CP Violation, Dark Matter and Extra
Dimensions in the D-Zero Experiment at the
Tevatron
Peter Neil Ratoff
Physics Department, Lancaster University, Lancaster LA1 4YB, United Kingdom
Abstract. The status of Run II of the Tevatron and the D experiment are reviewed and recent
results on the preparations for measurement of CP violation in B meson decays and searches for
the lightest SUSY particle and evidence for large extra dimensions are presented. Whilst signals
have yet to be established in these areas, the results shown illustrate the potential of the D
experiment to make measurements of cosmological significance in the next few years prior to
the turn-on of the LHC.
STATUS OF THE TEVATRON AND THE CDF AND D
EXPERIMENTS.
The Tevatron machine is a proton-antiproton collider located at the Fermi National
Accelerator Laboratory (FNAL) near Chicago. Two collision points are instrumented
with large multi-purpose particle detectors - the CDF and D experiments. During
Run I (1992-1996) approximately 0.1 fb-1 of data was collected at a centre-of-mass
energy of 1.8 TeV and the first evidence for the production and decay of top quarks
was observed. Between 1997 and 2001 the machine was substantially upgraded to
deliver higher luminosity collisions at a centre-of-mass energy of 1.96 TeV and by
2006 it is expected that the Run I integrated luminosity will have been increased 20fold. Beyond 2006 further upgrades to the machine might enable the two experiments
to each collect a total integrated luminosity of 10.0 fb-1. The Tevatron discovery
potential for a Standard Model Higgs boson is very good if this level of machine
performance can be achieved.
Since Run II operations started in March 2001 about 200 pb-1 integrated luminosity
has been delivered, although the first 10-20% of this was mainly devoted to detector
commissioning. The luminosity achieved thus far has been well short of the
laboratory's plans and so an intensive programme of machine development is
underway to achieve the required performance. Nevertheless, FNAL is strongly
committed to reaching the design goals for the Tevatron and the newly commissioned
Recycler ring should provide more antiprotons to the main ring.
The CDF and D collaborations have made very significant progress during 2002,
completing the commissioning of their upgraded detectors, improving their triggers
and data acquisition systems, calibrating and aligning their sub-detectors and refining
their reconstruction algorithms. The identification of "physics objects" such as
electrons, muons and jets and the determination of electromagnetic and jet energy
scales have proceeded with considerable success. The increase in the Tevatron
collision energy and luminosity has necessitated various detector upgrades to
accommodate higher event rates and backgrounds, principally in the front-end
electronics, trigger and data acquisition systems. This has considerably expanded the
physics capabilities of both experiments.
The remainder of this article is devoted to a review of the recent performance and
first results of the D collaboration with particular emphasis on physics of
cosmological significance - namely, CP violation in B meson decays and searches for
dark matter and large extra dimensions. Reviews of CDF work on these topics can be
found elsewhere (www-cdf.fnal.gov).
PERFORMANCE OF THE D DETECTOR
The upgraded D detector is shown in Figure 1. The main features of the upgraded
detector are an entirely new central tracking system comprising of a 2 Tesla solenoid,
a silicon microvertex tracker (SMT) and a scintillating fibre tracker (CFT), pre-shower
detectors placed in front of the calorimeter and layers of forward muon scintillators
and mini-drift chambers. The detector upgrades are complemented by new readout
electronics, trigger and data acquisition systems. Later in 2003 a displaced vertex
trigger (the silicon track trigger, or STT) will be installed, thereby completing the Run
II upgrade. The entire offline software suite has been rewritten in objected oriented
C++ code.
FIGURE 1. The upgraded D detector for Run II.
The performance of the upgraded detector is demonstrated by a range of standard
physics benchmarks such as the identification of electrons and muons that are basic
ingredients in the reconstruction of W and Z bosons (Figure 2). Based on these
techniques the inclusive production cross-sections for W and Z bosons have been
measured and found to be consistent with the Run I observations after taking into
account the effect of the higher beam energies.
