What to do with Multijet Events?

DØ note 4465 2004-06-03 What to do with Multijet Events? T. Hebbeker RWTH Aachen ABSTRACT Multijet events are frequently produced in p p collisions. Events with several jets might indicate physics beyond the Standard Model; such topologies are predicted for example in RPV-SUSY or in models with excited quarks. In this note it will be explored, to what extent the SM can be tested by measuring multijet production at the Tevatron. In particular our knowledge of absolute cross sections is evaluated. (MC event, particle level) 1

1 Definitions The subject of this note is multijet event production, and multi is defined as 3. In particular inclusive jet production and dijet measurements are not discussed. Also multijet studies which require leptons and/or missing energy in addition to jets are ignored. The structure of the jets and the particle density in between jets is not of interest here. A priori the analysis is not restricted to specific jet algorithms. 2 Previous Measurements at the Tevatron The CDF experiment has studied events with up to six (cone) jets in Run I [4, 5, 6, 7, 8]. One- and two-dimensional distributions (normalized to 1, i.e. in general no use of absolute cross sections) are compared to a lowest order (LO) matrix element (ME) generator, to the Herwig parton shower Monte Carlo (MC) and to a phase space model. Apart from the latter one, the measured distributions are well described, the ME predictions are best. Also the fraction of double parton interactions is studied [5], see below. In the first CDF multijet paper [4] also the absolute 3-jet cross section is compared between experiment and LO theory; for the selection cuts applied in this specific analysis the results are 1.2 ± 0.02 ± 0.6 pb (measured) and 1.8 ± 0.9 pb (calculated). In the other publications cross sections are not quoted, but from the given number of events one can calculate cross sections for the corresponding specific experimental cut configurations (assuming no inefficiencies) and compare these results to theory predictions, see below. DØ has studied the distributions of 3- and 4-jet events [10], with looser cuts than CDF. Also here the cone jet algorithm was used. The data were compared to several models, including a LO ME generator. The ratio of 3- and 2-jet events as a function of kinematical variables was studied in another paper [11], this time (5 years later) the measurements were compared to a ME generator of order α 3 s. The renormalization (= factorization) scale was fitted with the result µ R 1/3 E T. An absolute comparison of cross sections to theoretical models was not performed by DØ. Finally the regime of jets with rather low p T values ( 20 GeV) was explored [12]. Again only shapes were compared. Here the NLO generator does not describe the data as well as parton shower MC programs. The event with the highest multiplicity (8) has been reported by CDF [6]. Top-searches have been performed in the 6-jet channel by DØ [13, 14] and by CDF [9]. In both cases the top cross section measurement was possible only by requiring an additional b tag, improving the signal/noise ratio by an order of magnitude. The QCD background was estimated from the data (without b tag). Other searches - using pure multijet final states - have not been published by the Tevatron collaborations, see also [17]. 2

