This thesis contains phenomenological studies of top quark production in the forward region of phase space at the Large Hadron Collider (LHC). The production of highly forward top quarks has so far not been observed in nature. As the LHCb detector at the LHC is instrumented in the forward region, this opens the possibility of studying top quark properties in this yet unexplored region of phase space. This feasibility of performing cross section and charge asymmetry measurements of top quark pairs with available and future LHCb data is studied in detail. In both cases, potential analysis strategies are proposed, and sophisticated theoretical predictions are provided for both signal and background. By studying the expected experimental sensitivity of cross section measurements, the potential constraints on parton distribution functions is quantified. The sensitivity of the proposed charge asymmetry measurements with the full Run II LHCb data is also considered.

<p> The fractional quantum Hall effect (FQHE) in the half-filled second Landau level (filling factor &nu; = 5/2) offers new insights into the physics of exotic emergent quasi-particles. The FQHE is due to the collective interactions of electrons confined to two-dimensions, cooled to sub-Kelvin temperatures, and subjected to a strong perpendicular magnetic field. Under these conditions a quantum liquid forms displaying quantized plateaus in the Hall resistance and chiral edge flow. The leading candidate description for the FQHE at 5/2 is provided by the Moore-Read Pfaffian state which supports non-Abelian anyonic low-energy excitations with potential applications in fault-tolerant quantum computation schemes. The Moore-Read Pfaffian is the exact zero-energy ground state of a particular three-body Hamiltonian and explicitly breaks particle-hole symmetry. In this thesis we investigate the role of two and three body interaction terms in the Hamiltonian and the role of particle hole symmetry (PHS) breaking at &nu; = 5/2. We start with a PHS two body Hamiltonian (<i>H</i>₂) that produces an exact ground state that is nearly identical with the Moore-Read Pfaffian and construct a Hamiltonian H(&alpha;) = (1 &ndash; &alpha;)<i>H</i>₃ + &alpha; <i>H</i>₂ that tunes continuously between <i>H</i>₃ and <i> H</i>₂. We find that the ground states, and low-energy excitations, of <i>H</i>₂ and <i>H</i>₃ are in one-to-one correspondence and remain adiabatically connected indicating they are part of the same universality class and describe the same physics in the thermodynamic limit. In addition, evidently three body PHS breaking interactions are not a crucial ingredient to realize the FQHE at 5/2 and the non-Abelian quasiparticle excitations.</p><p>

<p> In this dissertation we study properties of superconformal field theories (SCFTs) that arise from a variety of constructions. We begin with an extended review of various techniques in supersymmetry that are relevant throughout the work. In Chapter 3, we discuss aspects of theories with superpotentials given by Arnold's <i>A,D,E</i> singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional <i> N</i> = 1 variants of supersymmetric QCD, with <i>U</i>(<i> N_c</i>) or <i>SU</i>(<i>N_c</i>) gauge group, <i>N_f</i> fundamental flavors, and adjoint matter fields <i>X</i> and <i>Y</i> appearing in <i> W_A,D,E</i>(<i>X,Y</i>) superpotentials. We explore these issues by considering various deformations of the <i>W_A,D,E</i> superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional <i> N</i> = 1 supersymmetric <i>SU</i>(2) gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the <i>N</i> = 2 Argyres-Douglas theory <i> H</i>₀, and a further deformation to an <i>N</i> = 1 SCFT with low <i>a</i> central charge. Then for the latter half of the dissertation we turn our attention to 4d SCFTs that arise from compactifications of M5-branes. In Chapter 6, we field-theoretically construct 4d <i>N </i> = 1 quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus <i>g</i> and <i>n</i> punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees <i>p</i> and <i>q</i>. In Chapter 7, we study the 't Hooft anomalies of the SCFTs that arise from these compactifications. In general there are two independent contributions to the anomalies: there is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface, and there is a set of contributions due to local data at the punctures. Using anomaly inflow in M-theory, we describe how this general structure arises for cases when the four-dimensional theories preserve <i>N</i> = 2 supersymmetry, and derive terms that account for the local data at the punctures.</p><p>

This dissertation concentrates on the existence, stability and dynamical properties of nonlinear waves in Bose-Einstein condensates (BECs) trapped in doublewell potentials (DWPs). The fundamental model of interest will be the nonlinear Schrödinger equation, the so-called Gross-Pitaevskii (GP) equation, contributed to the well-established mean-field description of BECs. In this context of the GP equation with DWP, a Galerkin-type few-mode approach provides us a powerful handle towards studying the stationary states and predicting the bifurcation diagram including the occurrence of spontaneous symmetry breaking (SSB). Such method and the corresponding phenomena are discussed based on a prototypical quasi-1D model in Chapter 2. The systematic analysis progresses by considering various modified models, starting with the ones involving different interatomic interactions, e.g., collisionally inhomogeneous interactions, long-range interactions, and competing of short- and long-range interactions. We observe how the basic SSB bifurcation structure persists or is appropriately modified in the presence of these interactions in Chapter 3. We also extend the study to multi-component systems, including nonlinearly coupled two-component settings and F = 1 spinor BECs (genuinely three-component settings) confined in DWPs, where besides the one-component stationary states, combined states involving two or three components appear as well, and novel SSB phenomena emerge within them. Finally the trapped stationary modes of a twodimensional (2D) GP equation with a symmetric four-well potential are explored, providing the picture of SSB in the fundamental 2D setting. These various systems are studied in Chapter 4 - 6. In all models, our analytical predictions based on the few-mode approximation are in excellent agreement with the numerical results of the full GP equations.

