Complex Relationships: Income Inequality, Trust and Corruption

The goal of this thesis is to investigate the link between income inequality and corruption and poses the following research question: Is there a positive relationship from income inequality to corruption and is this effect dependent on trust? The thesis attempts to contribute to the small but growing literature on this link by using recent data with a global coverage. In addition to the independent variables, income inequality and trust, relevant control variables were added to the model. For the analysis I use the method of Ordinary Least Squares (OLS). The results are surprising in that they reveal that income inequality has both a positive and negative correlation to corruption, depending on the level of trust. These are interesting results and contradict much of the literature. But as there are several issues concerning the quality and availability of the data, I refer from making strong conclusions. Most importantly, my findings reveal that there is a need for additional investigations into this very interesting topic.Masteroppgave i demokratibyggingSAMPOL650VIDSVHGMASV-DEMOKVIDSVMP0

Three-loop soft anomalous dimension of massless multi-leg scattering

Infrared (IR) singularities are a salient feature of any field theory containing massless fields. In Quantum Chromodynamics (QCD), such singularities give rise to logarithmic corrections to physical observables. For many interesting observables, these logarithmic corrections grow large in certain areas of phase space, threatening the stability of perturbative expansion and requiring resummation. It is known, however, that IR singularities are universal and exponentiate, allowing one to study their all-order behaviour in any gauge theory by means of so-called webs: specific linear combinations of Feynman diagrams with modified colour factors corresponding to those of fully connected trees of gluons. Furthermore, infrared singularities factorise from the hard cross-section into soft and jet functions. The soft function may be calculated as a correlator of Wilson lines, vastly simplifying the computation of IR poles and allowing analytic computation at high loop order. Renormalisation group equations then allow the definition of a soft anomalous dimension, which may then be directly computed either through differential equations or by a direct, diagrammatic method. Soft singularities are highly constrained by rescaling symmetry, factorisation, Bose symmetry, and high energy- and collinear limits. In the case of light-like external partons, this leads directly to a set of constraint equations for the soft anomalous dimension, the simplest solution of which is a sum over colour dipoles. At two loops, this so-called dipole formula is the only admissible solution, leading to the complete cancellation of any tripole colour structure. Corrections beyond the dipole formula may first be seen at three loops, and must take the form of weight five polylogarithmic functions of conformal invariant cross-ratios, correlating four hard jets through a quadrupole colour structure. In this thesis we calculate this first correction beyond the dipole formula by considering three-loop multiparton webs in the asymptotic limit of light-like external partons. We do this by computing all relevant webs correlating two, three and four lines at three loop order by means of an asymptotic expansion of Mellin-Barnes integrals near the limit of light-like external partons. We find a remarkably simple result, expressible entirely in terms of Brown's single-valued harmonic polylogarithms, consistent with high-energy and forward scattering limits. Finally, we study the behaviour of this correction in the limit of two partons becoming collinear, and discuss collinear factorisation properties

Long-distance singularities in multi-leg scattering amplitudes

We report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD amplitudes with any number of massless particles to three loops. The result displays some novel features: this is the first time non-dipole corrections appear, which directly correlate the colour and kinematic degrees of freedom of four coloured partons. We find that non-dipole corrections appear at three loops also for three coloured partons, but these are independent of the kinematics. The final result is remarkably simple when expressed in terms of single-valued harmonic polylogarithms, and it satisfies several non-trivial constraints. In particular, it is consistent with the high-energy limit behaviour and it satisfies the expected factorization properties in two-particle collinear limits.Comment: Talk given at Loops and Legs in Quantum Field Theory, 24-29 April 2016, Leipzig, Germany. 15pages, 4 figure

Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders

Scattering amplitudes of partons in QCD contain infrared divergences which can be resummed to all orders in terms of an anomalous dimension. Independently, in the limit of high-energy forward scattering, large logarithms of the energy can be resummed using Balitsky-Fadin-Kuraev-Lipatov theory. We use the latter to analyze the infrared-singular part of amplitudes to all orders in perturbation theory and to next-to-leading-logarithm accuracy in the high-energy limit, resumming the two-Reggeon contribution. Remarkably, we find a closed form for the infrared-singular part, predicting the Regge limit of the soft anomalous dimension to any loop order.Comment: 35 pages, 8 figure

Three-loop corrections to the soft anomalous dimension in multi-leg scattering

We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multi-leg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that non-dipole corrections appear already for three coloured partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally-invariant cross ratios for four coloured partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the non-dipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it only depends on the colour charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally we verify that our result is consistent with expectations from the Regge limit.Comment: v2: remaining diagrams computed; colour conservation accounted for; strict collinear factorization shown to hold. Some references added. 6 pages, 2 figure

Bootstrapping the QCD soft anomalous dimension

SCOAP

Typing myalgic encephalomyelitis by infection at onset: A DecodeME study [version 4; peer review: 2 approved]

