arXiv subjects

Richard Williams

Publications and source records attributed to Richard Williams.

At least 55 records · Page 3Linked to original sources

arXiv2013

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

We study baryons as three-body systems using the QCD degrees of freedom in the framework of covariant Bethe-Salpeter equations. The interaction among quarks is reduced to a vector-vector interaction via a single dressed-gluon exchange (Rainbow-Ladder truncation). The formalism allows for the study of the hadron spectrum as well as their internal properties. We will present the calculation of electromagnetic properties of spin-3/2 baryons. The model independent features of our results are assessed using two different models for the dressings.

hep-ph↗

arXiv2013

The role of vector meson dominance and running masses in the hadronic contributions to the muon $g-2$

We summarize our recent results for the quark loop part of the light-by-light scattering contribution as well as the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon. In particular we focus on the role played by the momentum dependence of the quark- and quark-photon vertex dressing functions. We give a detailed comparison of the Dyson-Schwinger description of this contribution to the corresponding picture emerging from hadronic models in particular the extended Nambu--Jona-Lasonio model (ENJL). We find that the details of the momentum dependence are important on a quantitative level. Especially 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 of the light-by-light contribution found in the ENJL model if realistic dressings are taken into account.

hep-ph↗

arXiv2013

How to calculate the practical significance of citation impact differences? An empirical example from evaluative institutional bibliometrics using adjusted predictions and marginal effects

Evaluative bibliometrics is concerned with comparing research units by using statistical procedures. According to Williams (2012) an empirical study should be concerned with the substantive and practical significance of the findings as well as the sign and statistical significance of effects. In this study we will explain what adjusted predictions and marginal effects are and how useful they are for institutional evaluative bibliometrics. As an illustration, we will calculate a regression model using publications (and citation data) produced by four universities in German-speaking countries from 1980 to 2010. We will show how these predictions and effects can be estimated and plotted, and how this makes it far easier to get a practical feel for the substantive meaning of results in evaluative bibliometric studies. We will focus particularly on Average Adjusted Predictions (AAPs), Average Marginal Effects (AMEs), Adjusted Predictions at Representative Values (APRVs) and Marginal Effects at Representative Values (MERVs).

cs.DL↗

arXiv2012

Gluon confinement and the two IR solutions

We examine the two solutions (massive and scaling) for the covariant Yang-Mills Dyson-Schwinger equations within stochastic quantization, and find that the scaling solution does not survive outside Landau gauge. We also see that the (rainbow) massive solution has less Faddeev-Popov effective action. Finally, we argue that gluon confinement has only been marginally established in experiment and suggest further empirical work.

hep-ph↗

arXiv2012

The role of momentum dependent dressing functions and vector meson dominance in hadronic light-by-light contributions to the muon g-2

We present a refined calculation of the quark-loop contribution to hadronic light-by-light scatter- ing that focuses upon the impact of the transverse components of the quark-photon vertex. These structures are compared and contrasted with those found within the extended NJL-models. We discuss similarities and differences between the two approaches and further clarify the important role of momentum dependent dressing functions. As expected we find that the transverse structures of the quark-photon vertex lead to a suppression of the quark-loop contribution to the anomalous magnetic moment of the muon. However, we find evidence that this suppression is overestimated within models with simple approximations for the quark-photon interaction.

hep-ph↗

arXiv2012

Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism

Three decades of work on the quantum field equations of pure Yang-Mills theory have distilled two families of solutions in Landau gauge. Both coincide for high (Euclidean) momentum with known perturbation theory, and both predict an infrared suppressed transverse gluon propagator, but whereas the solution known as "scaling" features an infrared power law for the gluon and ghost propagators, the "massive" solution rather describes the gluon as a vector boson that features a finite Debye screening mass. In this work we examine the gauge dependence of these solutions by adopting stochastic quantization. What we find, in four dimensions and in a rainbow approximation, is that stochastic quantization supports both solutions in Landau gauge but the scaling solution abruptly disappears when the parameter controlling the drift force is separated from zero (soft gauge-fixing), recovering only the perturbative propagators; the massive solution seems to survive the extension outside Landau gauge. These results are consistent with the scaling solution being related to the existence of a Gribov horizon, with the massive one being more general. We also examine the effective action in Faddeev-Popov quantization that generates the rainbow and we find, for a bare vertex approximation, that the the massive-type solutions minimise the quantum effective action.

