Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in ppbar Collisions at √s = 1.96 TeV

Primary authors: A. Annovi^a, P. Catastini^b, V. Cavaliere^c, L. Ristori^d
a: INFN Frascati, Italy; b: Harvard University; c: University of Illinois at Urbana-Champaign; d: INFN Pisa, Italy and Fermilab

In Phys.Rev.Lett.106:171801 (2011) / arxiv:1104.0699 we reported a study of the invariant mass distribution of jet pairs produced in association with a W boson using data collected with the CDF detector from an integrated luminosity of 4.3 fb⁻¹. The observed distribution had an excess in the 120-160 GeV/c² mass range not described by current theoretical predictions within the statistical and systematic uncertainties.

Here we update this previous result and present further studies of the excess using additional data collected through to November 2010 corresponding to an integrated luminosity of 7.3 fb^-1. The significance of the excess increases from 3.2 (for 4.3 fb^-1) to 4.1 standard deviations consistent with expectation from the increase in the data sample size. The event selection and analysis methodology remain unchanged from the original 4.3 fb^-1publication.

M_JJ distributions

Fig. 1: The dijet invariant mass distribution for the electron (LEFT) and muon (RIGHT) data. An excess in the 120-160 GeV region is observed in both samples.

In evaluating the significance of the excess we assume that the excess can be modeled with an additional Gaussian component. The Gaussian assumption is a simplified model since any dijet resonance is expected to have an asymmetric distribution with a more pronounced tail for masses below the peak due for example to QCD radiation and out-of-cone jet energy. Moreover, the exact shape of a dijet resonance depends on the specific physics process and the heavy flavor content of the decay products. To retain model independence and due to the relatively low statistics of the excess, we assume a simple Gaussian model for evaluating the significance of the excess.

Fig. 2: The dijet invariant mass distribution. The sum of electron and muon events is plotted. In the left plot we show the fits for known processes plus an additional hypothetical Gaussian component. In the right plot, by subtraction, only the diboson (WW, WZ) and hypothetical Gaussian contributions are shown. The band in the subtracted plot represents the sum of all background shape systematic uncertainties.
The muon sample has 158 ± 45 excess events and the electron sample 240 ± 55. The peak of the Gaussian excess is at 147 (± 4) GeV with an RMS of 14 GeV. The χ² is quoted for the fit region of 28 < M_JJ < 200 GeV.

The p-value with only statistical uncertainties is 9.49 x 10^-7, corresponding to 4.76 standard deviations.

Fig. 3: As Fig. 1 except here only the "new" data i.e. the 3 fb^-1 added to the original 4.3 fb^-1 data is shown. The significance of the excess in this data alone considering only statistical uncertainties is 2 standard deviations. The significance when the Njet=2 cut is relaxed to Njet ≥ 2 cut is 2.85 standard deviations.

Systematic Uncertainties

The systematic uncertainties are evaluated as they are in the publication. The largest uncertainties arise from the modeling of the W+jet sample and multijet QCD sample. In determining the significance of the excess with systematic variations we take the conservative approach of using the combination that returns the highest p-value (lowest significance) as our final result. This returns a p-value of 1.9× 10^-5 corresponding to a conventional significance of 4.1 standard deviations. The best description (shown in Fig. 4) of the data is obtained when the Q² scale in ALPGEN is doubled but this still results in a significance of 4.3 standard deviations.

Fig. 4: As Fig. 2 except that the systematic variation (ALPGEN Q² scale doubled) best fitting the data is shown.

Kinematic Distributions of events in the 115 < M_JJ < 175 GeV region

The kinematic distributions of events in the 115 < M_JJ < < 175 GeV region are shown here. Normalisations are obtained from the standard fit.

Inclusive Jet Selection

The analysis requires exactly two jets passing the selection criteria. We have also considered the case when we relax this criteria and require at least two jets passing the jet selections which is expected to be modeled better. The significance of the excess considering only statistical uncertainties remains essentially unchanged at 4.8 σ

Fig. 5: As Fig. 2 except the requirement of exactly two jets is relaxed such that the sample is more "inclusive" and contains at least two jets.

ALPGEN vs SHERPA Comparison

The W+jets shape is determined by ALPGEN (v2.1) interfaced to PYTHIA (v6.326) with the MLM matching scheme. We've performed a cross-check of this shape prediction using SHERPA (v1.2.2) with a Q cut of 15 GeV (to match ALPGEN) using CKKW matching. The SHERPA enhancement factors are: 20 (2-jets), 40 (3-jets), 80 (4-jets); further details are here. Further details of the ALPGEN parameters are here and PYTHIA here.

A comparison of SHERPA and ALPGEN M_JJ distributions is shown in Fig. 6. The (statistical-only) significance of the excess when the W+jets shape is modeled by SHERPA is 3.8 standard deviations compared to 4.8 with ALPGEN. Further comparisons of kinematics distributions between the two generators are here.

Fig. 6: (LEFTMOST): M_JJ compared to the data with the W+jets shape modeled by SHERPA. (LEFT-CENTER): Background subtracted M_JJ fit with the W+jets shape modeled by SHERPA. (RIGHT-CENTER): M_JJ compared to the data with the W+jets shape modeled by ALPGEN. (RIGHTMOST): A comparison (normalised to unit area) of the SHERPA and ALPGEN W+jets M_JJ distribution. Only statistical uncertainties are shown. Note the χ² quoted extends beyond the range of the plots shown.