Background: People with myalgic encephalomyelitis / chronic fatigue syndrome (ME/CFS) experience core symptoms of post-exertional malaise, unrefreshing sleep, and cognitive impairment. Despite numbering 0.2-0.4% of the population, no laboratory test is available for their diagnosis, no effective therapy exists for their treatment, and no scientific breakthrough regarding pathogenesis has been made. It remains unknown, despite decades of small-scale studies, whether individuals experience different types of ME/CFS separated by onset-type, sex or age. Methods: DecodeME is a large population-based study of ME/CFS that recruited 17,074 participants in the first 3 months following full launch. Detailed questionnaire responses from UK-based participants who all reported being diagnosed with ME/CFS by a health professional provided an unparalleled opportunity to investigate, using logistic regression, whether ME/CFS severity or onset type is significantly associated with sex, age, illness duration, comorbid conditions or symptoms. Results: The well-established sex-bias among ME/CFS patients is evident in the initial DecodeME cohort: 83.5% of participants were females. What was not known previously was that females tend to have more comorbidities than males. Moreover, being female, being older and being over 10 years from ME/CFS onset are significantly associated with greater severity.  Five different ME/CFS onset types were examined in the self-reported data: those with ME/CFS onset (i) after glandular fever (infectious mononucleosis); (ii) after COVID-19 infection; (iii) after other infections; (iv) without an infection at onset; and, (v) where the occurrence of an infection at or preceding onset is not known. Among other findings, ME/CFS onset with unknown infection status was significantly associated with active fibromyalgia. Conclusions: DecodeME participants differ in symptoms, comorbid conditions and/or illness severity when stratified by their sex-at-birth and/or infection around the time of ME/CFS onset

Two-parton scattering in the high-energy limit

Considering $2\to 2$ gauge-theory scattering with general colour in the high-energy limit, we compute the Regge-cut contribution to three loops through next-to-next-to-leading high-energy logarithms (NNLL) in the signature-odd sector. Our formalism is based on using the non-linear Balitsky-JIMWLK rapidity evolution equation to derive an effective Hamiltonian acting on states with a fixed number of Reggeized gluons. A new effect occurring first at NNLL is mixing between states with $k$ and $k+2$ Reggeized gluons due non-diagonal terms in this Hamiltonian. Our results are consistent with a recent determination of the infrared structure of scattering amplitudes at three loops, as well as a computation of $2\to 2$ gluon scattering in ${\cal N}=4$ super Yang-Mills theory. Combining the latter with our Regge-cut calculation we extract the three-loop Regge trajectory in this theory. Our results open the way to predict high-energy logarithms through NNLL at higher-loop orders.Comment: 62 pages, 7 figure

Pion Condensation in the Linear Sigma Model

In this thesis we study the phase diagram of quantum chromodynamics in an effective low-energy theory at zero baryon chemical potential but finite temperature and isospin density. We investigate pion condensation at finite temperature and isospin chemical potential $mu_I$ in two different approximation schemes of the linear sigma model; the Large-$N$ and Hartree approximations at leading order. While being a simple model, the linear sigma model allows for phase transitions of both the first and second order, as well as crossover transitions at the physical point. The large-$N$ approximation yields results typical for mean-field approaches, including a second order phase transition with critical exponent $nu = frac{1}{2}$. At the physical point we find that pion condensation occurs below a threshold temperature $T_c(mu_I)$ only for $mu_I geq m_pi$. Due to the symmetry of the $O(N)$ expansion, the large-$N$ approximation also obeys Goldstone's theorem, yielding a massless Goldstone mode in the pion condensed phase.By contrast, we find a large violation of Goldstone's theorem in the Hartree approximation, with the Goldstone mode achieving a mass of $200 ~hbox{MeV} approx 1.4~ m_pi$. It is possible that the Hartree approximation's violation of symmetry makes the Goldstone mode tachyonic at low temperatures. However, it appears that the Hartree approximation yields a phase structure much more similar to what has been found in lattice studies, with a first order phase transition at high isospin densities and crossover transitions at lower densities. We have only been able to study the Hartree approximation under the condition that either the chiral condensate or the pion condensate is zero, however, and accurate probing of the phase diagram at the physical point is therefore not possible

Complex Relationships: Income Inequality, Trust and Corruption

The goal of this thesis is to investigate the link between income inequality and corruption and poses the following research question: Is there a positive relationship from income inequality to corruption and is this effect dependent on trust? The thesis attempts to contribute to the small but growing literature on this link by using recent data with a global coverage. In addition to the independent variables, income inequality and trust, relevant control variables were added to the model. For the analysis I use the method of Ordinary Least Squares (OLS). The results are surprising in that they reveal that income inequality has both a positive and negative correlation to corruption, depending on the level of trust. These are interesting results and contradict much of the literature. But as there are several issues concerning the quality and availability of the data, I refer from making strong conclusions. Most importantly, my findings reveal that there is a need for additional investigations into this very interesting topic