FIGURE 2. Left, the Z boson peak in the electron-positron invariant mass distribution, and right, the W
boson Jacobian peak in the muon transverse mass distribution.
For the first time at the Tevatron, D has been able to reconstruct decays of Z
bosons into tau lepton pairs. This has been accomplished by searching for events with
an electron (from a tau decay into an electron and two neutrinos) pointing in the
opposite direction to a narrow single track jet produced by the hadronic decay of a tau
into a single charged pion and neutral pions. The invariant mass distribution of these
tau pairs is shown in Figure 3. The ability to reconstruct these particular Z boson
decays is important because they are a significant background in some SUSY particle
searches and Higgs boson searches.
FIGURE 3. Left, the Z boson peak in the tau pair invariant mass, and right, a candidate top-antitop
quark pair event decaying into an isolated high Pt electron and muon and several high Pt jets.
Putting together the capability of D to identify electrons, muons, high Pt jets of
hadrons and displaced vertices due to the decays of heavy flavour hadrons (more about
this in Section 3), a number of candidate top-antitop quark pair events have been
found (Figure 3). A 3 standard deviation signal for top-antitop production has been
established at a rate consistent with Run I observations (taking into account the higher
beam energies).
B PHYSICS
The most obvious advantage of studying the physics of B hadrons at the Tevatron is
the very large production cross-section (150 b at 2 TeV for b quark pairs) compared
to LEP (7 nb) or B factories (1 nb). Furthermore, hadron colliders are able to produce
B hadrons in all flavour combinations, in contrast to the B factories that operate at the
(4S) and hence only yield the light B mesons. D is a multipurpose detector capable
of reconstructing many B hadron final states and consequently offers a rich B physics
programme: cross-sections, B lifetimes, Bs mixing, CP violation in Bd and Bs and rare
decays.
A crucial element of the B physics programme at D is the trigger system. A
sophisticated 3 level trigger system reduces the 2.5 MHz crossing rate to the 50 Hz
rate of writing data out to disk (approx 0.25 MB per event). The most useful trigger
thus far for B physics has been the opposite sign dimuon pair trigger which provides a
simple and un-prescaled trigger in the central region (||<1.0, Pt > 3.5 GeV) and the
forward region (1.0<||<2.0, Pt > 2.0-2.5 GeV). However, it is also now proving
possible to trigger efficiently with a single muon trigger. In the near future D will
introduce a 2nd level track trigger (providing a track match to electron and muon
trigger 'objects') and a 2nd level displaced vertex trigger (the STT).
One of the first Run II measurements has been the inclusive B cross-section based
on the identification of muons with large Pt relative (Pt,rel) to a jet axis. The B hadron
content has been extracted via a fit to the Pt,rel distribution. After unfolding the jet
energy resolution the dominant systematic error in the measurement is uncertainty on
the jet energy scale correction. As in Run I, the inclusive B jet cross-section as a
function of the jet transverse energy (Et) is roughly a factor of 2 higher than the
predictions of perturbative QCD (Figure 4).
FIGURE 4. Left, the inclusive B hadron cross-section as a function of Et compared to the predictions
of perturbative QCD and, right, the J/  +- sample collected with the dimuon trigger.
A wide range of B physics measurements has become accessible using an inclusive
J/  +- sample (75,000 events) collected with the dimuon trigger from an
integrated luminosity of 40 pb-1 (Figure 4). For example, using this sample, the
lifetimes of various B mesons have been measured. In Figure 5, the invariant mass of
J/, K+ combinations shows a peak corresponding to the lightest charged B meson
(Bu) and using events from the signal region the B+ lifetime can be extracted from the
decay length distribution of the B+ decay vertices. The result obtained is an average
lifetime of 1.76  0.24 (stat) ps which is in good agreement with the PDG average
value of 1.674  0.018 ps. A particular advantage of this measurement is that the B+
decay final state is fully reconstructed and is free of hadronisation or momentum
uncertainties. Similar analyses have been performed on neutral B mesons (Bd and Bs)
using the J/ , J/ K0 and J/ K* final states, also yielding results in agreement with
PDG average values.
