### Browsing by Subject "Theoretical Physics"

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- ItemOpen AccessThe anomalous magnetic moment of baryons in cavity QCD(1992) Lindebaum, R J; Viollier, Raoul DUsing a generalised form of the Gell-Mann and Low theorem, all the diagrams in cavity QCD to order as that contribute to the magnetic moment are calculated. The calculations are performed for massive quarks so a mass renormalisation scheme has been developed to cope with the new divergences this brings into the self-energy insert diagrams. The results of this work show that no improvement on the simple SU(3) model is made by including these corrections. These calculations point to a smaller value of αs than that which is usually used.
- ItemOpen AccessThe anomalous magnetic moment of the nucleon in cavity QCD(1991) O'Connor, M SPerturbative quantum chromodynamics is developed in a spherical cavity using a symmetric form of the Gell-Mann and Low theorem. This formalism allows one to generate any desired term in the perturbation series, in a manner which is similar to the familiar Feynman rules in free space. All corrections to order eg² in the electromagnetic and strong coupling constants which contribute to the magnetic moment of a baryon are generated using this formalism. The O(eg²) radiative corrections to the magnetic moment of the nucleon are calculated here in an arbitrary covariant gauge. The gauge-dependent parts are found to vanish identically, and the divergences arising from the loop diagrams cancel amongst each other, making renormalization unnecessary. However, it is shown here that one can, if it is necessary, remove the divergences from the cavity diagrams by subtracting from them a singular factor which is found using dimensional regularization in the analogous free-space diagrams.
- ItemOpen AccessBound states of heavy and light quarks in the framework of quantum chromodynamics(1985) Gavin, Elizabeth Jane Ogle; Viollier, Raoul DThe spectra of the D, F, B and E mesons have been calculated using the MIT bag model together with a static potential related to the Fourier transform of the "dressed" gluon propagator. The heavy quark has been assumed to coincide with the centre of the bag, while the Light antiquark was treated relativistically using the Dirac equation. The spectra obtained are compared with experimental data as well as with the results of other models of these Qq mesons. The ratio mb/mc obtained in the fit to experimentally known states is compared with the result expected from the hyperfine splitting of the D and B mesons. It appears that tris ratio is model dependent. More experimental data are required to further evaluate the validity of this model.
- ItemOpen AccessCanonical strangeness conservation in the hadron gas model of relativistic heavy ion collisions(2001) Yacoob, SahalThe CERN WA97 results display a strong strangeness enhancement at mid-rapidity which is dependent on the strangeness of the particle concernec, and saturates at values of participating nucleons greater than 120. These results are phenomenologically described by the mixed canonical ensemble, with canonical (exact) strangeness conservation involving all strange resonances, and grand canonical conservation of charge and baryon number. It is shown that the data are well described by an equilibrium hadron gas. Other explanations of these data are reviewed.
- ItemOpen AccessDirect pion-nucleus interactions in the resonance region(1983) Field, Gaynor Mary; Frahn, W EThe direct reactions of pions with nuclei in the energy region of the πN(3,3) resonance are examined in the eikonal formalism. In particular, the angular and energy dependence of the elastic scattering of πsup(+-) from the calcium isotopes 40Ca, 48Ca is studied, using a detailed phenomenological approach. Excellent agreement is obtained with experimental data. A closely related investigation is also made of the inelastic excitation of low-lying collective states of 40Ca, 48Ca by pions. The resulting one-parameter fits yield deformation lengths which are compared with simple collective model predictions. The total cross-sections for neutral pion scattering from 40Ca, 48Ca in the resonance region are investigated as well, and predictions are made
- ItemOpen AccessFluctuating Open Heavy Flavour Energy Loss in a Strongly Coupled Plasma with Observables from RHIC and the LHC(2021) Ngwenya, Blessed Arthur; Horowitz, WilliamWe present predictions for the suppression (using the nuclear modification factor) of B-mesons using AdS/CFT techniques assuming a strongly coupled quark-gluon plasma (QGP). These energy loss predictions are presented for collision energies √ sNN = 2.76 TeV for central collisions and √ sNN = 5.5 TeV for various centrality classes. There are some uncertainties in terms of how we phenomenologicaly apply energy loss calculations computed in AdS/CFT. One uncertainty is related to how the diffusion coefficient behaves as a function of momentum in AdS/CFT. We make predictions for the two known limits, one where the diffusion coefficient depends on momentum and one where the diffusion coefficient is momentum independent. There also exists systematic theoretical uncertainties associated with the mapping of parameters in N = 4 SYM theory to QCD. We look at two reasonable sets of parameters to try and capture these uncertainties. We will also present results of the v2(pT ) for B-mesons describing the azimuthal anisotropy at √ sNN = 2.76 TeV for central collisions and √ sNN = 5.5 TeV for central, semi-central and peripheral collisions.
