In this dissertation, four different topics are investigated in high energy physics beyond the standard model. In the first chapter, diffeomorphism invariance breaking in gravity is studied in the concept of emergent symmetry, which has not been studied before in this concept. In the second chapter, this investigation is extended by studying the cosmological evolution of the scale factor in our diffeomorphism violating model. In the third chapter, a higher derivative model of four-form fields is considered. The model presents a counter-example for several accepted no-goes in the literature. Finally, in the last chapter, another commonly accepted conjecture is questioned, which assumes that the tree unitarity violation in an effective field theory determines the domain of validity of the theory and predicts the onset of new physics. It is argued that this is parametrically incorrect in the case of chiral perturbation theory and is probably theoretically incorrect in general.

Donoghue's effective field theory of quantum gravity is extended to include the interaction of massless particles. The collinear divergences which accompany massless particles are examined first in the context of QED and then in quantum gravity. A result of Weinberg is extended to show how these divergences vanish in the case of gravity. The scattering cross section for hypothetical massless scalar particles is computed first, because it is simpler, and the results are then extended to photons. Some terms in the cross section are shown to correspond to the Aichelburg-Sexl metric surrounding a massless particle and to quantum corrections to that metric. The scattering cross section is also applied to calculate quantum corrections to the bending of starlight, and though small, the result obtained is qualitatively different than in the classical case. Since effective field theory includes the low-energy degrees of freedom which generate collinear divergences, the results presented here will remain relevant in any future quantum theory of gravity.

Includes bibliographical references. / Obtained via the maximisation of a modified entropy, the Tsallis distribution has been used to fit the transverse momentum distributions of identified particles from several high energy experiments. We propose a form of the distribution described in Cleymans and Worku, 2012, and show it to be thermodynamically consistent. Transverse momenta distributions and fits from ALICE, ATLAS, and CMS using both Tsallis and Boltzmann distributions are presented.

Recent surprising discoveries of collective behaviour of low-pT particles in pA collisions at LHC hint at the creation of a hot, uid-like QGP medium. The seemingly conflicting measurements of non-zero particle correlations and RpA that appears to be consistent with unity demand a more careful analysis of the mechanisms at work in such ostensibly minuscule systems. We study the way in which energy is dissipated in the QGP created in pA collisions by calculating, in pQCD, the short separation distance corrections to the well-known DGLV energy loss formulae that have produced excellent predictions for AA collisions. We find that, shockingly, due to the large formation time (compared to the 1/μ Debye screening length) assumption that was used in the original DGLV calculation, a highly non-trivial cancellation of correction terms results in a null short path length correction to the DGLV energy loss formula. We investigate the e ect of relaxing the large formation time assumption in the final stages of the calculation - doing so throughout the calculation adds immense calculational complexity - and find, since the separation distance between production and scattering centre is integrated over from 0 to ∞, ≿ 100% corrections, even in the large path length approximation employed by DGLV.

We 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.

We 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.

Includes bibliographical references (leaves: 73-77) / The 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.

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.

Includes abstract. / Includes bibliographical references (p. 47-48). / The 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.

Includes bibliographical references. / The 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.