3 Theoretical Expectations 3.1 QCD matrix element calculation A full 1 matrix element calculation exists only for final states with a maximum of six partons - and only in leading order. The calculations are accessible in form of the event generator Alpgen [19]. NLO calculations exist only for 2-jet and 3-jet final states [21]. In the following Alpgen [19] (version 1.3) is used, together with the Pythia [22] interface for the subsequent parton shower evolution and for the hadronization phase. A particular matching scheme [20] is not used; the jet algorithm is simply applied to the hadron level. After generating one samples of events with 2, 3, 4, 5 and 6 partons, they are added together according to their cross sections. Parton configurations are generated with slightly looser cuts, e.g. on η, as later used in the jet algorithm. Detector effects are not simulated. All cross sections presented in this section are exclusive n-jet cross sections, calculated for p p collisions at 1.96 TeV. The renormalization scale µ R is calculated using model 1 in Alpgen, i.e. µ R = p T where the averaging is done over all partons generated. This choice agrees with the fit results given in [11]. The CTEQ5L parametrization of the structure functions is used, and the value α s (m Z ) = 0.127. Heavy quarks (b, t) are not produced, their contribution to the cross section is small. Figure 1 shows the predicted multijet cross sections for different cuts on the p T value of the leading jet, for the seedless cone jet algorithm [1] and some typical jet selection cuts (E T > 30 GeV, η < 2.5). It must be mentioned that the event generation is time consuming, in particular for the 6-jet parton configurations ( 20 unweighted events / hour / GHz-CPU). Also jet cross sections calculated with the kt algorithm [2] have been studied, for a D parameter of 1. The cross sections are similar to those calculated for cones with R = 1, the differences amount to 20% or less. In order to estimate the theoretical uncertainties the following aspects have been looked into: higher order effects in the parton cross sections structure function variations the parton-particle transition For these studies multijet samples with the typical jet cuts η < 2.5 and p T > 30 GeV have been used. The cross section uncertainty due to missing higher orders can be estimated by a variation of the renormalization = factorization scale µ R. Here the range from 0.5 p T to 2 p T is considered. Clearly, this choice has been made before - nevertheless it is 1 Full means that all gluon and quark-antiquark configurations in the final state are included; in Alpgen this is the case except for q q q q q q, which probably gives a negligible contribution to the jet cross section. 3

Figure 1: Jet production cross section as a function of jet multiplicity, as predicted by Alpgen, at particle level. All jets must fulfill p T > 30 GeV (upper curve). When imposing an additional harder p T cut on the leading jet, one obtains the lower curves. 4

quite arbitrary. One justification comes from the study [11], not allowing for bigger deviations. And one can compare with the K factor for 3-jet production ( 1.25) calculated to NLO [21], which is consistent with my error estimate. The missing higher order contributions constitute the dominant source of theoretical uncertainties, which are shown in table 1. My estimate of the influence of the structure functions is based on the study in [16], assuming that the uncertainty is only a function of j p T (summing over all jets) and of j η of the event, independent of the topology of the final state. The resulting cross section uncertainties are smaller than 10% for low jet multiplicities and do not exceed 25% for 6 jets in the final state (average j p T = 350 GeV). To assign an error to the parton shower/hadronization step is difficult, too [20]. The order of magnitude can be estimated by comparing jet cross sections at parton level (Alpgen pure) and at particle level (after passing through Pythia and applying the jet algorithm and jet cuts). For all cases which were studied (this section and the following ones) the two differ by less than a factor of 2 (the parton cross section tends to be larger than the particle cross section) - but since the parton level is certainly not a good description of what a detector records, only part of the difference should be considered as a systematic error; I assign only 1/3 of the difference as uncertainty. Since the effect is anyway smaller than the renormalization scale uncertainty, there is no need to discuss this in depth. In the following it is assumed that theoretical uncertainties are given by the factors f (to be applied in both directions!) as listed in table 1, combining all the abovementioned errors. n 2 3 4 5 6 f 1.4 1.7 2.0 2.3 2.6 Table 1: Estimated total theoretical uncertainty on n-jet cross sections X. The true value is in the interval [X/f... X f] (at the 1 σ level). The cross sections of figure 1 are shown again in figure 2 and in figure 3 - this time the theoretical uncertainties are included. Figure 3 shows the cross section normalized to the 2 jet production cross section. When computing ratios the correlations as suggested by the renormalization scale study are exploited, e.g. for X 3 /X 2 a relative uncertainty of +1.2 0.8 is assumed. Since the differences between parton level and particle level are not dramatic, one can check some dependencies on the parton level, to save on CPU time. Figure 4 shows the cross section dependence on the lower p T cut applied to all jets, and figure 5 illustrates how the cross sections rise with increasing η range allowed for the jets. 5