- ItemOpen AccessA gauge-invariant, symmetry-preserving truncation of JIMWLK(2018) Moerman, RobertWilliam; Weigert, HeribertThe colour glass condensate captures quantum chromodynamics in its application to high-energy collider experiments in the spirit of an effective field theory. In deeply inelastic lepton-hadron scattering experiments, as well as in hadron-hadron collisions, the internal degrees of freedom of in-state hadrons are dominated by a dense medium of gluonic matter called the colour glass condensate. Interactions with this medium by some (dilute) probe are most naturally described in terms of Wilson-lines and their correlators. The energy-dependence of these correlators is given by the JIMWLK (Jalilian-Marian+Iancu+McLerran+Weigert+Leonidov+Kovner) equa- tion which, when applied to a correlator, generates an infinite tower of coupled Dyson-Schwinger- like equations referred to as a Balitsky Hierarchy. In this thesis, I present a novel method for truncating, in a gauge-invariant and symmetry- preserving manner, the Balitsky hierarchy associated with matrices of Wilson-line correlators. This truncation is realized by parameterizing the energy-dependence of the symmetric and anti- symmetric parts of these matrices independently via energy-evolution operators which evolve ini- tial conditions in a manner akin to the time-evolution of Hermitian operators in the Heisenberg picture of quantum mechanics. These energy-evolution operators are path-ordered exponentials whose exponents are expanded in terms of energy-dependent "colour structure functions". I show how the properties of contributions to the expansion of these exponents (at each order in the expansion) are constrained by the group theory of SU(Nc).
- ItemOpen AccessHadronic gas description of relativistic heavy ion collisions incorporating exact conservation of quantum numbers(1997) Muronga, Azwinndini; Cleymans, JeanThe hadron production (especially kaon production) and the hadronic ratios (especially K/π) in heavy ion collisions are studied assuming that particles are produced in a hadron gas at both thermal and chemical equilibrium. The final state in relativistic ion collision is described by a hadronic gas model which is governed by two freeze out parameters, namely, temperature T and baryon density B/V. It is found that for large interaction volumes and/or large net baryon number, a description using the grand canonical ensemble could be justified. For a small system however, corrections arising solely from exact strangeness and baryon number conservation cannot be neglected. Analytic results for the partition function and the particle numbers are presented. A detailed numerical evaluation is made. A comparison of the behaviour of the results with the experimental information is made. A review of kaon production and K/π ratio and the comparisons of the hadron gas model with recent experimental results is made.
- ItemOpen AccessHeavy neutrino matter at finite temperature(1998) Joubert, Charles ErasmusWe study, for a system of massive fermions which interact only gravitationally, the phase transition that is associated with gravitational collapse. It is shown that by cooling a non-degenerate gas of massive neutrinos below some critical temperature, a condensed phase emerges, consisting of quasi-degenerate super-massive neutrino stars. These compact dark objects could play an important role in structure formation in this universe, as they might in fact provide the seeds for galactic nuclei and quasi-stellar objects.
- ItemOpen AccessIntroduction to lattice gauge theories(1988) La Cock, Pierre; Cleymans, JeanThe thesis is organized as follows. Part I is a general introduction to LGT. The theory is discussed from first principles, so that for the interested reader no previous knowledge is required, although it is assumed that he/she will be familiar with the rudiments of relativistic quantum mechanics. Part II is a review of QCD on the lattice at finite temperature and density. Monte Carlo results and analytical methods are discussed. An attempt has been made to include most relevant data up to the end of 1987, and to update some earlier reviews existing on the subject. To facilitate an understanding of the techniques used in LGT, provision has been made in the form of a separate Chapter on Group Theory and Integration, as well as four Appendices, one of which deals with Grassmann variables and integration.
- ItemOpen AccessIntroduction to supersymmetry(1987) Schreiber, Gunhild Ursula; Viollier, Raoul DThe tendency in theoretical physics, particularly in the past few decades, has been towards unification: over the years it has emerged that increasingly many physical phenomena can be explained by a common underlying theory. Symmetry principles, both global and local, play an important role in this unification programme. Global symmetries often account for approximate regularities we observe in nature - local or gauge symmetries are understood as basic symmetries which lie at the heart of the interactions of the constituents of matter.
