arXiv subjects

Richard Williams

Publications and source records attributed to Richard Williams.

61 records · Page 4Linked to original sources

arXiv2009

Probing the gluon self-interaction in light mesons

We investigate masses and decay constants of light mesons from a coupled system of Dyson--Schwinger and Bethe--Salpeter equations. We explicitly take into account dominant non-Abelian contributions to the dressed quark-gluon vertex stemming from the gluon self-interaction. 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 influence of the gluon self-interaction on the properties of mesons. As a first result we find indications of a nonperturbative cancellation of the gluon self-interaction contributions and pion cloud effects in the mass of the rho-meson.

hep-ph↗

arXiv2009

Baby steps beyond rainbow-ladder

We discuss the impact of including corrections beyond single gluon exchange in light mesons within the nonperturbative framework of Dyson-Schwinger equations (DSE) and Bethe-Salpeter equations (BSE). We do this by considering unquenching effects in the form of hadronic resonance contributions, notably pion exchange, and by the inclusion of the dominant gluon self-interactions to the quark-gluon vertex. Thus we make steps towards an ab initio description of light mesons by functional methods.

hep-ph↗

arXiv2008

Pion-cloud effects in the BSE description of mesons

We investigate the effect of including hadronic resonance contributions in the description of light quarks and mesons. To this end we take into account the back-coupling of the pion onto the quark propagator within the non-perturbative continuum framework of Schwinger-Dyson equations (SDE) and Bethe-Salpeter equations (BSE), in essence describing the so-called \emph{pion-cloud}. As a result of our study we find that an unquenching of this form provides for considerable effects in the spectrum of light mesons.

hep-ph↗

arXiv2008

On Gribov's supercriticality picture of quark confinement

Some years ago Gribov developed the so-called supercritical light quark confinement scenario. Based on physical arguments he conjectured a drastic change in the analytical properties of the quark propagator when the back-reaction of Goldstone bosons (pions) is considered. We investigate this scenario and provide numerical solutions for the quark propagator in the complex plane with and without the pion back-reaction. We find no evidence for the scenario Gribov advocated. As an aside we present a novel method to solve the quark Dyson-Schwinger equation in the complex plane and discuss new characteristics of dynamical chiral symmetry breaking in our truncation scheme.

hep-ph↗

arXiv2008

Finite volume effects and dynamical chiral symmetry breaking in QED3

We investigate the impact of finite volume effects on the critical number of flavours, N_f^c, for chiral symmetry restoration in QED3. To this end we solve a set of coupled Dyson-Schwinger equations on a torus. For order parameters such as the anomalous dimension of the fermion wave function or the chiral condensate we find substantial evidence for a large dependence on the volume. We observe a shift in N_f^c from values in the range of 3.61 \le N_f^c \le 3.84 in the infinite volume/continuum limit down to values below N_f \le 1.5 at finite volumes in agreement with earlier results of Gusynin and Reenders in a simpler truncation scheme. These findings explain discrepancies in N_f^c between continuum and lattice studies.

hep-ph↗

arXiv2008

Beyond the rainbow: effects from pion back-coupling

We investigate hadronic unquenching effects in light quarks and mesons. To this end we take into account the back-coupling of the pion onto the quark propagator within the non-perturbative continuum framework of Schwinger-Dyson equations (SDE) and Bethe-Salpeter equations (BSE). We improve on a previous approach by explicitly solving both the coupled system of DSEs and BSEs in the complex plane and the normalisation problem for Bethe-Salpeter kernels depending on the total momentum of the meson. As a result of our study we find considerable unquenching effects in the spectrum of light pseudoscalar, vector and axial-vector mesons.

hep-ph↗

arXiv2008

U_A(1) anomaly and eta' mass from an infrared singular quark-gluon vertex

The $U_A(1)$ problem of QCD is inevitably tied to the infrared behaviour of quarks and gluons with its most visible effect being the $η^\prime$ mass. A dimensional argument of Kogut and Susskind showed that the mixing of the pseudoscalar flavour-singlet mesons with gluons can provide a screening of the Goldstone pole in this channel if the full quark-quark interaction is strongly infrared singular as $\sim 1/k^4$. We investigate this idea using previously obtained results for the Landau gauge ghost and gluon propagator, together with recent determinations for the singular behaviour of the quark-gluon vertex. We find that, even with an infrared vanishing gluon propagator, the singular structure of the quark-gluon vertex for certain kinematics is apposite for yielding a non-zero screening mass.

hep-ph↗