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Richard Williams

Publications and source records attributed to Richard Williams.

At least 37 records · Page 2Linked to original sources

Sampling Issues in Bibliometric Analysis

Bibliometricians face several issues when drawing and analyzing samples of citation records for their research. Drawing samples that are too small may make it difficult or impossible for studies to achieve their goals, while drawing samples that are too large may drain resources that could be better used for other purposes. This paper considers three common situations and offers advice for dealing with each. First, an entire population of records is available for an institution. We argue that, even though all records have been collected, the use of inferential statistics, significance testing, and confidence intervals is both common and desirable. Second, because of limited resources or other factors, a sample of records needs to be drawn. We demonstrate how power analyses can be used to determine in advance how large the sample needs to be to achieve the study's goals. Third, the sample size may already be determined, either because the data have already been collected or because resources are limited. We show how power analyses can again be used to determine how large effects need to be in order to find effects that are statistically significant. Such information can then help bibliometricians to develop reasonable expectations as to what their analysis can accomplish. While we focus on issues of interest to bibliometricians, our recommendations and procedures can easily be adapted for other fields of study.

stat.AP↗

Probing the quark-gluon interaction with hadrons

We present a unified picture of mesons and baryons in the Dyson-Schwinger/Bethe-Salpeter approach, wherein the quark-gluon and quark-(anti)quark interaction follow from a systematic truncation of the QCD effective action and includes all its tensor structures. The masses of some of the ground state mesons and baryons are found to be in reasonable agreement with the expectations of a `quark-core calculation', suggesting a partial insensitivity to the details of the quark-gluon interaction. However, discrepancies remain in the meson sector, and for excited baryons, that suggest higher order corrections are relevant and should be investigated following the methods outlined herein.

hep-ph↗

Hadronic Observables from Dyson-Schwinger and Bethe-Salpeter equations

In these proceedings we present a mini-review on the topic of the Dyson-Schwinger/Bethe-Salpeter approach to the study of relativistic bound-states in physics. In particular, we present a self-contained discussion of their derivation, as well as their truncation such that important symmetries are maintained.

hep-ph↗

Hadronic bound-states in SU(2) from Dyson--Schwinger Equations

By using the Dyson-Schwinger/Bethe-Salpeter formalism in Euclidean spacetime, we calculate the ground state spectrum of $J\leq 1$ hadrons in an SU(2) gauge theory with 2 fundamental fermions. We show that the rainbow-ladder truncation, commonly employed in QCD studies, is unsuitable for a description of an SU(2) theory. This we remedy by truncating at the level of the quark-gluon vertex Dyson-Schwinger equation in a diagrammatic expansion. Results obtained within this novel approach show good agreement with lattice studies. These findings emphasize the need to use techniques more sophisticated than rainbow-ladder when investigating generic strongly interacting gauge theories.

hep-ph↗

The quark-gluon vertex in Landau gauge bound-state studies

We present a practical method for the solution of the quark-gluon vertex for use in Bethe--Salpeter and Dyson--Schwinger calculations. The efficient decomposition into the necessary covariants is detailed, with the numerical algorithm outlined for both real and complex Euclidean momenta. A truncation of the quark-gluon vertex, that neglects explicit back-coupling to enable the application to bound-state calculations, is given together with results for the quark propagator and quark-gluon vertex for different quark flavours. The relative impact of the various components of the quark-gluon vertex is highlighted with the flavour dependence of the effective quark-gluon interaction obtained, thus providing insight for the construction of phenomenological models within Rainbow-Ladder. Finally, we solve the corresponding Green's functions for complex Euclidean momenta as required in future bound-state calculations.

