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

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

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

DecodeME: Community recruitment for a large genetics study of myalgic encephalomyelitis / chronic fatigue syndrome

BACKGROUND: Myalgic encephalomyelitis / chronic fatigue syndrome (ME/CFS) is a common, long-term condition characterised by post-exertional malaise, often with fatigue that is not significantly relieved by rest. ME/CFS has no confirmed diagnostic test or effective treatment and we lack knowledge of its causes. Identification of genes and cellular processes whose disruption adds to ME/CFS risk is a necessary first step towards development of effective therapy. METHODS: Here we describe DecodeME, an ongoing study co-produced by people with lived experience of ME/CFS and scientists. Together we designed the study and obtained funding and are now recruiting up to 25,000 people in the UK with a clinical diagnosis of ME/CFS. Those eligible for the study are at least 16 years old, pass international study criteria, and lack any alternative diagnoses that can result in chronic fatigue. These will include 5,000 people whose ME/CFS diagnosis was a consequence of SARS-CoV-2 infection. Questionnaires are completed online or on paper. Participants’ saliva DNA samples are acquired by post, which improves participation by more severely-affected individuals. Digital marketing and social media approaches resulted in 29,000 people with ME/CFS in the UK pre-registering their interest in participating. We will perform a genome-wide association study, comparing participants’ genotypes with those from UK Biobank as controls. This should generate hypotheses regarding the genes, mechanisms and cell types contributing to ME/CFS disease aetiology. DISCUSSION: The DecodeME study has been reviewed and given a favourable opinion by the North West – Liverpool Central Research Ethics Committee (21/NW/0169). Relevant documents will be available online (www.decodeme.org.uk). Genetic data will be disseminated as associated variants and genomic intervals, and as summary statistics. Results will be reported on the DecodeME website and via open access publications