Figure 2: Jet production cross section as a function of jet multiplicity, as predicted by Alpgen, at particle level. The estimated uncertainties are shown as upper and lower line around the Alpgen prediction. In addition the cross section calculated with the Pythia parton shower program are displayed. 6

Figure 3: Jet production cross section normalized to the 2-jet cross section, as predicted by Alpgen, at particle level. The estimated uncertainties are shown as upper and lower line around the Alpgen prediction. 3.2 QCD parton shower generator The Pythia [22] generator (version 6.205, within root [3]) is used ( stand-alone - no Alpgen!) to simulate multijet production 2. The standard hadronization parameters are used and the cone algorithm (see previous subsection) is applied to construct jets from the final state particles, excluding neutrinos. The resulting jet cross sections are in reasonable agreement with the Alpgen predictions for low jet multiplicities, but become much smaller than the ME predictions for n 4, see figure [22] 3. This is not surprising, since the parton shower approach is not expected to perform well in simulating several well separated high energy partons. Therefore the difference between Alpgen and Pythia is not considered as a theoretical uncertainty on multijet production, and the errors estimated for Alpgen are not increased. 2 MSEL=1; the variables CKIN(3) and CKIN(4) are used to subdivide the sample in disjunct subsamples, thus ensuring decent event statistics for all jet multiplicities. 3 The figure does not show the Pythia results for 5 and 6 jets, since it takes a huge amount of CPU time to generate high multiplicity jet events. 7

Figure 4: Jet production cross section as a function of p T threshold for the jets, as predicted by Alpgen on the parton level. All cross sections are normalized to p T = 30 GeV. 8

Figure 5: Jet production cross section as a function of η max, as predicted by Alpgen on the parton level. All cross sections are normalized to η max = 2.5. 9

4 Comparison Experiment - Theory In section 2 previous Tevatron publications on multijet events have been summarized. Here four cross sections (given implicitly in those papers) are compared with the Alpgen predictions at particle level - to see if the theoretical uncertainties as estimated in the previous section are realistic. This comparison is not straightforward, since not all experimental details are known. In particular, it has been assumed that the cross section for a given set of cuts is simply given by the published number of selected events and the corresponding integrated luminosity - trigger and detection efficiencies are all assumed to be one. Systematic errors (see next section!) are unknown and thus neglected. Furthermore, the seedless cone jet algorithm as defined in [1] is applied to the events generated by Alpgen - while the experiments CDF and DØ used other variants of the cone algorithm. # jets cuts reference exp. cross section exp. / pb cross section theory / pb 3 A [10] 38300 ± 200 (stat) 35000 ± 800 (stat) 3 B [7] 6.7 ± 0.3 (stat) 16 ± 10 (stat) 4 A [10] 6750 ± 75 (stat) 4500 ± 200 (stat) 6 C [8] 48 ± 1 (stat) 89 +25 15 (stat) Table 2: Comparison of measured and calculated (Alpgen+Pythia) multijet cross sections. A E T > 20 GeV, E (1st jet) > 60 GeV, η < 3, m > 200 GeV, R ij > 1.4 B C E T > 20 GeV, η < 3, j E > 420 GeV, m > 600 GeV E T > 20 GeV, η < 3, j E > 320 GeV Table 3: Cuts used for multijet event selection All measurements have been performed at s = 1.8 TeV and use a cone jet algorithm with R = 0.7. The theoretical cross section values given in table 2 are computed with Alpgen plus Pythia (for showering and hadronization), with the default treatment of the renormalization scale, see above. Afterwards the cuts as outlined in table 3 were applied at particle level. The statistical error given is sometimes quite large, since the generation is slow and often inefficient with regard to the final cuts (i.e. most generated events are rejected for example with the cut on the invariant mass of the multi jet system m of 600 GeV). All calculated cross sections are in good agreement with the measured ones, the difference is comfortably covered by the statistical and theoretical systematic errors. 10

