Preface: What are we doing in general?
is dedicated to the study of the
fundamental building blocks
of matter and tries to explain how they bind together to form atoms, molecules and so on.
The goal is to describe everything with the simplest possible theory. A large number of
was and is conducted to improve our knowledge, and over many years of active research, the so-called
(SM) of particle physics has emerged.
This very successfull theory describes three of the four fundamental interactions:
The fourth one,
is too weak to be measureable in particle interactions. Hence, gravity is so far ignored in the Standard Model,
but will have to be included some time in the future, because otherwise interactions at very high energies
cannot be described correctly. According to the SM, three families of
and interact via the aforementioned forces. Quarks and leptons are spin-1/2 particles, called
They define the matter fields and interact by exchanging integer-spin
which are sometimes also called force carrier particles. For example, the
W± and Z0
are the force carriers of the electroweak interaction, which combines
electromagnetism and the weak interaction. |
Even though we have learned a lot over the
we are unfortunately still pretty far away from the one (simple) theory to describe and explain each and everything,
the sought-after Theory Of Everything, or how we usually call it: the
grand unified theory
Among many possible candidate theories,
represents a very promising approach. SUSY not only addresses many of the problems
that still persist in the SM, but also offers a possibility to unify all
R-parity Violating Supersymmetry – What in the world is this?
SUSY predicts the existence of a partner particle for each SM particle, differing only by half a unit in
but otherwise sharing the same
spin-1/2 particles (leptons & quarks) are assigned bosonic partners with spin-0, called
sleptons and squarks.
For instance, the superpartner of an electron is a selectron,
for a muon a smuon, and so on. Spin-0 particles are
also called scalar particles, explaining the origin of
the "s" in front of the Standard Model particle's name.
On the other hand, all of the SM
(W± and Z0 bosons
photon γ) and the
(five particles as opposed to one in the SM) have fermionic partners.
These form - yet to be discovered - observable massive particles, called
All leptons / sleptons carry a lepton quantum number L, while
all baryons (quarks/squarks) carry a baryon quantum number B.
The lepton, baryon and spin quantum numbers of the (s)particles
are connected via
Rp = (-1)3B+L+2S
ordinary particles always have: Rp = +1
and SUSYparticles always have:
Rp = -1.
Two different types of SUSY models have to be distinguished:
models, which respect R-parity and conserve B and L, i.e. R-parity conserving SUSY (RPC-SUSY),
and models, which violate either B or L, called R-parity violating SUSY (RPV-SUSY) in the following.
In the former, the lightest supersymmetric particle
is stable since a decay in SM particles
would violate either L or B. In case the LSP is electrically neutral, it would provide a nice
The latter models do not offer such a candidate, as supersymmetric particles are allowed to
decay into SM particles and no heavy stable particle is left anymore.
However, RPV-SUSY may well be what is realized in nature and sets the stage for our analyses.
Searching for RPV-SUSY at the Tevatron
Due to the Proton-Antiproton (hadronic) initial state of the
and the assumption that sparticles are only produced via the LLE term,
(connecting (s)lepton fields), sparticles
will be produced in pairs via RPC-processes.
The strength of the considered RPV-couplings has to be weak, since otherwise we would not be able
to reproduce well-known particle properties, like their masses or branching ratios, e.g. the decays of
In general, if there is a competition between an RPV-coupling and SM couplings, like those of the SM
gauge interactions, the SM couplings will be dominant. Hence, R-parity violation is only visible in
the decay of the LSP, which would be absolutely stable in case of RPC-SUSY. |
The dominant production process in RPV-SUSY is chargino and/or neutralino pair
production through the annihilation of two quarks into a photon, or a Z, or a W boson.
decay predominantly into the
LSP (the lightest neutralino) and an
associated W or Z boson. The pair of LSPs then decays into at least four leptons via one of the
More leptons ("additional") may be produced via decays of the W or Z bosons.
RPC-SUSY trilepton analyses
can only look for these "additional" leptons as the LSP is stable.
In order to find the desired leptons in the quite large number
of mostly hadronic particles produced in each
we have used the
DØ detector, a standard, multipurpose particle physics
The necessary sub-systems used to detect leptons are three different kinds of detectors:
which is utilized to precisely reconstruct where a particle came from (its origin, or vertex), its trajectory, and momentum;
to measure the energy of charged and neutral particles.
Calorimeters are essential for measuring electrons, photons and
the muon detector
is used to identify muons, distinct from other particles in being
That means, they are the only SM-particles (except the ghost-like neutrinos) able to survive the calorimeter.
Events of a particular process are produced more frequently if the
for this process, i.e. the effective area is large compared to others.
Nevertheless, cross sections in particle physics are tiny, which is why they are usually measured
in "barn" with 1 barn (b) = 10-24 cm2. The luminosity, another commonly used
variable, is the proportionality factor between the cross section and the produced number of events:
N = L⋅σ. A high luminosity leads to a large
number of events.
Selection and Analysis of Trilepton Events
Data collected with the
DØ detector from April 2002 to August 2004,
corresponding to an integrated luminosity of L∼360 pb-1 was used. Three analyses were
developed to search for events containing at least three charged
in the following flavor combinations: |
These so-called multilepton events may stem from chargino/neutralino pair production and could hence
indicate the existence of supersymmetry. Unfortunately, supersymmetry is not the only source for this
type of events; instead they may well be produced from a wide variety of other, already well-known
processes such as W or Z boson production. The real work now consists in sorting out, which events
are due to known processes and which could possibly have been produced in supersymmetric interactions.
