation, taking into account the statistical and systematic correlations between different data points, are shown separately for the central and forward regions in Table 6.The number of degrees of freedom (NDF) is 17, which is the number of bins minus one to account for the constraint imposed by the normalization.

None of the models used in the analysis describes the data satisfactorily.Even though PYTHIA 6 was adjusted with the Tevatron data, it fails to describe the LHC data since the χ 2 /NDF is large.No significant difference is observed between the tunes D6T and Z2.The PYTHIA 8 tune 4C generator describes the data better than PYTHIA 6 over the entire phase space, but the disagreement in the forward region is not negligible.The HERWIG++ event generator describes   the data better than the other MC generators in the central region, but the agreement is poor in the forward region.Finally, when MADGRAPH is used with the exact 2 → 3 matrix element calculations at LO, the global description of the data is improved with respect to PYTHIA 6 alone.

The impact of the color coherence effects is studied by switching them on and off for the first emission in the initial-and final-state showers in PYTHIA 6.One can observe in Fig. 6 that the agreement between the data and the simulation deteriorates when the color cohe ence effects in the MC events are suppressed.More quantitatively, the χ 2 divided by the number of de-  grees of freedom increases up to 7.7 in the central region and 11.5 in the forward region.The first emission in the initial-and final-state showers contributes roughly the same order.Using PYTHIA, it has been verified that the impact of the non-perturbative component of the QCD calculation (hadronization and underlying event) is negligible for this analysis.One conclusion from this PYTHIA study, as shown Fig. 6, is that the d ta clearly support larger color coherence effects than in present MC implementations.
β 0 0.51

Summary

Color coherence effects in multijet events have been studied in a sample of pp collisions corresponding to an integrated luminosity of 36 pb −1 , collected with the CMS detector at √ s = 7 TeV.Distributions of the variable β, which was previously used in similar analyses at the Tevatron, are used to measure the angular correlation between the second and third jets in transverse-momentum order, in the pseudorapidit and azimuthal angle space.The measurements, unfolded for detector effects, are compared to the predictions of the MC event genera-

Figure 2 :
2
Figure 2: Observed ∆η 23 distributions, corrected for detector effects, compared to MC predictions by PYTHIA 6, PYTHIA 8, HERWIG++, and MADGRAPH + PYTHIA 6.The MC samples are normalized to the total number of events in data.


Figure 3 :
3
Figure 3: Observed ∆φ 23 distributions, corrected for detector effects, compared to

C predictions by PY
the total number of events in data.


Figure 4 :
4
Figure 4: Observed β distributions for the data, corrected for detector effects, and for the MC generators (PYTHIA 6, PYTHIA 8, HERWIG++, and MADGRAPH + PYTHIA 6) in the central (|η 2 | ≤ 0.8) and forward (0.8 < |η 2 | ≤ 2.5) regions.The error bars show the statistical uncertainties, while the yellow shaded bands correspond to the combined systematic uncertainty.


Figure 5 :
5
Figure 5: The ratio of the

rious MC prediction
to the measured β distribution.The error bars show the statistical uncertainty of the data.The yellow band represents the systematic uncertainty, while the green band represents the total uncertainty.


Figure 6 :
6
Figure 6: The MC predictions for the β distribution from PYTHIA 6, with and without color coherence effects in the first branching of the initial-and final-state showers, compared to the measurement.The error bars show the uncorrelated statistical uncertainty of the data.The yellow band represents the systematic uncertainty, while the green band represents the total uncertainty.


Table 3 :
3
Typical systematic and statistical uncertainties in the normalized β spectrum and the statistical errors.
Uncertainty sources|η 2 | ≤ 0.8 0.8 < |η 2 | ≤ 2.5Jet energy scale (JES)1.0%1.0%Jet energy resolution (JER)0.4%0.5%Jet angular resolution (JAR)0.5%0.6%Physics model (PM) used in unfolding0.6%0.7%Statistical uncertainty4.0%3.7%

Table 4 :
4
The unfolded β distributions and their uncertainties for the central region |η 2 | ≤ 0.8.All uncertainties are symmetric and given in percent (%).β (degree) F η 2 (β) σ Stat σ JES σ JER σ JAR σ PM σ
Syst

Table 5 :
5
The unfolded β distributions and their uncertainties for the forward region 0.8 < |η 2 | ≤ 2.5.All uncertainties are symmetric and given in percent (%).β (degree) F η 2 (β) σ Stat σ JES σ JER σ JAR σ PM σ
Syst

Table 6 :
6
Values of χ 2 for comparisons of the β distribution for the data with the pred ctions of various MC generators.The number of degrees of freedom for both regions is 17.PYTHIA 8, HERWIG++, and MADGRAPH + PYTHIA 6 in the central and forward rapidity regions.We have shown that the variable β is sensitive to color coherence effects, and insensitive to the hadronization and underlying event.It is necessary to implement the color coherenc effects in MC simulations to better describe the data.Although the MC models in the analysis include this effect by default, none of them describes the data satisfactorily for all β values.The PYTHIA 6 expectations predict weaker color coherence effects than those observed, while PYTHIA 8 exhibits a better agreement with the data.The MADGRAPH MC generator, which uses the exact 2 → 3 matrix element calculations at LO matched to PYTHIA 6 for parton showering, improves the agreement with data with respect to PYTHIA 6 alone, while HERWIG++ describes the data in the central region better than the other MC generators but shows discrepancies in the forward region.
χ 2 /NDF
AcknowledgementsWe congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort.In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computin