The agreement is even better than expected from the theoretical errors as estimated in the previous section. Thus the Alpgen generator seems to work pretty well! More multijet data are needed for more detailed comparisons, in particular ratios of jet cross sections as displayed in figure 3 would be useful. 5 Experimental issues Here only two aspects are discussed: jet energy scale and multiple interactions. Figure 4 tells us the effect of jet energy scale offsets (and/or scale uncertainties), which is quite important for high jet multiplicities. A change in the jet energy scale by 10% implies a change in the 6-jet cross section by a factor of 5! Thus it is of utmost importance to control the jet energy scale at a level of < 5%, else the experimental uncertainties exceed the theoretical ones. Multiple interactions might occur inside the same p p pair [5], or via different p p pairs colliding during the same bunch crossing. The first effect can not be seen, while in the second case separate primary vertices can be measured. Obviously the probability for additional p p interactions is luminosity dependent. Both effects are small (percent level) for the current Tevatron machine parameters [5, 15, 24] and can be neglected. As an example, one can estimate the production of double events with 3+3 jets, and compare to the production of genuine 6-jet events: With an instantaneous luminosity of L = 5 10 31 /cm 2 /s and a 3-jet cross section of X 3 10 5 pb (figure 1) the average number of 3-jet events per crossing is n 3 = L X 3 t 3 10 6 (1) where t 500 ns is the average time difference between two bunch crossings following each other. The probability for getting two 3-jet events at the same time is n 3+3 = n 3 2 2 5 10 12 (2) This number must be compared to the probability for one genuine 6-jet event (X 6 30 pb): Thus n 3+3 /n 6 < 1%. n 6 = L X 6 t = 8 10 10 (3) 11

6 Searches in the multijet channel Here QCD multijet events constitute the main background, which must be subtracted. In order to do so, one can reduce the theoretical and experimental uncertainties on the absolute QCD cross sections by measuring multijet production outside the signal region and extrapolating. Example: If the 6-jet cross section is measured for a jet threshold of p T = 20 GeV, one can extrapolate to the 40 GeV cross section with a precision of 10% (renormalization scale variation 0.5-2). a) Top. The top is not a new particle anymore, but cross section and mass measurements are important, and could in principle be done via the 6-jet channel. However, the total cross section is only 8 pb (of which only a few percent will turn into 6-jet events, depending on the jet definition), smaller than the 6-jet cross section (10 100 pb for η < 2.5, p T > 30 GeV). Thus additional features (b tag) must be exploited. b) RPV-Susy. If λ > 0, one expects events with many jets and no missing energy. A typical production cross section (process χ 0 χ ± ) is - at best - of the order of 1pb [18] for Susy parameters not yet ruled out. Again, the chances are dim to find an excess here. c) Excited quarks. If they are pair produced and decay into gluon plus quark, one expects 4-jet events. Pythia [22] predicts for a mass of 200 GeV and compositeness scale Λ = 500 GeV a cross section of 600 pb ( η < 2.5, p T > 30 GeV), one order of magnitude lower than the 4-jet QCD cross section. However, the topoplogies of the two event classes are quite different, in particular the measured dijet invariant mass distribution might show the excited quark contribution. 7 Conclusions Theoretical uncertainties in the predicted multijet cross sections are large, so that precision tests of QCD are not possible. However, a detailed comparison of data and theory for n-jet cross sections is important, and its outcome is far from obvous, since the cross sections fall steeply when increasing n. A post-analysis of Run I data shows that Alpgen is able to reproduce the measured multijet cross sections within the estimated uncertainties. A detailed comparison between Run II data and theory will help in tuning the models (e.g. via an effective renormalization scale) so that absolute multijet background predictions might become precise enough for search analyses. Last not least, calculations with NLO precision for the multijet cross sections are most welcome... 12

8 Acknowledgements I thank Pavel Denime, Carsten Magass, Michelangelo Mangano, Christophe Royon and Markus Wobisch for interesting discussions. 13

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