- ItemOpen AccessMassive quark self-energy in cavity QCD(1991) Cuthbert, J A; Viollier, Raoul DThe greatest obstacle in calculating the self-energy Feynman diagram is that it is, in principle, linearly divergent. So far the self-energy of a massive quark in cavity quantum chromodynamics has only been calculated for the lowest cavity mode ls1/2. The methods used so far, have been based on the multiple reflection formalism, in which the zero reflection term is extracted out analytically and evaluated separately using Pauli-Villars regularization. This thesis is based on the dimensional regularization scheme, adapted for use in the cavity, by Stoddart et al., who calculated the self-energy for a massless quark. This involves analytically isolating the divergences using dimensional regularization and then removing the divergences using the minimal subtraction (ms) scheme or some similar subtraction scheme. In this thesis, the self-energies of massive quarks have been calculated using the ms scheme for a number of low-lying cavity modes. The ls1/2 results have also been compared with the Pauli-Villars regularization scheme used by Goldhaber, Jaffe and Hansson.
- ItemOpen AccessNLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem(2017) Ibrahim, Abdullah Khalil Hassan; Horowitz, William AWe calculate to next-to-leading order accuracy the high-energy elastic scattering cross section for an electron off of a classical point source. We use the MS renormalization scheme to tame the ultraviolet divergences while the infrared singularities are dealt with using the well known Kinoshita-Lee-Nauenberg theorem. We show for the first time how to correctly apply the Kinoshita-Lee-Nauenberg theorem diagrammatically in a next-to-leading order scattering process. We improve on previous works by including all initial and final state soft radiative processes, including absorption and an infinite sum of partially disconnected amplitudes. Crucially, we exploit the Monotone Convergence Theorem to prove that our delicate rearrangement of this formally divergent series is uniquely correct. This rearrangement yields a factorization of the infinite contribution from the initial state soft photons that then cancels in the physically observable cross section. Since we use the MS renormalization scheme, our result is valid up to arbitrarily large momentum transfers between the source and the scattered electron as long as α log(1/δ) << 1 and α log(1/δ) log(Δ/E) << 1, where Δ and δ are the experimental energy and angular resolutions, respectively, and E is the energy of the scattered electron. Our work aims at computing the NLO corrections to the energy loss of a high energetic parton propagating in a quark-gluon plasma.
- ItemOpen AccessPion electromagnetic form factor in the Kroll-Lee-Zumino model at zero and finite temperature(2008) Willers, Bernard; Dominguez, Cesareo A; Viollier, Raoul DThe renormalizable Abelian quantum field theory model of Kroll, Lee and Zumino is used to calculate next-to-leading order corrections to the pion electromagnetic form factor in vector meson dominance. At zero temperature the predictions for both the form factor and electromagnetic radius are found to improve greatly over the tree level result, and are in good agreement with the experimental data. A calculation of the vertex and self energy functions in the Matsubara formalism at finite temperature do not agree with the results of the Gale & Kapusta calculations. The resulting prediction for the radius is found to increase with temperature, consistent vith ideas about haclronic deconfinernent.
- ItemOpen AccessA quantum field theory for the interaction of pions and rhos(2017) Moodley, Preshin; Dominguez, Cesareo A; Schilcher, Karl; Tupper, Gary; Spiesberger, HubertWe extend the Kroll-Lee-Zumino model in its particle content to include the charged rho vector mesons and the neutral pion meson. This entailed using the larger SU(2) gauge group. The masses for the vector mesons were generated via spontaneous symmetry breaking using the Higgs mechanism. The Lagrangian was then quantized and gauge fixed using the generalized class of Rɛ gauges. Tree scattering lengths were calculated for pion-pion scattering and the values for the a₀⁰ and a₀² scattering lengths are found to be comparable with experiment. The one particle irreducible diagrams that contribute to the one loop corrections to the tree scattering lengths are renormalized.
- ItemOpen AccessThe quark-hadron transition and hot hadronic matter in the early universe(1987) Von Oertzen, Detlof Wilhelm; Rafelski, Johann; Cleymans, JeanVarious calculations· of the evolution of the hadron gas in the early universe are carried out. To determine the starting point for the evolution equations a phase transition between the quark-gluon plasma phase and the hadron gas phase is constructed. A simple calculation leads to an estimate of the chemical potential of baryons at the quark-hadron phase transition in the early universe. We investigate how the transition temperature depends on the equations of state for the bagged quark and the hadron phase. A particle density evolution model is introduced which predicts the temperature at which particle species drop out of equilibrium (freeze-out) in an expanding universe. We then construct dynamical evolution equations to describe the reactions of interacting pions and photons. In order to model a more realistic hadron gas, we include kaons and finally nucleons and hyperons into the model universe. The results indicate that this type of model should be extended to include more interacting particle species and that a more realistic evolution model is dependent on obtaining accurate reaction cross-sections.