FIGURE 5. Left, the invariant mass of J/, K+ combinations,
and right, the decay length distribution of B+ decay vertices.
Whilst these lifetime measurements are neither new or especially interesting, they
do however illustrate the potential of D to reconstruct exclusive B decay final states
which are of importance to B mixing and CP violation studies. Indeed, the J/ K0
final state is one of the 'golden' channels for CP violation studies, whilst high statistics
Bs mixing measurements can only be made at hadron colliders. The D capability to
observe these signals is well illustrated in Figure 6.
A very promising observation has been the use of the single muon trigger to
identify semi-leptonic B decays. Figure 7 shows the K, invariant mass in jets
containing a high Pt muon, indicating the observation of B+ decays into a neutral D
meson and a muon. Because of the relatively large semi-leptonic branching ratios of B
mesons, such partially reconstructed decay modes (the neutrino from the SL decay is
not detected) are expected to be abundant at the Tevatron. Even a small luminosity
sample of 2.1 pb-1 (2% of current Run II data) yields a substantial signal of nearly 800
FIGURE 6. Left, the invariant mass of (J/, K0) combinations, and right,
the invariant mass of (J/, ) combinations.
FIGURE 7. The K, invariant mass in jets containing a high Pt muon.
B   D X events. Other decay channels (B   D* X, B   D+ X, B   Ds X)
will follow. This technique provides excellent opportunities for various B meson
measurements, including mixing and CP violation. It also offers a good source of B
mesons for technical studies (e.g. triggering and b-tagging).
Initial studies of b-tagging efficiencies (b) and tagging power (b* D²) where D is
the so-called 'Dilution factor' (difference divided by sum of correctly and wrongly
tagged events) using either a 'muon tag' or a 'jet charge tag' indicate that tagging
powers of about 3% are currently achievable. However, it is expected that larger
tagging powers will be obtained as the understanding of the detector performance
improves. Thus, in the coming year or so, it is anticipated that the first measurement of
Bs mixing will be performed at the Tevatron. Progress will also be made towards the
observation of CP violation in Bd and Bs decays.
SEARCHES FOR NEW PHENOMENA
The current D searches for new phenomena naturally fall into several categories,
although only those with direct cosmological significance will be reported here.
Topics include model-independent searches for e + X final states, SUGRA inspired
SUSY searches for jets plus missing Et (squarks) and tri-leptons (gauginos), GMSB
inspired SUSY searches for di-photons plus missing Et, searches for leptoquarks (1st
and 2nd generation), new gauge boson and large extra dimensions.
SEARCHES FOR SUSY DARK MATTER
SUSY MODELS
SUSY is the best motivated scenario today for physics beyond the Standard Model.
It doesn't contradict the precise Electroweak data, it predicts a light Higgs boson, it
achieves unification of the gauge couplings at the GUT scale and is an essential
element of string theories. It also provides an explanation for the Cold Dark Matter in
the Universe. SUSY must be a broken symmetry otherwise the SUSY mass scale
would be the same as the Standard Model mass scale. A variety of models have been
proposed, differing mainly in the nature of the "messenger interactions". Most
experimental results at the Tevatron have been obtained in the context of either
Supergravity (SUGRA) models or Gauge Mediated SUSY Breaking (GMSB) models.
