
Search
for diboson (W^{+}W^{} or W^{±}Z°) resonances in electron + missing Et + 2 jets final
state 

We
report on a search for resonances decaying into a pair of gauge bosons, W^{+}W^{}
or W^{±}Z°. In this search mode, one W decays through a leptonic
(electron) mode and the other boson decays into two jets. Based on ~3/fb data,
three resonance hypotheses, G* (R/S graviton), Z’ and W’, are tested and their
cross section limits at 95% confidence level are calculated.
Before an event is considered for the WW reconstruction process, it is required to have only one electron in the central region with Et > 30 GeV, a missing Et > 30 GeV, 2 or 3 jets with eta < 2.5 and jet Et > 30 GeV, and an overall Ht > 150 GeV. Ht is defined as the sum of the electron Et, the missing Et and the jet Et of all jets with raw Et > 8 GeV and eta < 2.0. Further optimization using Et cuts is applied in cross section limit calculations (see below). The plots and tables shown below are before the optimization.
The WW invariant mass is constructed by first combining the electron with the missing Et assuming that they are from a W. Due to unknown missing Ez, if there are 2 real solutions, both solutions are kept. Next, two jets are combined to form the other W candidate with the requirement that 65 GeV < M(jj) < 95 GeV. When there are more than 2 jets, the pair that gives a M(jj) closest to the W mass is selected. Finally, the WW candidates are combined for WW invariant mass.
Left plot is a stackup of the reconstructed WW invariant mass distributions from various SM backgrounds overlayed with the observed data (+ symbols).
Right plot is a comparison of data and
background integrated over ±1.5 sigma (horizontal error bar) of reconstructed G* signal.
The sigma is determined by fitting the reconstructed mass shape with a Gaussian
function. The vertical error bars for the data and the signal are staggered for
clarity. The background error bars include statistical and systematic
errors.

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WZ invariant mass reconstruction is similar to WW’s except that the twojet invariant mass is required to be within 75 GeV < M(jj) < 105 GeV. When there are more than 2 jets, the pair that gives a M(jj) closest to the Z mass is selected.
Left plot is a stackup of reconstructed WZ invariant mass distributions from various SM backgrounds overlayed with observed data (+ symbols).
Right plot is a comparison of data and background integrated over ±1.5 sigma (horizontal error bar) of reconstructed W’ signal. The sigma is determined by fitting the mass shape with a Gaussian function. The vertical error bars for the data and the signal are staggered for clarity. The background error bars include statistical and systematic errors.



Contributions from 12 standard model processes are taken into account for the background estimation. Of these, 11 are evaluated by Monte Carlo simulation. The background from QCD jet events is estimated using jet triggered data and the fake rate (a jet faking an electron) as a function of Et.
Left table: Data and breakdown of background processes for WW invariant mass.
Right table: Data and breakdown of background processes for WZ invariant mass.
The systematic error includes 6% luminosity uncertainty.

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The uncertainties included in background calculation in decreasing importance are:
· Jet Energy Scale uncertainty (JES)
· Cross section uncertainty
· Luminosity uncertainty
· Statistical uncertainty in the Monte Carlo
The dominating uncertainty is JES at ~ 13%. The cross
section and luminosity uncertainties are ~6% each.
Signal acceptance is defined as signal detection efficiency times the integrated luminosity. This quantity is an input to the cross section limit calculations as described below. The uncertainties included in decreasing importance are:
· Jet Energy Scale uncertainty (JES)
· Luminosity uncertainty
· Initial State Radiation uncertainty (ISR)
· Final State Radiation uncertainty (FSR)
· Parton Distribution Function uncertainty (PDF)
· Statistical uncertainty in the Monte Carlo
The dominating uncertainties are JES and luminosity (6%). For JES, it varies from 12% (170 GeV mass) to 6% (700 GeV mass) for G*, 13% (170 GeV) to 5% (700 GeV) for Z’, and 9% (190 GeV) to 6% (700 GeV) for W’.
A Bayesian method is used to calculate 95% confidence level cross section limits. The calculation requires signal acceptance (signal detection efficiency times integrated luminosity), estimated background, and observed data as input. To calculate signal detection efficiency, MC events for G*, Z’ and W’ are generated for a set of selected mass points and a mass window of ±1.5 sigma of the reconstructed signal is used. The data and background invariant mass plots shown above (on the right side of WW and WZ mass plots) reflect this set of mass points with ±1.5 sigma mass windows.
Further optimization is carried out to improve sensitivities at higher mass regions. Additional higher Et cuts for constituent particles (electron, missing Et, jets) are applied in two different ways: One is to require a higher Et cut on all 4 participant particles ranging from 40 GeV to 80 GeV in 10 GeV steps. The other is to require a higher Et cut on one of each boson’s decay daughters, i.e. either the electron or the missing Et (W > e nu) and one of the jets (W/Z > jj). The increased Et runs from 40 to 120 GeV in 10 GeV steps. These 2 series of cuts make up a total of 15 variations of Et cuts including the original Et > 30 GeV cut. For each particle, at each mass point, the expected cross section limits are calculated for the 15 cuts. The series that gives the most of the best expected limit is chosen for that particle and the cut that gives the best expected limit in that series is chosen to give the final result. The following plots are results from this optimization.
Left: Cross section x branching ratio
limits at 95% CL for G*. Red line is expected limit. Yellow band is ±1 sigma of
expected limit. Green band is ±2 sigma of expected limit. Black line with dots
is data limit. Blue line is theoretical cross section of G* from Pythia 6.216 and using a constant k factor
1.3 (Phys. Rev.
Lett. 99, 171801 (2007)).
Right:
Cross section limits divided by theoretical cross section. Mass regions with
ratio below 1 are excluded. Expected cross section limits exclude G* mass
region < 632 GeV. Data exclude mass region < 607 GeV.