hep-th↗

arXiv2012

Baryon properties from the covariant Faddeev equation

A calculation of the masses and electromagnetic properties of the Delta and Omega baryon together with their evolution with the current quark mass is presented. Hereby a generalized Bethe-Salpeter approach with the interaction truncated to a dressed one-gluon exchange is employed. The model dependence is explored by investigating two forms for the dressed gluon exchange.

hep-ph↗

arXiv2011

Model comparison of Delta and Omega masses in a covariant Faddeev approach

We compute the vector-meson, nucleon and delta/omega-baryon masses and their evolution with the current-quark mass using a covariant generalized Bethe-Salpeter equation approach. The interaction kernel is truncated to a dressed gluon exchange. We study the model dependence of our results with the quark-gluon dressing to assess the validity of the truncation.

hep-ph↗

arXiv2011

A first estimate of triply heavy baryon masses from the pNRQCD perturbative static potential

Within pNRQCD we compute the masses of spin-averaged triply heavy baryons using the now-available NNLO pNRQCD potentials and three-body variational approach. We focus in particular on the role of the purely three-body interaction in perturbation theory. This we find to be reasonably small and of the order 25 MeV Our prediction for the Omega_ccc baryon mass is 4900(250) in keeping with other approaches. We propose to search for this hitherto unobserved state at B factories by examining the end point of the recoil spectrum against triple charm.

hep-ph↗

arXiv2011

Hadronic contribution to the muon g-2: a Dyson-Schwinger perspective

We summarize our results for hadronic contributions to the anomalous magnetic moment of the muon ($a_μ$), the one from hadronic vacuum-polarisation (HVP) and the light-by-light scattering contribution (LBL), obtained from the Dyson-Schwinger equations (DSE's) of QCD. In the case of HVP we find good agreement with model independent determinations from dispersion relations for $a_μ^\mathrm{HVP}$ as well as for the Adler function with deviations well below the ten percent level. From this we conclude that the DSE approach should be capable of describing $a_μ^\mathrm{LBL}$ with similar accuracy. We also present results for LBL using a resonance expansion of the quark anti-quark T-matrix. Our preliminary value is $a_μ^\mathrm{LBL}=(217 \pm 91) \times 10^{-11}$.

hep-ph↗

arXiv2011

Leading-order calculation of hadronic contributions to the muon $g-2$ using the Dyson-Schwinger approach

We present a calculation of the hadronic vacuum polarization (HVP) tensor within the framework of Dyson--Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, $a_μ$. We find $a_μ^{HVP}= 6760\times 10^{-11}$ which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of $a_μ^{HVP}$ and find good agreement within our approach. We also discuss the implications of our result for a corresponding calculation of the hadronic light-by-light scattering contribution to $a_μ$.

hep-ph↗

arXiv2011

Effects of Anisotropy in QED3 from Dyson-Schwinger equations in a box

We investigate the effect of anisotropies in the fermion velocities of 2+1 dimensional QED on the critical number N_f^c of fermions for dynamical mass generation. Our framework are the Dyson-Schwinger equations for the gauge boson and fermion propagators formulated in a finite volume. In contrast to previous Dyson-Schwinger studies we do not rely on an expansion in small anisotropies but keep the full velocity dependence of fermion equations intact. As result we find sizable variations of N_f^c away from the isotropic point in agreement with other approaches. We discuss the relevance of our findings for models of high-T_c superconductors.

hep-ph↗

arXiv2011

Hadronic light-by-light scattering in the muon g-2: a Dyson-Schwinger equation approach