The physics environment and expected SUSY phenomenology are quite different at
electron-positron and hadron collider machines. In a hadron collider final states
consisting of squark pairs ( q~ q~ ), gluino pairs ( g~ g~ ) or squark-gluino pairs ( q~ g~ ) are
expected to dominate. The squarks and gluinos are expected to be quite heavy, leading
~0 ,
to multi-step cascade decay such as g~  q + q~  q + q + ~ 0  q + q + Z + 
2
where
1
~ and ~ are the next-to-lightest and lightest neutralinos. Consequently many
0
0
2
1
high transverse momentum jets and leptons are produced with large missing transverse
energy.
In SUGRA models SUSY breaking is communicated to the physical sector by
gravitational interactions. Grand Unification Scale (GUT) parameters combined with
the Renormalisation Group Equation lead to a low energy scale phenomenology. In
the highly constrained minimal SUGRA model there are just 5 parameters - the
common scalar mass m0 , the common gaugino mass m 1 , the common trilinear
2
coupling value
A,
0
the ratio of the vacuum expectation values of the two Higgs
doublets tan and the sign of the Higgsino mass parameter . The Lightest
~0 which is an excellent Cold Dark Matter
Supersymmetric Particle (LSP) is 
1
candidate.
R-parity is a discrete multiplicative quantum number that distinguishes Standard
Model particles from their SUSY counterparts. It is equal to
(1)
3B L2S
where B, L
and S are the baryon number, lepton number and spin quantum numbers, and is
therefore +1 for Standard Model particles and -1 for the corresponding SUSY
particles. It is usually assumed to be a conserved quantity but R-parity violation (RPV)
can be introduced via trilinear Yukawa coupling terms in the Superpotential. This
implies that the LSP is unstable and cannot be a Cold Dark Matter candidate.
Experimental signatures may be very different as a result and single sparticle
production is possible. In minimal SUGRA just one RPV coupling is assumed to
dominate. If the coupling is large enough resonant production will occur, otherwise
pair production will dominate.
In GMSB models the "messenger sector" couples to the source of SUSY breaking
and the physical sector of the Minimal Supersymmetric Standard Model (MSSM)
through gauge interactions. The identity of the Next-to-Lightest Supersymmetric
~0
Particle (NLSP) and its lifetime determine the phenomenology. If the NLSP is 
1
then it should decay to a photon and a gravitino whilst if the NLSP is a charged
slepton then it should decay to a charged lepton and a gravitino.
JETS AND MISSING TRANSVERSE ENERGY
A generic signature for squarks and gluinos which, in SUGRA inspired models,
cascade decay to quarks and gluons ( jets) and 2 LSP’s (  missing ET) is jets plus
missing Et. This analysis is a simple 'proof of principle' study based on just 4 pb-1
luminosity. Selected events are required to have at least one jet with Pt > 100 GeV and
topological cuts are applied to the angles between jets and the direction of the missing
Et. Physics backgrounds were simulated (with real missing Et) and the large QCD
instrumental background was determined from an empirical fit to data. The missing Et
distribution of selected events is shown in Figure 8. For Et>100 GeV, 3 events survive
compared to a predicted background of 2.71.8 events. With a larger statistical
sample the analysis will be repeated and meaningful limits on SUSY parameters will
be set.
FIGURE 8. Left, the missing Et distribution of events with large Pt jets and missing Et,
and right, the dielectron invariant mass distribution in the trilepton analysis.
TRILEPTONS
Pair production of gauginos can result in trilepton final states. For example if the
lightest chargino is produced with the 2nd lightest neutralino, a possible resulting final
state could be 3 charged leptons, a neutrino and 2 LSPs. This is a 'golden' channel for
mSUGRA searches with very low standard model backgrounds but requiring
extremely high statistics samples. At present (with 40 pb-1) the sensitivity in this
channel is still about a factor of 7 away from being able to extend the excluded
domain in SUSY parameter space. After the application of a series of selection cuts
on electron momenta and missing Et there were no surviving event candidates and the
expected background was 0.00.2 events. The dielectron invariant mass of the sample
before the application of most of the cuts is shown in Figure 8, illustrating the
dominant contribution of Z decays to the background.