hep-ph↗

Spectra of heavy mesons in the Bethe-Salpeter approach

We present a calculation of the spectrum of charmonia, bottomonia and B_c-meson states with `ordinary' and exotic quantum numbers. We discuss the merits and limitations of a rainbow-ladder truncation of Dyson-Schwinger and Bethe-Salpeter equations and explore the effects of different shapes of the effective running coupling on ground and excited states in channels with quantum numbers J <= 3. We furthermore discuss the status of the X(3872) as a potential (excited) quark-antiquark state and give predictions for the masses of charmonia and bottomonia in the tensor channels with J=2,3.

hep-ph↗

Electromagnetic baryon form factors in the Poincare-covariant Faddeev approach

Baryons are treated as three-quark systems using QCD degrees of freedom in Poincare-covariant bound-state equations. The quark self-energy as well as the interaction between quarks are approximated by a vector-vector interaction via a single dressed-gluon exchange (rainbow-ladder truncation), thereby allowing a unified study of quark, meson and baryon properties. Here we will focus on the calculation of electromagnetic properties of spin-1/2 and spin-3/2 ground state baryons.

hep-ph↗

The muon g-2: Dyson-Schwinger status on hadronic light-by-light scattering

We give a status report on the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment from the Dyson-Schwinger approach. We discuss novel, model-independent properties of the light-by-light amplitude: we give its covariant decomposition in view of electromagnetic gauge invariance and Bose symmetry, and we identify the relevant kinematic regions that are probed under the integral. The decomposition of the amplitude at the quark level and the importance of its various diagrams are discussed and related to model approaches.

hep-ph↗

Regge behaviour within the Bethe-Salpeter approach

We present a calculation of the spectrum of light and heavy quark bound states in the rainbow-ladder truncation of Dyson-Schwinger/Bethe-Salpeter equations. By extending the formalism include the case of total angular momentum J=3, we are able to explore Regge trajectories and make prediction of tensor bound states for light and heavy quarkonia.

hep-ph↗

Dynamical mass generation in unquenched QED using the Dyson--Schwinger equations

We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson--Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a renormalized fully unquenched system of equations. This we compare with the results for two hybrid vertices incorporating the Curtis--Pennington vertex in the fermion equation. We conclude that the KP vertex is as yet incomplete, and its relative gauge-variance is due to its lack of massive transverse components in its design.

hep-ph↗

Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach

We extend the calculation of relativistic bound-states of a fermion anti-fermion pair in the Bethe-Salpeter formalism to the case of total angular momentum $J=3$. Together with results for $J \le 2$ this allows for the investigation of Regge trajectories in this approach. We exemplify such a study for ground and excited states of light unflavored mesons as well as strange mesons within the rainbow-ladder approximation. For the $ρ$- and $ϕ$-meson we find a linear Regge trajectory within numerical accuracy. Discrepancies with experiment in other channels highlight the need to go beyond rainbow-ladder and to consider effects such as state mixing and more sophisticated quark-antiquark interaction kernels.

hep-ph↗

On propagators and three-point functions in Landau gauge QCD and QCD-like theories

Recent progress in our studies of propagators and three-point functions in Landau gauge for QCD and QCD-like theories is presented. Special emphasis is put on the properties of the three-gluon vertex and the quark-gluon vertex. The effect of unquenching is investigated. Furthermore, an exploratory study for a large number of light flavours is described, from where clear evidence for the qualitative behaviour of propagators in the so-called conformal window can be extracted.

hep-ph↗

Non-perturbative features of the three-gluon vertex in Landau gauge

We present a calculation of the three-gluon vertex from its Dyson-Schwinger equation in Landau-gauge Yang-Mills theory. All tensor structures are considered and back-coupled self-consistently. Within the chosen truncation, two-loop diagrams as well as diagrams containing Green's functions beyond the primitively divergent ones are neglected. Only the three-gluon vertex is chosen to be dynamical; the other propagators and vertex functions are provided as separate solutions of their Dyson-Schwinger equations or by Ansatz. For both scaling- and decoupling-type solutions we observe, in agreement with other studies, a sign change in the tree-level tensor dressing at a non-perturbative scale.