This thesis considers coarse-grained models of DNA and RNA, developed in particular to study nanotechnological applications as well as some important biophysical processes. We first introduce sequence-dependent thermodynamics into a previously developed coarse-grained rigid base-pair model of DNA. This model is then used to study sequence-dependent effects in multiple DNA systems including: the heterogeneous stacking transition of single strands, the fraying of a duplex, the effects of stacking strength in the loop on the melting temperature of hairpins, the force-extension curve of single strands, and the structure of a kissing-loop complex. We further apply the DNA model to study in detail the properties of an autonomous unidirectionally propagating DNA nanotechnological device, called the ``burnt bridges motor''. We then apply the coarse-graining methods developed for the DNA model to construct a new sequence-dependent coarse-grained model of RNA, which aims to capture basic thermodynamic, structural and mechanical properties of RNA molecules. We test the model by studying its thermodynamics for a variety of secondary structure motifs and also consider the force-extension properties of an RNA duplex. This RNA model allows for efficient simulations of a variety of RNA systems up to hundreds or even thousands of base-pairs. Its versatility is further demonstrated by studying the thermodynamics of a pseudoknot folding, the formation of a kissing loop complex, the structure of a hexagonal RNA nanoring, and the unzipping of a hairpin.

The identification of the relic particles which presumably constitute cold dark matter is a key challenge for astroparticle physics. Indirect methods for their detection using high energy astro- physical probes such as cosmic rays have been much discussed. In particular, recent ‘excesses’ in cosmic ray electron and positron fluxes, as well as in microwave sky maps, have been claimed to be due to the annihilation or decay of dark matter. In this thesis, we argue however that these signals are plagued by irreducible astrophysical backgrounds and show how plausible con- ventional physics can mimic the alleged dark matter signals. In chapter 1, we review evidence of, and possible particle candidates for, cold dark matter, as well as our current understanding of galactic cosmic rays and the state-of-the-art in indirect detection. All other chapters contain original work, mainly based on the author’s journal publications. In particular, in chapter 2, we consider the possibility that the rise in the positron fraction observed by the PAMELA satellite is due to the production through (hadronic) cosmic ray spallation and subsequent acceleration of positrons, in the same sources as the primary cosmic rays. We present a new (unpublished) analytical estimate of the range of possible fluctuations in the high energy electron flux due to the discreteness of plausible cosmic ray sources such as supernova remnants. Fitting our result for the total electron-positron flux measured by the Fermi satellite allows us to fix the only free parameter of the model and make an independent prediction for the positron fraction. Our explanation relies on a large number of supernova remnants nearby which are accelerating hadronic cosmic rays. Turning the argument around, we find encouraging prospects for the observation of neutrinos from such sources in km^3-scale detectors such as IceCube. Chapter 3 presents a test of this model by considering similar effects expected for nuclear secondary-to-primary ratios such as B/C. A rise predicted above O(100)GeV/n would be an unique confirmation of our explanation for a rising positron fraction and rule out the dark matter explanation. In chapter 4, we review the assumptions made in the extraction of the `WMAP haze' which has also been claimed to be due to electrons and positrons from dark matter annihilation in the Galactic centre region. We argue that the energy-dependence of their diffusion means that the extraction of the haze through fitting to templates of low frequency diffuse galactic radio emission is unreliable. The systematic effects introduced by this can, under specific circumstances, reproduce the residual, suggesting that the ‘haze’ may be just an artefact of the template subtraction. We present a summary and thoughts about further work in the epilogue.