DIPHOTONS
In GMSB if the lightest neutralino is the NLSP it will be pair produced and each
will decay into a photon and a gravitino (the LSP). Thus the final state will consist of a
pair of photons and missing transverse energy. The principal backgrounds are from
multijets, direct photons, W+photon, W+jets and Z ee. Two isolated photons with
Pt>20 GeV are required and further topological cuts are applied. The instrumental
QCD background is determined from the data by inverting the photon quality cuts.
The missing Et distribution of the diphoton event sample is shown in Figure 9 along
with the cross-section limit at 95% confidence level. Using the theoretical prediction
for a particular choice of SUSY parameters ('Snowmass' slope) a limit on the NLSP
neutralino mass can be deduced. With a 50 pb-1 sample the Run I limit is almost
reached.
FIGURE 9. Left, the missing Et distribution of diphoton events,
and right, limits on the LSP neutralino mass derived from the diphoton analysis.
SEARCHES FOR LARGE EXTRA DIMENSIONS
The existence of large extra dimensions have been proposed by various authors as
an alternative solution to SUSY of the gauage hierarchy problem. In these models the
exchange of a Kaluza-Klein graviton is expected to influence the cross-sections for ee,
 and  final states due to the Feynman diagrams illustrated in Figure 10.
FIGURE 10. Feynman diagrams contributing to the dilepton final state at the Tevatron.
G is a Kaluza-Klein graviton.
The differential cross-section for these processes may be expressed in terms of a
parameter  that is proportional to the inverse fourth power of the fundamental Planck
scale (Ms). In addition to the Standard Model term in the differential cross-section,
there is an interference term (between /Z and G exchange) that is proportional to 
and another term due to pure G exchange that is proportional to ². To solve the
hierarchy problem one can have Ms in the TeV range with n>2 where n is the number
of extra dimensions (n=1 is ruled out and n=2 is tightly constrained).
For this analysis two discriminating variables are used: the dilepton or diphoton
mass and the scattering angle in the rest frame. For the ee or  final state, 2
electromagnetic 'objects' are required with Pt>25 GeV and missing Et<25 GeV. The
physics backgrounds are determined by simulation and the QCD instrumental
backgrounds are derived from data. Distributions in the 2-dimensional space of the
dilepton invariant mass and the lepton scattering angle are shown in Figure 11 for the
data, the Standard Model expectation, the QCD background and the simulated extra
dimensions signal. From a 50 pb-1 sample a fit to the  parameter yields Ms > 1.12
TeV (at 95% CL) in the GRW formalism. This is close to the Run I limit from D and
similar to the LEP limit.
The same type of analysis has been performed in the dimuon channel, requiring
2 opposite sign muons with Pt > 15 GeV and a dimuon invariant mass greater than 40
GeV. The Drell-Yan background is determined by simulation and the QCD
instrumental background is derived from data. With a sample of 30 pb-1, a fit to the 
parameter yields Ms > 0.79 TeV (at 95% CL) in the GRW formalism. This is a new
channel at the Tevatron and yields a similar limit to LEP results.
FIGURE 11. The differential distributions in the dilepton invariant mass and lepton scattering angle for
the dielectron/diphoton final state.
SUMMARY AND CONCLUSIONS
D is almost fully operational following major upgrades for Run II of the
Tevatron, although some trigger improvements such as the STT remain to be
implemented. The Run I data sample (100 pb-1) has now been exceeded and physics
results are emerging from the first 30-50 pb-1 of data. The B physics potential of D
has been established. Good lepton, photon, jet and missing Et detection enables D to
perform many new physics searches. Measurements of cosmological significance can
be expected in the coming few years with data samples of > 5 pb-1. Topics to be
addressed will include CP violation in the B meson system (unitarity triangle angles,
beyond the MSM?), dark matter candidates or limits (e.g. neutralino LSP) and large
extra dimensions or limits.