The nature of QCD radiation from heavy quarks is currently a phenomenon that is not well understood. In the case of the heaviest of the six quark flavours, the top quark, it is known that gluon radiation carries away momentum from the quarks although the effect has not been quantified. This may be causing errors in the reconstructed top mass and the aim of this investigation was to use Monte Carlo simulations in order to elucidate the nature of the radiation pattern, which may contribute towards a reduction the top mass uncertainty.
Pressing questions in the field include the nature of an extra hadronic jet observed in several top quark candidate events and the total energy, and therefore mass, which is lost from the top quarks through gluon radiation. There is also an uncertainty in the nature of the quark-gluon radiation vertex, which may be resolved by a direct calculation of the angles at which gluons are radiated from these heavy quarks. This investigation is based upon the CDF detector at Fermilab's Tevatron proton-antiproton collider, where the top quark was discovered in 1995. The measurement made of the top mass is subject to statistical and systematic errors of approximately five per cent, although it is hoped that this will be greatly improved with data from Run II.
The Tevatron synchrotron is currently the world's most powerful particle accelerator. It is situated at the Fermi National Accelerator Laboratory near Chicago, Illinois, and originally began operations in 1983. The Tevatron itself consists of a four-mile long underground ring in which bunches of protons and antiprotons are accelerated to energies of 1 TeV, giving a centre of mass collision energy of 2 TeV
The first stage of the process involves producing protons. This is done in the Cockroft-Walton pre-acelerator, in which hydrogen gas is negatively ionised so that each atom has two electrons. The ions are then accelerated by a linear accelerator to 400 MeV and then passed through a carbon foil which removes the electrons to leave only protons. A circular accelerator bends the beam of protons into a circular path and then boosts the energy to 8 GeV. The next stage is the Main Injector (the bottom ring in the picture), which has several functions. The first is that it accelerates protons to 150 GeV\@. Secondly, it produces 120 GeV protons to be sent to the antiproton source, which collides them with a nickel target and stores resulting antiprotons. When there are enough antiprotons they are sent back to the main injector, which boosts their energy to 150 GeV\@. Finally, the protons and antiprotons are fed into the Tevatron. An antiproton recycler stores the antiprotons that return from the Tevatron so that they can be used again.
The Tevatron (top ring) receives the 150 GeV protons and antiprotons and accelerates them to 1 TeV in opposite directions. The bunches travel at 99.9999% of the speed of light and are kept in line by 1,000 helium-cooled superconducting magnets. The beams are brought together in the CDF and D0 detectors positioned on the Tevatron ring.
The Collider Detector at Fermilab (CDF) Collaboration was the first to measure the mass of the top quark and is officially credited with its discovery in 1995, although data from the D0 experiment was used alongside the CDF data in further calculations. CDF is a general-purpose particle detector and between Run I (1992-1996) and Run II (2001-present) underwent a substantial upgrade.the picture shows the installation of the silicon vertex detector. This is the centremost tracking detector, which determines the trajectories of charged particles via the electron-hole pairs they create as they pass through the solid state silicon ionisation chambers. After the silicon vertex detector is the Central Outer Tracker, a gas drift chamber which operates via the detection of charged ions. A solenoid coil sits between the tracking detectors and calorimiters to bend the tracks of charged particles so that their momentum and energy can be determined.
The calorimeters (electromagnetic and hadronic) are constructed from alternating layers of absorbers and scintillation detectors, which cause particles to shower and enable a calculation of the energy lost at each stage. The inelastic production of secondary particles causes energy to be deposited in each absorbing layer until all or most of the primary particle's energy is lost. In the electromagnetic calorimeters, high energy electrons and positrons lose most of their energy by bremsstrahlung and photons lose energy via the production of electron-positron pairs. The depth of penetration of an electromagnetic shower is related to the radiation length and increases logarithmically with primary energy. This means that the physical size of elecromagnetic calorimeters increases slowly with the energy of the particles it is designed to detect. The penetration of hadronic showers is determined by the nuclear absorption length, which is generally longer than radiation length and so the hadronic calorimeters are thicker than the electromagnetic ones. The calorimeter modules at CDF are divided up into smaller cells, enabling the determination of position as well as energy. The outermost detectors are the muon chambers, which detect highly penetrating muons via scintillation detectors. The presence of quarks, heavy bosons and gluons is detected via the products of their decay chains and neutrinos are inferred from missing energy which is required to comply with the laws of conservation of energy and momentum. The entire CDF detector is 27 metres long, ten metres high and weighs around 500 tons.
The top quark is the heaviest of the set of six quarks predicted by the Standard Model of Particle Physics and is the heaviest known fundamental particle. Formulated in the 1960s, the predictions of the Standard Model have so far proven accurate and in 2001 the final predicted particle, the tau neutrino, was discovered at the Tevatron. The top quark was the final quark to be discovered because due to its mass it requires large collision energies to be produced.
