Invariant Mass Distribution of Jet Pairs Produced in Association
with a W boson in ppbar Collisions at √s = 1.96 TeV
(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
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.
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
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 < MJJ < 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.
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
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 < MJJ <
175 GeV region
The kinematic distributions of events in the 115 < MJJ <
< 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
Further details of the
ALPGEN parameters are here and
A comparison of SHERPA and ALPGEN MJJ 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): MJJ compared to the data with the
W+jets shape modeled by SHERPA. (LEFT-CENTER): Background subtracted
MJJ fit with the W+jets shape modeled by SHERPA.
(RIGHT-CENTER): MJJ 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 MJJ 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 pTJJ cut
The MJJ distribution when the pTJJ 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 pTJJ 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 <
MJJ < 160 GeV region and the 100 < MJJ
< 120 GeV OR
160 < MJJ < 180 GeV "sideband" regions.
We determine the ratio NTAG / NUNTAG
for several b-tag types where NUNTAG is the number of
events without any b-tag information and NTAG can be
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
- 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.
Table 1: b-tag rate in the muon (LEFT) and electron (RIGHT) samples.
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.
We compare NLO to
LO predictions for the top background and determine the significance
when the t-tbar background is increased by 50%.
We apply different ΔφJJ cuts to examine whether
the excess is due to back-to-back jets.
Quark vs Gluon Jets
The ratio of the leading-jet ET and the sub-leading jet ET 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 ET[JET-2] / ET[JET-1] increases we
preferentially select quark jets at MJJ values > 100 GeV
(see Fig. 9 [courtesy of Adam Martin]).
The variation of quark and gluon-jet fractions as a function of
MJJ for our standard selection (LEFT),
ET[JET-2]/ET[JET-1] > 0.6 (CENTER) and >
MJJ distributions and fits for the quark-jet enhanced
selection: ET[JET-2]/ET[JET-1] >
0.6. This returns a (statistical-only) significance of 3.6 σ.
MJJ distributions and fits for the quark-jet enhanced
selection: ET[JET-2]/ET[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 ΔRJJ
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
ΔRJJ and ΔφJJ distributions in
the excess region and compared them to two models: a WH model
(mH=160 GeV decaying to light quarks) and a technicolor
[mass=250 GeV] decaying into
GeV]). These two models predict very different ΔRJJ
and ΔφJJ 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 ET and the pT of the
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
Cross section of excess evaluated using the D0 methodology
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 (mH=150 GeV) production for the acceptance. This
yields a cross section of 0.82 + 0.83 - 0.82 pb at MJJ=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.