Jet Energy Scale

In this analysis the standard CDF uncertainty on the Jet Energy Scale (JES) is used. This is 3% - see Nucl.Instrum.Meth.A566:375-412 (2006). In Fig.7 we show the effect of applying a JES shifted by +7% (i.e. more than twice the established systematic uncertainty). The (statistical-only) significance is reduced from 4.76σ to 4.1σ.

Fig. 7: As Fig.2 except the JES is shifted by +7% (more than twice the systematic uncertainty).

Increasing the pT_JJ cut

The M_JJ distribution when the pT_JJ cut is raised from the default of 40 GeV to 60 GeV is shown in Fig. 8. The significance (statistical-only) is reduced to 3.4σ.

Fig. 8: As Fig.2 except the pT_JJ cut is increased from the default of 40 GeV to 60 GeV.

b-tagging in the excess region

We perform a comparison between the b-tagging rate in the 120 < M_JJ < 160 GeV region and the 100 < M_JJ < 120 GeV OR 160 < M_JJ < 180 GeV "sideband" regions. We determine the ratio N_TAG / N_UNTAG for several b-tag types where N_UNTAG is the number of events without any b-tag information and N_TAG can be sub-classed as:

0 T : neither of the two jets has a positive SECVTX Tight tag.
1 T : at least one of the two jets has a positive SECVTX Tight tag.
2 T : both jets have a positive SECVTX Tight tag.
0 L : neither of the two jets has a positive SECVTX Loose tag.
1 L : at least one of the two jets has a positive SECVTX Loose tag.
2 L : both jets have a positive SECVTX Loose tag.

No significant enhancement of b-tagged events is observed in the "excess" region compared to the sideband regions. This highlights that the excess is not arising solely from b-bbar events and that the excess is not due to an under-estimated t-tbar content since in these events at least one of the jets should give rise to a b-quark in the "excess" region.

Table 1: b-tag rate in the muon (LEFT) and electron (RIGHT) samples.

Modeling cross-checks

We have considered alternate models and varied cuts to enhance backgrounds to demonstrate the integrity of our background estimates.

Top enhanced region
We a sub-samples that are enriched in t-tbar by selecting events with at compare their kinematic properties to predictions.

Top modeling
We compare NLO to LO predictions for the top background and determine the significance when the t-tbar background is increased by 50%.

Δφ distributions
We apply different Δφ_JJ cuts to examine whether the excess is due to back-to-back jets.

Quark vs Gluon Jets
The ratio of the leading-jet E_T and the sub-leading jet E_T is expected to be different in the case of quark and gluon jets which has implications for the jet energy-scale calibration. As the ratio E_T[JET-2] / E_T[JET-1] increases we preferentially select quark jets at M_JJ values > 100 GeV (see Fig. 9 [courtesy of Adam Martin]).

Fig. 9: The variation of quark and gluon-jet fractions as a function of M_JJ for our standard selection (LEFT), E_T[JET-2]/E_T[JET-1] > 0.6 (CENTER) and > 0.8 (RIGHT).

Fig. 10: M_JJ distributions and fits for the quark-jet enhanced selection: E_T[JET-2]/E_T[JET-1] > 0.6. This returns a (statistical-only) significance of 3.6 σ.

Fig. 11: M_JJ distributions and fits for the quark-jet enhanced selection: E_T[JET-2]/E_T[JET-1] > 0.8. This returns a (statistical-only) significance of 3.2 σ.

Model dependence of jet system
In our original publication we studied the ΔR_JJ system and noted that a reweighting of this distribution (using the sidebands) can change the significance of the excess by ±1 standard deviation. In evaluating our significance we have assumed a model-independent Gaussian distribution. We have however also investigated the ΔR_JJ and Δφ_JJ distributions in the excess region and compared them to two models: a WH model (m_H=160 GeV decaying to light quarks) and a technicolor model (techni-ρ^±/techni-ρ⁰ [mass=250 GeV] decaying into W+techni-π⁰/W+techni-π^± [mass=145 GeV]). These two models predict very different ΔR_JJ and Δφ_JJ distributions and as a result the experimental acceptance depends strongly on which model is chosen. The WH acceptance is a factor of two smaller than that derived from the technicolor model. The two models are similarly discrepant with respect to the leading-jet E_T and the pT of the dijet system.

Luminosity and jet properties
We have studied the dijet mass spectrum as a function of time and instantaneous luminosity. The excess appears in all data sub-samples and, within statistical uncertainties, the corresponding number of events scales with the integrated luminosity. The charged track multiplicity of the jets is not characterised by low multiplicities as would be expected from τ leptons. Furthermore the EM fraction of the jets does not support the hypothesis that the jets are due to misidentified electrons.

Cross section of excess evaluated using the D0 methodology

In Phys.Rev.Lett.106:171801 a crude estimate of the cross section of the excess was performed yielding 4 pb. In the D0 paper the cross section is evaluated by taking the excess event number from a Gaussian signal and using a MC simulation of WH → lνbb (m_H=150 GeV) production for the acceptance. This yields a cross section of 0.82 + 0.83 - 0.82 pb at M_JJ=145 GeV. Using this same prescription we obtain 3.1 ± 0.8 pb and 3.0 ± 0.7 pb for the 4.3 fb^-1 and 7.3 fb^-1 samples respectively.