hep-ph↗

The substantive and practical significance of citation impact differences between institutions: Guidelines for the analysis of percentiles using effect sizes and confidence intervals

In our chapter we address the statistical analysis of percentiles: How should the citation impact of institutions be compared? In educational and psychological testing, percentiles are already used widely as a standard to evaluate an individual's test scores - intelligence tests for example - by comparing them with the percentiles of a calibrated sample. Percentiles, or percentile rank classes, are also a very suitable method for bibliometrics to normalize citations of publications in terms of the subject category and the publication year and, unlike the mean-based indicators (the relative citation rates), percentiles are scarcely affected by skewed distributions of citations. The percentile of a certain publication provides information about the citation impact this publication has achieved in comparison to other similar publications in the same subject category and publication year. Analyses of percentiles, however, have not always been presented in the most effective and meaningful way. New APA guidelines (American Psychological Association, 2010) suggest a lesser emphasis on significance tests and a greater emphasis on the substantive and practical significance of findings. Drawing on work by Cumming (2012) we show how examinations of effect sizes (e.g. Cohen's d statistic) and confidence intervals can lead to a clear understanding of citation impact differences.

cs.DL↗

The three-gluon vertex in Landau gauge

We present the first Dyson-Schwinger calculation of the three-gluon vertex in Landau-gauge QCD in which its full covariant structure is back-coupled self-consistently. We truncate a Bose-symmetrized version of the DSE at the level of one-loop diagrams, model the four-gluon vertex, and neglect terms that contain non-primitively divergent n-point functions; the ghost-gluon vertex is taken bare to good approximation. Fit functions for the ghost and gluon propagators that interpolate between scaling and decoupling are presented. In all aspects of our study Bose symmetry is manifest, from the truncation to the basis decomposition and to the momentum invariants. We explore the uniform and soft-collinear infrared limits and obtain the expected infrared exponents. The presence of a zero crossing in the tree-level component of the vertex is confirmed for both scaling- and decoupling-type scenarios. The zero crossing appears at a scale ~1 GeV; however, its location might be sensitive to the four-gluon vertex and missing components in the DSE.

hep-ph↗

Non-contact interactions and the hadronic light-by-light contribution to the muon g-2

We summarise recent results for the quark loop part of the light-by-light scattering contribution to the muons anomalous magnetic moment. In particular we focus on the impact of a momentum dependent quark and quark-photon vertex. We compare the Dyson-Schwinger description with that of the extended Nambu--Jona-Lasinio model (ENJL) and find important quantitative differences. In particular the transverse parts of the quark-photon-vertex, which serve as a dynamical extension of simple vector meson dominance models, do not yield the large suppression as found in the ENJL model.

hep-ph↗

Triply heavy baryon mass estimated within pNRQCD

Potential-NRQCD offers an effective-theory based approach to heavy-quark physics. While meson Q-anti_Q computations are tractable in pure alpha_s-perturbation theory, more complex many-body quark systems transcend it. A possibility inherited from nuclear physics is to employ the perturbative static potentials in a numerical diagonalization, eventually obtaining the exact lowest eigenvalue in each channel for a given-order perturbative potential. The power counting is manifest in the potential instead of the spectrum. The NNLO-potential for the 3-body problem is already available, so we have addressed triply-heavy baryons in this initial work with a computer-aided 2-parameter variational treatment.

nucl-th↗

Delta and Omega electromagnetic form factors in a three-body covariant Bethe-Salpeter approach

The electromagnetic form factors of the Delta and Omega baryons are calculated in the framework of Poincare-covariant bound-state equations. The quark-quark interaction is truncated to a single dressed-gluon exchange where for the dressings we use two different models and compare the results. The calculation predicts an oblate shape for the electric charge distribution and a prolate shape for the magnetic dipole distribution. We also identify the necessity of including pion-cloud corrections at low photon-momentum transfer.

hep-ph↗