We update our search for the scalar super-symmetric partner of the top quark from 1.9 fb-1 to 2.7 fb-1 of CDF Run II data in the decay channel:

Stop Decay Chain

We assume a 100% branching ratio of the stop squark into a b quark and chargino, and allow for the chargino to decay through a variety of channels to the dilepton decay mode. These stop events produce signatures similar to those of SM top quark decays, and can potentially be hiding in Tevatron data.

We place limits on the dilepton branching ratio, at theory cross section, of pair produced stop events, for stop masses between 115 and 197 GeV, neutralino masses between 44 and 91 GeV, and at chargino masses of 105.8 and 125.8 GeV

Public Note

[1 page ppt] [2 page ppt]


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Observed 95% CL in the Neutralino Mass v. Stop Mass plane, for various dilepton
branching ratios, at chargino masses of 105.8 GeV (left) and 125.8 GeV (right).
We assume electrons, muons and taus all equally contribute to the dilepton final state.

Introduction:

Due to the large mass of the top quark, the mass splitting between the first and second generations of super-symmetric stop quarks can be large, allowing t~1 to possibly be the lightest squark, and possible even lighter than the top quark.

With the following assumptions, the stop quarks will decay into final state event signatures similar to that of pair produced top quarks:

Assumptions

Since stop squarks are scalar particles, the pair production cross-section is about an order of magnitude smaller than for a fermionic quark of similar mass. Below are shown the cross-sections of stop at various masses, and also diagrams of the dominant production mechanisms at the Tevatron. 

Production Diagrams


If the mass splitting between chargino and neutralino is small, such that
then the W bosons in the event will no longer be on shell, and additional diagrams are allowed:
StopDecayDiagrams

These diagrams contribute to the decay of the chargino, and can significantly enhance the dilepton branching ratio without significantly altering the event kinematics. Hence we set 95% CL exclusion limits at various dilepton branching ratios.



Analysis Method:

Since the event signature of pair-produced stop events is the same as for the much more abundant top anti-top events, special consideration was needed so as to be able to make any excesses statistically significant, or in the event of no excess, to place physically realistic limits.
We choose to perform this search in the dilepton decay channel, where we look for events with two oppositely-charged high pT leptons identified as either electrons or muons. We also make use of b-tag information of the two high ET hadronic jets expected from the decay of the stop quarks.
Additionally a counting experiment would not be powerfull enough to either set limits, or establish an excess, so we performed a kinematic analysis. It was found using traditional event variables, such as missing transverse energy or scalar sum of pT's (HT), did not provide much discrimnation between stop and top events, additionally multivariate methods performed less than ideally due to the large amount of SUSY paramater space explored, and the fact that slightly changing stop, chargino, or neutralino mass greatly reduced the sensitivity of the multivariate methods. For a more robust anallysis we choose to reconstruct the stop-mass of the event to discriminate between the Standard Model, and stop signal.
For more information on how the stop mass is reconstructed, please see the Public Note.


Event Selection

Typically in high energy physics analysis the event selection cuts are chosen by the analyzers to maximize some intermediate figure of merit, such as signal over square-root of background. Once this is done then a subset of the event selection cuts may be further modified in order to reduce the impact of the dominant systematics.

For this analysis we chose to optimize the event selection cuts based on expected exclusion, taking into account all of the systematics, from the very beginning. We first performed a broad dilepton analysis in control regions were no signal is expected; this ensured we could both accurately model kinematic quantities, as well as reliably predict the rate of observed events for an arbitrary set of event selection cuts.
When then created prescriptions for calculating all of our systematic uncertainties, for an arbitrary set of event selection cuts. With the ability to calculate both the expected number of events, as well as the systematic uncertainties for an arbitrary set of event selection cuts, we then proceded to optimize the selection cuts to maximize our expected exclusion.

Genetic Event Selection

To identify the set of event selection cuts that maximized our expected sensitivity, we started with a very loose set of pre-selection cuts and then used a Genetic Algorithm to further refine the cuts imposed. Our pre-selection cuts required the event to have two oppositely charged leptons with pT>20 GeV/c, and two hadronic jets with ET>12 GeV/c2, an invariant mass of the leptons to be greater than 20 GeV/c2, and if the lepton invariant mass is near the Z-mass then a missing transverse energy significance cut is imposed.

The Genetic optimization algorithm then performed in the following way.
  1. First it created a large number of random sets of event selection cuts.
    The quantities included in the optimization:
    • Lepton pT ranges
    • Jet ET ranges
    • The Missing Transverse Energy expected from the undetected two neutrinos and two massive neutralinos
    • A cut in the plane of the sum of transverse momenta of all objects in the event (HT), verses the azimuthal-angles between the lead two jets times azimuthal-angle between the leptons
    • A cut on the azimuthal angle between the Missing Transverse Energy and any jets or leptons in the event, or if Missing Transverse Energy was higher than a certain value, this cut was not imposed
    Values for these cuts were allowed to be different in the b-tagged and non-b-tagged channels.
  2. For each set of cuts, the number of Standard Model, and signal events is then estimated. Similarly, all of the systematic uncertainties are also calculated for each individual set of cuts.
  3. The expected exclusion is then calculated for each set of cuts, using the reconstructed stop mass as the discriminating kinematic variable.
  4. Of the the large number of cuts this process was done for, the half of cuts that preformed the best are kept, while the rest are discarded.
  5. The surviving cuts then under go sexually-reproduction,
    e.g. Between 2 individual sets of cuts, the cut values are swapped at random, mutated, crossed-over, or passed along to offspring sets of cuts.
  6. This process is then repeated with the 'offspring' sets of cuts until no further improvement in expected sensitivity is seen.
An animation of this Can be seen here (261k)

In this way expected event yields and systematic uncertainties was calculated for thousands of sets of cuts before finding a set that maximized our expected sensitivity to exclude the new physics.
So whereas in a typical high-energy physics analysis, final event selection is one of the first steps of the analysis, for this search, it was nearly the last step of the analysis.

Results

The event selection cuts that maximized the sensitivity are shown below with the resulting expected and observed number of events.

The B-Tagged channel



The Non-b-Tagged channel


Plotted below is the exclusions derived from these event selection cuts.


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Observed 95% CL in the Neutralino Mass v. Stop Mass plane, for various dilepton
branching ratios.


Below stop signal is plotted at the dilepton branching ratio excluded at the 95% level for various chargino, neutralino, and stop masses. The data are clearly consistent with the standard model.

B-Tagged Channel

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Anti-B-Tagged Channel

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