We determine the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon using the framework of Dyson-Schwinger and Bethe-Salpeter equations of QCD. Our result for the pseudoscalar ($π^0, η, η'$) meson exchange diagram is commensurate with previous calculations. In our calculation of the quark loop contribution we improve previous approaches by implementing constraints due to gauge invariance. As a consequence, our value $a_μ^{\textrm{LBL;quarkloop}} = (136 \pm 59)\times 10^{-11}$ is significantly larger. Taken at face value, this then leads to a revised estimate of the total $a_μ=116\,591\,891.0(105.0)\times 10^{-11}$.

hep-ph↗

arXiv2011

A fresh look at hadronic light-by-light scattering in the muon g-2 with the Dyson-Schwinger approach

We present first results for the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon a_μ in the framework of Dyson-Schwinger and Bethe-Salpeter equations. We determine the quark loop and pseudoscalar (π^0, η, η') meson exchange diagram using a phenomenological model for the combined strength of the gluon propagator and the quark-gluon interaction as the only input. Our result for meson exchange, a_μ^{LBL;PS}=(84 \pm 13) x 10^{-11}, is commensurate with previous calculations. However, our number for the quark loop contribution, a_μ^{LBL;quarkloop} = (107 \pm 2 \pm 46) x 10^{-11}, is significantly larger due to dressing effects in the quark propagator and the quark-photon vertex. Taken at face value, this then leads to a revised estimate of the total a_μ=116 591 865.0(96.6) x 10^{-11}, which reduces the difference between theory and experiment to about 1.9 σ.

hep-ph↗

arXiv2010

Hadronic contribution to the muon g-2 from a Dyson-Schwinger perspective

A novel approach towards the hadronic contributions to the anomalous magnetic moment of the muon $a_μ$ is presented, namely the Dyson-Schwinger equations of QCD. It has the advantage of being valid for all momentum scales and has the potential to address off-shell amplitudes. We present our first results for the pseudoscalar (PS) meson exchange and the quark loop contributions. The meson exchange ($π^0, η, η'$), $a_μ^{\textrm{LBL;PS}}=(84 \pm 13)\times 10^{-11}$, is commensurate with previous calculations, while the quark loop contribution $a_μ^{\textrm{LBL;quarkloop}} = (107 \pm 48)\times 10^{-11}$, is strongly enhanced by vertex dressing effects in the quark photon vertex. Taken seriously this leads to the estimate of $a_μ=116\,591\,865.0(96.6)\times 10^{-11}$, giving a 1.9 $σ$ deviation between theory and experiment.

hep-ph↗

arXiv2010

Volume behaviour of quark condensate, pion mass and decay constant from Dyson-Schwinger equations

We solve the coupled system of Dyson-Schwinger and Bethe-Salpeter equations for the quark propagator and the pion Bethe-Salpeter amplitude on a finite volume. To this end we use a truncation scheme that includes pion cloud effects in the quark propagator and light mesons. We study volume effects in the quark condensate, the pion mass and the pion decay constant and compare to corresponding results in other approaches. In general we find large effects for volumes below V=(1.8 fm)^4.

hep-ph↗

arXiv2009

Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

We investigate masses of light mesons from a coupled system of Dyson--Schwinger (DSE) and Bethe--Salpeter equations (BSE), taking into account dominant non-Abelian, sub-leading Abelian, and dominant pion cloud contributions to the dressed quark-gluon vertex. The axial-vector Ward-Takahashi identity preserving Bethe-Salpeter kernel is constructed and the spectrum of light mesons calculated. Our model goes significantly beyond the rainbow-ladder. We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions from simple truncation schemes.

hep-ph↗

arXiv2009

Bethe-Salpeter studies of mesons beyond rainbow-ladder

We investigate the masses of light mesons from a coupled system of Dyson-Schwinger and Bethe-Salpeter equations. The dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex are explicitly taken into account. We also include unquenching effects in the form of hadronic resonance contributions via the back-reaction of pions. We construct the corresponding Bethe--Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the relative impact of different corrections beyond rainbow-ladder on the properties of mesons. We find that sub-leading Abelian corrections are further suppressed dynamically, and that our results supersede early qualitative predictions with significantly simpler truncation schemes.

hep-ph↗