arXiv subjects

J. C. R. Bloch

Publications and source records attributed to J. C. R. Bloch.

16 recordsLinked to original sources

arXiv2003

Two-loop Improved Truncation of the Ghost-Gluon Dyson-Schwinger Equations: Multiplicatively Renormalizable Propagators and Nonperturbative Running Coupling

The coupled Dyson-Schwinger equations for the gluon and ghost propagators are investigated in the Landau gauge using a two-loop improved truncation that preserves the multiplicative renormalizability of the propagators. In this truncation all diagrams contribute to the leading order infrared analysis. The infrared contributions of the nonperturbative two-loop diagrams to the gluon vacuum polarization are computed analytically, and this reveals that infrared power behaved propagator solutions only exist when the squint diagram contribution is taken into account. For small momenta the gluon and ghost dressing functions behave respectively like (p^2)^{2κ} and (p^2)^{-κ}, and the running coupling exhibits a fixed point. The values of the infrared exponent and fixed point depend on the precise details of the truncation. The coupled ghost-gluon system is solved numerically for all momenta, and the solutions have infrared behaviors consistent with the predictions of the infrared analysis. For truncation parameters chosen such that κ=0.5, the two-loop improved truncation is able to produce solutions for the propagators and running coupling which are in very good agreement with recent lattice simulations.

hep-ph↗

arXiv2003

Regarding proton form factors

The proton's elastic electromagnetic form factors are calculated using an Ansatz for the nucleon's Poincare' covariant Faddeev amplitude that only retains scalar diquark correlations. A spectator approximation is employed for the current. On the domain of q^2 accessible in modern precision experiments these form factors are a sensitive probe of nonperturbative strong interaction dynamics. The ratio of Pauli and Dirac form factors can provide realistic constraints on models of the nucleon and thereby assist in developing an understanding of nucleon structure.

nucl-th↗

arXiv2002

Vortex induced confinement and the IR properties of Green functions

Simulations of SU(2) lattice gauge theory are used to establish a relation between the IR properties of Green functions and confinement. Using Landau gauge where the gauge configurations are restricted to the first Gribov regime, results on the ghost-, gluon form-factor and the running coupling constant are presented. Finally, we discuss the behavior of the ghost form-factor of the de-confined phase at high temperatures.

hep-th↗

arXiv2002

Numerical Investigation of Fermion Mass Generation in QED

We investigate the dynamical generation of fermion mass in quantum electrodynamics (QED). This non-perturbative study is performed using a truncated set of Schwinger-Dyson equations for the fermion and the photon propagator. First, we study dynamical fermion mass generation in quenched QED with the Curtis-Pennington vertex, which satisfies the Ward-Takahashi identity and ensures the multiplicative renormalizability of the fermion propagator. We apply bifurcation analysis to determine the critical point for a general covariant gauge. In the second part of this work we investigate the dynamical generation of fermion mass in full, unquenched QED. We develop a numerical method to solve the system of three coupled non-linear equations for the dynamical fermion mass, the fermion wavefunction renormalization and the photon renormalization function. Much care is taken to ensure the high accuracy of the solutions. We also discuss in detail the proper numerical cancellation of the quadratic divergence in the vacuum polarization integral and the need to use smooth approximations to the solutions.

hep-ph↗

arXiv2002

Multiplicative renormalizability and quark propagator

The renormalized Dyson-Schwinger equation for the quark propagator is studied, in Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability, and reproduces the correct leading order perturbative behavior, non-trivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced, with infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.

hep-ph↗

arXiv2001

Multiplicative renormalizability of gluon and ghost propagators in QCD

We reformulate the coupled set of continuum equations for the renormalized gluon and ghost propagators in QCD, such that the multiplicative renormalizability of the solutions is manifest, independently of the specific form of full vertices and renormalization constants. In the Landau gauge, the equations are free of renormalization constants, and the renormalization point dependence enters only through the renormalized coupling and the renormalized propagator functions. The structure of the equations enables us to devise novel truncations with solutions that are multiplicatively renormalizable and agree with the leading order perturbative results. We show that, for infrared power law behaved propagators, the leading infrared behavior of the gluon equation is not solely determined by the ghost loop, as concluded in previous studies, but that the gluon loop, the three-gluon loop, the four-gluon loop, and even massless quarks also contribute to the infrared analysis. In our new Landau gauge truncation, the combination of gluon and ghost loop contributions seems to reject infrared power law solutions, but massless quark loops illustrate how additional contributions to the gluon vacuum polarization could reinstate these solutions. Moreover, a schematic study of the three-gluon and four-gluon loops shows that they too need to be considered in more detail before a definite conclusion about the existence of infrared power behaved gluon and ghost propagators can be reached.