- ItemOpen AccessThe ratio gA/gV in cavity QCD(1991) Page, Philip R; Viollier, Raoul DBRS invariant quantum chromodynamics in a spherical cavity is developed using canonical quantization. The weak vector and axial form factors are defined, employing a classical external W- field. The Gell-Mann and Low theorem is extended to include non-diagonal matrix elements and degenerate perturbation theory. The Sucher form of the Gell-Mann and Low theorem is employed to calculate corrections of order GFg² in the weak and strong coupling constants to gA and gv for neutron beta decay. Up and down quarks are assumed massless. The gauge-independent divergences from the loop diagrams cancel each other and can be regularized dimensionally, making renormalization unnecessary. We find that the weak vector and axial current coupling constants are respectively: 9v = 1.0000 gA = 1.0883 + 0.2425 αs', where the preferred value of αs = 2.2 in the M.I.T. bag model gives gA = 1.62.
- ItemOpen AccessReps for JIMWLK: applications of representation theory to a novel approach to the JIMWLK equation(2018) Rayner, Jonathan; Weigert, HeribertIn recent work, R. Moerman and H. Weigert have introduced a truncation scheme for the Balitsky hierarchy, arguing that this is the most general possible method for obtaining finite Nc approximate solutions to the JIMWLK equation, while ensuring that these solutions obey several key properties that are known to be true of any exact solution to JIMWLK [1]. To carry out this truncation, it becomes necessary to systematically construct an orthogonal basis for the space of color singlets with purely adjoint indices. The primary contribution of this dissertation is to construct a basis that makes significant strides towards this goal, using irreducible representations of the permutation group Sk and recently-developed Hermitian Young projection operators [2–4]. Our method directly produces the basis for these singlets, avoiding the need to construct a basis for all multiplets and project out the singlets, as is common in other approaches. In our basis, orthogonality holds both between elements associated with non-isomorphic and isomorphic representations, with the exception of representations that are identical (and not just isomorphic). In working through the robust mathematical framework that describes this construction, we show that failures of orthogonality are a direct result of these basis elements being associated with identical induced representations arising from derangements with differing cycle structure, which suggests a possible strategy for constructing a fully-orthogonal basis in future research. We also prove that this basis always consists of elements that are real or purely imaginary and show how to determine these properties at the level of representations using characters and Frobenius reciprocity. We then shift gears to prove a small number of analytic properties of the images of commonly-used Wilson line operators. Explicitly, we provide a proof that hasn’t existed in the literature previously that the image of the dipole operator in the complex plane is the hypocycloid with Nc-cusps and we prove that all Wilson line operators that appear in the amplitude matrix used in the JIMWLK evolution of two quark-antiquark pairs are bounded by the unit circle.
- ItemOpen AccessA review and application of the Hadron gas model to heavy ion collisions(1996) Elliott, Duncan MarkA review and application of the Hadron Gas model to data gathered from heavy ion collision experiments in search of the Quark Gluon Plasma. The Hadron Gas model is extended by ensuring overall charge conservation of the collision system at freeze-out. Conclusions of thermal and chemical equilibrium at freeze-out are drawn from an analysis of the data of Si-Au collisions at BNL-AGS, and compared with the literature on thermal analyses of Si-Au collisions.
- ItemOpen AccessRho-Meson propagator at two-loop order in the Kroll-Lee-Zumino quantum field theory(2017) Lushozi, Mawande; Dominguez, Cesareo A; Schilcher, KarlThe Kroll-Lee-Zumino theory, an Abelian renormalizable quantum field theory of charged pions and a neutral ρ meson, provides a framework to compute corrections to the tree-level Vector-Meson-Dominance model. Despite a large ρππ coupling (gρππ ≈ 5), the loop suppresion factor of 1=(4π)² helps give reasonably small NLO (one-loop) corrections. When it comes to describing hadronic physics, one might say, these one-loop results achieve moderate to excellent success. Where the one-loop results show less than impressive agreement with experiment, it seems plausible that the NNLO (two-loop) corrections would remedy the situation. In this thesis the two-loop contribution to the ρ⁰ meson is calculated. It turns out to be larger than the one-loop result and so one must conclude that perturbation theory breaks down at this level.