Browsing by Author "Weigert, Heribert"

Now showing 1 - 6 of 6
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    Equilibration of a scalar field theory: a comparison of methods
    (2014) Myers, Jason; Weigert, Heribert
    The Large Hadron Collider is a huge particle collider that, among other things, collides heavy ions together at massive energies. In such heavy ion collisions a new state of matter called the Quark Gluon Plasma (QGP) is formed where, in this state, quarks are no longer confined to hadrons but are free to move about. Studying this state is expected to lead to a far greater understanding of QCD as this is the only known state where one can find free quarks and gluons, the degrees of freedom of QCD. The QGP is known to be a very hot, very dense medium that is rapidly expanding, so one needs techniques that allow for the study of a Quantum Field Theory in an extreme and very dynamical environment.
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    Exclusive J/Ψ Vector-Meson production in high-energy nuclear collisions: a cross-section determinaton in the Colour Glass Condensate effective field theory and a feasibility study using the STARlight Monte Carlo event generator
    (2014) Ramnath, Andrecia; Weigert, Heribert; Hamilton, Andrew
    The cross-section calculation for exclusive J /Ψ vector-meson production in ultra-peripheral heavy ion collisions is approached in two ways. First, the setup for a theoretical calculation is done in the context of the Colour Glass Condensate effective field theory. Rapidity-averaged n-point correlators are used to describe the strong interaction part of this process. The JIMWLK equation can be used to predict the energy evolution of a correlator. In order to facilitate practical calculations, an approximation scheme must be employed. The Gaussian Truncation is one such method, which approximates correlators in terms of new 2-point functions. This work takes the first step beyond this truncation scheme by considering higher-order n-point functions in the approximation. An expression for the cross-section is written, which takes parametrised 2- and 4-point correlators as input. This expression can be used as the basis for a full cross-section calculation. The second part of the thesis is a feasibility study using Monte Carlo simulations done by the STARlight event generator. A prediction is made for how many exclusive J /Ψ vector-mesons are expected to be detected by ATLAS in a data set corresponding to 160 μb−1 total integrated luminosity. It is found that the muon reconstruction efficiencies for low pT muons is too poor in ATLAS to do this analysis effectively. On the order of 150 candidate events are expected from all the Pb-Pb collision data collected in 2011. The feasibility study acts as a preliminary investigation for a full cross-section measurement using ATLAS collision data. Once this is completed, it can be compared with the theoretical prediction for the cross-section.
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    A gauge-invariant, symmetry-preserving truncation of JIMWLK
    (2018) Moerman, RobertWilliam; Weigert, Heribert
    The 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).
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    Hadronic matter: from vacuum to extreme temperature in the presence of magnetic fields
    (2016) Hernandez, Luis Alberto; Dominguez, Cesareo A; Weigert, Heribert; Schilcher, Karl
    This work consists of two themes. First, we work with Finite Energy QCD Sum Rules (FESR) approach in the vacuum. We tackle the problem of quark-hadron duality violation (DV), using the vector and axial-vector hadronic spectral function from tau-decay. A pinched integration kernel is introduce in the FESR in order to quench potential duality violations on the real axis in the complex squared energy plane and effectively extend the analysis well beyond the kinematical Ƭ-decay end-point. As the sum rules are well satisfied, we conclude that possible DV must be buried under the experimental uncertainties. Also, using the latest updated ALEPH data on hadron decays, we use FESR to determine the vacuum condensates of dimension d = 2 and d = 4, to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension d = 6 and d = 8, and values of the chiral perturbation theory L10 and C87.
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    Rapidity evolution of observables at high energies using the Gaussian truncation
    (2018) Adamiak, Daniel; Weigert, Heribert
    Today, the biggest predictive uncertainties in the Standard Model arise from theoretical uncertainties in quantum-chromo-dynamics contributions to cross-sections measured at high-energy collider experiments. At high energies, the quantum-chromo-dynamics of particle collisions is well described through the use of the colour-glass condensate. In this domain, the interaction of coloured objects with the CGC medium is well explained through the use of path-ordered colour rotations, called Wilson Lines, as well as their correlators. The rapidity evolution of these correlators is given by the JIMWLK equation. However, this leads to an infinite hierarchy of coupled differential equations, which are impossible to solve in a closed form and truncations become necessary. The most common truncation relies on the large Nc limit, which is relatively crude and subtly breaks gauge invariance. To get around this, we can perform a gauge invariant truncation of this hierarchy in the form of the Gaussian truncation for the correlators of these Wilson lines. Initial comparison to HERA data for the total and rapidity gap cross-sections show a noticeable improvement in comparison to data which only depend on the dipole correlator. We extend this method to incorporate observables that depend on more complicated correlators and present the machinery for how to compute their rapidity dependence with the Gaussian truncation.
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    Reps for JIMWLK: applications of representation theory to a novel approach to the JIMWLK equation
    (2018) Rayner, Jonathan; Weigert, Heribert
    In 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.