Table: Optimal cuts applied to G*, where “2, 40” denotes the “2 particles, Et > 40 GeV” cut as described above.

Typical G*
Signal/Background/Data at a Selected Cut: WW invariant
mass plot with optimal cut (2,120)
for 600 GeV G* (see table above). Expected G* signals at 600 GeV is shown in
the blue hatched histogram.
Left Plot: In linear scale.
Middle Plot: In log scale
Right Table: Data and background
compositions of WW for this cut (2,120): { (Et(ele)  missing Et) && (one
of the jets) } > 120GeV.



Left: Cross section x branching ratio limits
at 95% CL for Z’. Red line is expected limit. Yellow band is ±1 sigma of
expected limit. Green band is ±2 sigma of expected limit. Black line with dots
is data limit. Blue line is theoretical cross section of Z’ from Pythia 6.216
and using a constant k factor 1.3 (Phys.
Rev. Lett. 102. 031801 (2009)).
Right: Cross section limits divided by theoretical cross section. Mass regions with ratio below 1 are excluded. Expected cross section limits exclude 257 GeV < M_{Z’} < 630 GeV. Data exclude mass region 247 GeV < M_{Z’} < 544 GeV.


Table: Optimization cuts applied to Z’, where “2, 40” denotes the “2 particles, Et > 40 GeV” cut as described above.

Observed and expected 95% C.L. Z’ exclusion
region. The gauge coupling strength g·cos θ_{W} for W and Z is
replaced by xi·g·cos θ_{W} for Z’, where
xi=c·(M_{W}/M_{Z’})^{2}
is a suppression factor set by Z’ mass (M_{Z’}) and a free parameter c. The blue line shows xi values when c=1, which is PYTHIA default and
normally used to set Z’ mass limits.

Typical Z’
Signal/Background/Data at a Selected Cut: WW invariant
mass plot with optimal cut (4,60)
for 600 GeV Z’ (see table above). Expected Z’ signals at 600 GeV is shown in
the blue hatched histogram. Note that
this is a different cut from G* at the same mass energy.
Left Plot: In linear scale.
Middle Plot: In log scale
Right Table: Data and background
compositions of WW for this cut (4,60): { (Et(ele) && missing Et
&& (both jets) } > 60 GeV.



Left: Cross section x branching ratio
limits at 95% CL for W’. Red line is expected limit. Yellow band is ±1 sigma of
expected limit. Green band is ±2 sigma of expected limit. Black line with dots
is data limit. Blue line is theoretical cross section of W’ from a NLO
calculation (Z.
Sullivan, Phys. Rev. D 66 075011, (2002)).
Right: Cross
section limits divided by theoretical cross section. Mass regions with ratio
below 1 are excluded. Expected cross
section limits exclude 381 GeV < M_{W’} < 420 GeV. Data exclude
mass region 284 GeV < M_{W’} < 515 GeV.


Table: Optimal cuts applied to W’, where “2, 40” denotes the “2 particles, Et > 40 GeV” cut as described above, “4, 50” denotes the “all 4 particles, Et > 50 GeV” cut.

Observed and expected 95% C.L. W’ exclusion
region. The gauge coupling strength g·cos θ_{W} for W and Z is
replaced by xi·g·cos θ_{W} for W’, where
xi=c·(M_{W}/M_{W’})^{2}
is a suppression factor set by W’ mass (M_{W’}) and a free parameter c. The blue line shows xi values when c=1, which is PYTHIA default and
normally used to set W’ mass limits. CDF run 1 result is also shown for
comparison.

Typical W’
Signal/Background/Data at a Selected Cut: WZ invariant
mass plot with optimal cut (4,60)
for 600 GeV W’ (see table above). Expected W’ signals at 600 GeV is shown in
the blue hatched histogram. Note that
although this is the same cut as Z’ at 600 GeV this is WZ invariant mass
instead of WW.
Left Plot: In linear scale.
Middle Plot: In log scale
Right Table: Data and background
compositions of WZ for this cut (4,60): { (Et(ele) && missing Et
&& (both jets) } > 60 GeV.



The
following table summarizes mass exclusion regions derived from cross section
limit plots above.