The mass of the top quark was established from data produced during CDF Run I as 175.9 GeV wiht a statistical uncertainty of 4.8 GeV and a systematic uncertainty of 4.9 GeV . The top mass is of particular interest because it is much heavier than the other quarks; the bottom quark, as the next heaviest, has a mass of only 5 GeV. The top mass also lies in the energy range of 150 - 200 GeV, which is currently of interest in particle physics. The hypothesised Higgs boson is predicted to lie within this region and its mass is constrained by the mass of the top quark, along with that of the W boson. The Higgs particle or set of particles is thought to be responsible for the breaking of electroweak symmetry in the early universe and will hopefully explain why the mediators of the weak interaction, the W and Z bosons, are very heavy while the photon, mediator of the electromagnetic force, is massless. It is important to know the top mass as accurately as possible as a difference of 5% in the top mass corresponds to a difference of around 100% in the mass of the Higgs.The top quark is produced at the Tevatron via the annihilation of two incoming valence quarks from the colliding proton and antiproton. In the parton model, a high energy proton is considered to be a composite object made up of quasi-free quarks and gluons. Each of these particles carries a fraction of the proton's momentum. The partons are confined within the proton as the net colour charge of all macroscopically observable particles must be zero. At short distances or very high energies the coupling constant is small and the quarks within the proton can move almost freely as the coupling to surrounding quarks and gluons can be neglected. However, coupling increases with the interquark distance and the result is that the quarks are confined within a particle with a radius of the order of one fermi - the approximate size of a proton. When protons are collided at high energies the valence quarks can be knocked beyond this radius and annihilate to produce new particles. The remaining 'spectator' quarks also hadronise.
Tops and antitops are most commonly produced in pairs from a gluon created by the annihilating valence quarks. It is also possible for the proton and antiproton to each radiate gluons which then annihilate with each other to create a t-tbar pair but this is very rare and so has been neglected in this study. Due to the large mass of the top quark its lifetime is too short to allow it to hadronise so top hadrons are never observed. More than 99% of the time the top quarks decay to W bosons and a b-bbar pair.
Quantum Chromodynamics is the study of the colour interactions between quarks. These interactions are mediated by the strong force and its exchange particle, the massless gluon. The mathematical theory behind QCD was produced in the 1970s and is has become increasingly important as colliders of higher and higher energies have been built. QCD is particularly important to the study of heavy quark and hadronic jet production as gluons carry the colour charge and cause quarks to be bound into hadronic states. All quarks can radiate gluons and it is known that these gluons take with them some of the quark's energy and momentum. In the case of the top quark, this can cause a considerable uncertainty on the mass because the nature of this energy loss is not well understood. Gluon emission occurs because as a quark becomes more isolated from other quarks the coupling, and therefore the potential energy, of the binding colour force increases. At a critical point the potential stored in the colour field manifests itself as spontaneously emitted gluons, which then split into quark-antiquark pairs. These recombine into colourless hadronic states, creating a highly collimated hadronic jet in the direction of the original quark.
In a large proportion of top events an extra isolated hadronic jet has been observed in the detector and it is thought that this may be the result of the hadronisation of high energy gluon emissions from the top and antitop quarks. However gluons also radiate from the initial parton quarks and the bottom quark decay products of the W bosons. Thus in order to calculate the energy loss from the top quarks due to gluon radiation, the gluons of different origins have to be distinguished from each other.
The radiated gluons themselves are not directly observed but are instead detected via their hadronic decay products. Gluons create quark-antiquark pairs which then hadronise into jets containing mostly pions.
The main success of this investigation has been to isolate the region in the lab frame in which jets produced by QCD radiation from top quarks may be the most easily identified. There have been a few surprises in the apparent distribution asymmetries between gluons radiating from t and tbar quarks and in the wider scope of the investigation, quarks and antiquarks generally. The gluons radiating from the top quark pair were found to have a very similar mean transverse momentum (PT) to those radiating from the bottom quarks, although the initial parton quark gluons radiated away on average approximately half this amount of momentum per gluon. There was a disparity in the total momentum radiated from each quark with respect to its antiquark partner, the antiquarks losing less momentum in total compared to the quarks. This effect was most pronounced in the case of the initial parton quarks. The PT of the maximum PT gluons also showed a marked difference between quarks and antiquarks. The top quarks were found to lose on average 14.42 GeV in PT through gluon radiation and the PT of gluons from the antitops totalled on average 13.78 GeV. In a previous study by Orr et al, shoulders on the lower and upper sides of the Breit-Wigner peaks of the reconstructed top mass were found when the the extra hadronic jets often found in top events were included or omitted, respectively. Thus it was found that the mass of the top cannot be unambiguously determined in either case. However, if the jet source can be determined as most likely being the top quarks then the decision can be made to include the jet. The finding of this investigation was that in the pseudorapidity regions of -2.0 to -3.5 and 2.5 to 4.0, gluon jets are more likely to be from top quarks than bottom quarks. Jets arising from the initial parton quarks have a lower mean PT and as such, over large statistics, can be eliminated. The asymmetries between gluon PT for quarks and antiquarks may also be useful in determining whether a jet arose from the t or tbar. A comparison with real CDF data needs to be made in order to establish whether this is possible. Once the findings of this investigation have been compared to experimental data, progress can be made towards the improvement of jet clustering algorithms and the reduction of the uncertainty on the top mass.
This project also included an investigation of the top quark's dead cone, a region around the direction of flight in which gluons cannot be emitted as this would violate the conservation of energy and momentum.
The theoretical calculations of the top quark dead cone did not agree well with the results suggested by the HERWIG simulations. For the t and tbar the angular distribution of gluon radiation suggested a dead cone that is of the order of 10\% of the size of that calculated using kinematics and approximtely only 20\% of that calculated by an approximation based on the centre of mass energy of the system. The initial parton quarks are generally assumed to be almost massless in gluon radiation studies and HERWIG creates an artificial cut off region close to the direction of momentum. However, this cut off region was found to be a much better approximation to the centre of mass QCD calculation in this case, agreeing to within an order of magnitude. The understanding of this process is still somewhat limited and again the results need to be compared to experimental data in order to work out what is really happening.