The largest and most important sources of "background" events are:
W production in association with jets, which may well be misidentified as electrons or taus,
diboson production, i.e. WW, WZ, and ZZ, and the pair production of heavy quarks, such as
"b anti-b" or "c anti-c".
In order to achieve a separation of SUSY candidate events from the large amount of background
events, a number of variables with differing distributions for background and SUSY events was
analyzed. The following figures show distributions of three different quantities for data
(black squares with error bars), the background expected from simulations
and the expected SUSY signal (solid red lines). Further explanations
are given below each of the figures.
- eel: two electrons and a third lepton: either an electron or a muon
- µµl: two muons and a third lepton: either an electron or a muon
- eeτ: two electrons and a tau lepton
Dielectron invariant mass
This variable corresponds to the mother particle, if no undetectable particles
are produced. In case a Z boson is produced and decays into two electrons, the
invariant mass of the two electrons describes the mass of the Z boson, consistent
with the prominent peak around 80-100 GeV.
Missing transverse energy (MET)
is not really "missing", but could not be detected due to weakly interacting
particles (neutrinos). Due to energy & momentum conservation, the produced
particles are expected to be balanced in the transverse plane; an imbalance
(MET) indicates undetected particles.
Neural Network (NN) output
for a loose Z→ττ→µτhad
selection. This variable serves as identification criterion for tau leptons. A lepton
is said to be a tau candidate if NN >0.9 and if its transverse energy deposited in
is above 10 GeV.
Apart from the selection criteria detailed in the above figures a number of further criteria was applied
to the data and the simulated backgrounds. The most important ones are thresholds on the transverse momenta
(pT) of all three lepton candidates, and requirements on the invariant masses of the two leading
leptons in case of the
In the µµl analysis, two-dimensional criteria have been
applied in the two dimensional parameter regions, defined by: dimuon invariant mass/missing transverse energy
(Mµµ, MET), and
dimuon angular distance/missing transverse energy
For the eeτ analysis, events with invariant masses
below 18 GeV and above 80 GeV are excluded to reject as many events as possible from any of
the resonances: J/psi, Upsilon (low masses), and W and Z bosons (high masses). Additionally,
all three analyses require the presence of moderate missing energy, i.e. in the range of 10-15 GeV.
Results and Interpretation in the context of RPV-SUSY
After the last stage of the selection, the results of the three analyses are combined in order
to achieve the highest possible sensitivity for each
As mentioned, we are indeed expecting all kinds of leptons due to the additional leptons, coming from
the cascade decays of the produced charginos. The analyses are classified in terms of the signal over
background ratio (S/B). Events selected in more than one analysis are assigned to the analysis with
the highest S/B ratio and removed from the other analyses.
As no excess of events is observed in data, compared to the SM expectations, we set limits at the 95%
confidence level (CL). Given the hypothesis that the signal exists, we are hence looking for the maximal
the signal can have, so that the SM simulations are still compatible with the observed number of events in data.
This is equivalent to testing two hypothesis: |
hypothesis 1: S+B events from signal and background simulations
are needed to explain the observed number of events in data
hypothesis 2: B events from background simulations alone
are sufficient to explain the number of data events
To decide which of the two hypothesis fits better the observed data, we form the ratio of the
confidence levels for both hypothesis:
CLS= CLS+B / CLB
The normalization to the background expectation is done to get rid of its fluctuations.
When CLS equals 5%, it defines the value of the signal cross section
that can still be excluded at the 95% confidence level.
As no event is observed in data, this is equivalent to calculating only the probablility of having
observed zero events, when expecting S events from the signal.
(m0=1 TeV, tanβ=5,
The next-to-leading order cross section and 95% C.L. limits for the
couplings as a function of the neutralino (chargino) mass. The exclusion domains,
lie above the respective observed limit curve.
no-GUT MSSM scenario
Observed and expected exclusion domains at the 95% CL in the neutralino- chargino
mass plane of the considered MSSM model for the
couplings with their strengths set to 0.01, 0.01, and 0.003, respectively
In the mSUGRA scenario
(m0=1 TeV, tanβ=5,
neutralino (resp. chargino) masses up to 119, 118, and 86 GeV (resp. 231, 229, and 166 GeV)
are excluded by the three combined analyses
for the three couplings
The lower mass bounds for
in case of µ<0 are very similar.
A study of the
dependence on tanβ for the
coupling shows a slight improvement of the lower bounds of ∼10 (20) GeV on the
neturalino (chargino) mass.
In the no-GUT MSSM model, we exclude chargino masses under 210 GeV (resp. 130 GeV)
for neutralino masses greater than 50 GeV (resp. 30 GeV) for the
(resp. λ133) couplings.
The cut-off of the exclusion domain towards low neutralino masses is due to the combined effect
of the mean decay length of the lightest neutralino (chosen to lie below one cm) and the
strengths of the RPV-couplings.
Our results are the most competitive to date, compared to the
results in the MSSM scenario, where a chargino mass below 103 GeV was excluded for all
LLE-couplings, and also compared to the Tevatron
Run I results
in the mSUGRA scenario.