In this work we investigate themes related to many-body systems in which multiple ground states are accessible, a condition known as frustration. Frustration can arise in a number of contexts, and we consider the consequences of this situation with some examples from condensed-matter physics. In some magnetic materials interactions between spins are such that no single spin configuration provides a unique ground state. In the class of frustrated magnets where the number of ground states is extensive, thermal fluctuations are strong even at temperatures significantly below the interaction strength. At such temperatures spins are highly correlated, and small perturbations may have profound consequences. In this thesis we provide an example of this. By considering classical n-component spins with nearest-neigbour exchange on a frustrated octahedral lattice we show that – in the limit where exchange interactions are large – the system is in a disordered, correlated phase where correlations have the form of a dipole field. This is termed a Coulomb phase. From this phase we induce an ordering transition, lifting the degeneracy with weak, additional short-range interactions. By studying the transition in the solvable limit of n → ∞, we discover that the transition has identical thermodynamics to that of a magnetic system interacting through long-range, dipolar forces. Finally, we provide a more apposite characterisation of the transition, where the high-temperature side of the transition is described through the fluctuations of solenoidal fields, and the ordering corresponds to a condensation of these fields. In a separate part of the thesis, we investigate the influence of disorder on frustrated lattices. We study a two-dimensional tight-binding model with nearest-neighbour hopping and on-site disorder. Restricting the allowed states to being those from the low-lying manifold of ground states, the disorder feeds through to act as effective disorder in the hopping terms, which decay algebraically with distance. The quasi-long range nature of this effective hopping leads to a situation in which the resultant single-particle eigenstates are critical, and we probe their behaviour numerically with a transfer matrix calculation.

The 7σ discrepancy between the charge radius of the proton as extracted from electronic hydrogen to the determination from muonic hydrogen, coined the proton ``radius puzzle", challenges our understanding of physics based on the standard model. High-precision measurements have been conducted on muonic deuterium to study whether the discrepancy with ordinary atoms persists or varies with mass number. For the success of this experimental campaign accurate theoretical calculations of the nuclear structure corrections in muonic deuterium (μD) are required. In this work we contributed by accurately and precisely calculating them using state-of-the-art nuclear potentials derived from chiral effective field theory. We performed a multipole expansion of the electromagnetic operator and accounted for Coulomb, relativistic and finite-nucleon-size corrections. Our determinations will impact the accuracy of the experimental program. / October 2015

Theoretical predictions for generic multi-scale observables in Quantum Chromodynamics (QCD) typically suffer from large Sudakov logarithms associated with the emission of soft or collinear radiation, whose presence spoils the perturbative expansion in the coupling strength which underlies most calculations in QCD. A canonical way to improve predictions wherever these logarithms appear is to resum them to all perturbative orders, which can conveniently be achieved using Effective Field Theory (EFT) methods. In an age of increasing automation using computers, this task is still mostly performed manually, observable-by-observable. In this thesis we identify the 2-loop soft function as a crucial ingredient for the resummation of QCD Sudakov logarithms to Next-to-next-to-leading logarithmic (NNLL) accuracy in Soft-Collinear Effective Theory (SCET), for wide classes of observables involving two massless colour-charged energetic particles, such as dijet event shapes at lepton colliders, or colour singlet production at hadron colliders. We develop a method to evaluate these soft functions using numerical methods based on sector decomposition and the choice of a convenient parametrisation for the phase space. This allows the factorisation of all implicit (real emission) and explicit (virtual correction) divergences made manifest by dimensional and analytic regularisation. The regulator pole coefficients can then be evaluated numerically following a subtraction and expansion, and two computational tools are presented to perform these numerical integrations, one based on publicly available tools, the other based on our own code. Some technical improvements over naive straightforward numerical evaluation are demonstrated and implemented. This allows us to compute and verify two of three colour structures of the 2-loop bare soft functions for wide ranges of observables with a factorisation theorem. A number of example results - both new and already known - are shown to demonstrate the reach of this approach, and a few possible extensions are sketched. This thesis therefore represents a crucial step towards automation of resummation for generic observables to NNLL accuracy in SCET.

String theory is currently the best-known candidate for a theory of quantum gravity, having the necessary ingredients to describe all known elementary particles and interactions. It also includes several novel features, arising, for instance, from the additional six compact dimensions required for its internal consistency, making it the natural arena to construct extensions of the Standard Model. In this thesis, we analyze some of the new phenomenological aspects introduced by string theory within the framework of low energy effective theories, focusing on their applications to cosmology, astrophysics and collider experiments. We first consider a particular realization of the brane-world scenario in branonium bound states, showing that the orbital motion of a probe antibrane about a central brane stack leads to a resonant amplification of its world-volume scalar modes. We analyze the cosmological development of this process and also its potential relevance for either dark or baryonic matter generation in the early universe. We then focus on the spectrum of quark and lepton string excitations in warped compactifications, modeled by an effective 5-dimensional Randall- Sundrum throat. Motivated by the observed fermion mass hierarchy, we show that the spin-3/2 Regge excitation of the right-handed top quark is the lightest of such resonances in a significant region of parameter space, possibly lying below the TeV scale, and discuss its potential signatures at the Tevatron and at the LHC. Finally, we study the emission of sub-eV scalar particles by maximally rotating Kerr black holes, motivated by the recent string axiverse proposal. We focus on the spectrum of unstable scalar bound states in the superradiant regime, leading to an exponentially large axion cloud around astrophysical black holes, and analyze two semi-analytical methods for computing the growth rate of this instability, comparing the obtained results with previous analytical and numerical analyses.