hep-ph↗

arXiv1999

Selected nucleon form factors and a composite scalar diquark

A covariant, composite scalar diquark, Fadde'ev amplitude model for the nucleon is used to calculate pseudoscalar, isoscalar- and isovector-vector, axial-vector and scalar nucleon form factors. The last yields the nucleon sigma-term and on-shell sigma-nucleon coupling. The calculated form factors are soft, and the couplings are generally in good agreement with experiment and other determinations. Elements in the dressed-quark-axial-vector vertex that are not constrained by the Ward-Takahashi identity contribute ~20% to the magnitude of g_A. The calculation of the nucleon sigma-term elucidates the only unambiguous means of extrapolating meson-nucleon couplings off the meson mass-shell.

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arXiv1999

Memory effects and thermodynamics in strong field plasmas

We study the evolution of a strong field plasma using a quantum Vlasov equation with a non-Markovian source term and a simple collision term, and calculate the time dependence of the energy- and number-density, and the temperature. The evolution of a plasma produced with RHIC-like initial conditions is well described by a low density approximation to the source term. However, non-Markovian aspects should be retained to obtain an accurate description of the early stages of an LHC-like plasma.

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arXiv1999

K -> pi pi and a light scalar meson

We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi transitions using a Dyson-Schwinger equation model. Exploiting the feature that QCD penguin operators direct K^0_S transitions through 0^{++} intermediate states, we find an explanation of the enhancement of I=0 K -> pi pi transitions in the contribution of a light sigma-meson. This mechanism also affects epsilon'/epsilon.

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arXiv1999

Nucleon form factors and a nonpointlike diquark

Nucleon form factors are calculated on q^2 in [0,3] GeV^2 using an Ansatz for the nucleon's Fadde'ev amplitude motivated by quark-diquark solutions of the relativistic Fadde'ev equation. Only the scalar diquark is retained, and it and the quark are confined. A good description of the data requires a nonpointlike diquark correlation with an electromagnetic radius of 0.8 r_pi. The composite, nonpointlike nature of the diquark is crucial. It provides for diquark-breakup terms that are of greater importance than the diquark photon absorption contribution.

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arXiv1999

Diquarks: condensation without bound states

We employ a bispinor gap equation to study superfluidity at nonzero chemical potential: mu .neq. 0, in two- and three-colour QCD. The two-colour theory, QC2D, is an excellent exemplar: the order of truncation of the quark-quark scattering kernel: K, has no qualitative impact, which allows a straightforward elucidation of the effects of mu when the coupling is strong. In rainbow-ladder truncation, diquark bound states appear in the spectrum of the three-colour theory, a defect that is eliminated by an improvement of K. The corrected gap equation describes a superfluid phase that is semi-quantitatively similar to that obtained using the rainbow truncation. A model study suggests that the width of the superfluid gap and the transition point in QC2D provide reliable quantitative estimates of those quantities in QCD.

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arXiv1999

Pair creation: back-reactions and damping

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back-reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period tau_pl. Allowing for collisions, these oscillations are damped on a time-scale, tau_r, determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless tau_r >> tau_pl and tau_pl approx. 1/Lambda_QCD approx 1 fm/c.

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arXiv1999

Describing a1 and b1 decays

Two-body pion-radiating and weak decays of light axial-vector mesons and the rho are studied as a phenomenological application of the QCD Dyson-Schwinger equations. Models based on the rainbow-ladder truncation are capable of providing a good description and, in particular, yield the correct sign and magnitude of the a1 -> rho pi and b1 -> omega pi D/S ratios, with no additional mechanism necessary.

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arXiv1998

QCD in the Infrared with Exact Angular Integrations

In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but in the current paper we go beyond this approximation and perform an exact calculation of the angular integrals. The powers of the infrared behaviour of the propagators are changed substantially. We find the very intriguing result that the gluon propagator vanishes in the infrared exactly like p^2, whilst the ghost propagator is exactly as singular as 1/p^4. We also find that the value of the infrared fixed point of the QCD coupling is much decreased from the y-max estimate: it is now equal to 4π/3.

hep-ph↗

arXiv1998

Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation

A recent claim that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson-Schwinger equations are taken to be bare. The running coupling is shown to be uniquely determined by the equations and to have a large finite infrared limit.

hep-ph↗

arXiv1995

Numerical cancellation of photon quadratic divergence in the study of the Schwinger-Dyson equations in Strong Coupling QED

The behaviour of the photon renormalization function in strong coupling QED has been recently studied by Kondo, Mino and Nakatani. We find that the sharp decrease in its behaviour at intermediate photon momenta is an artefact of the method used to remove the quadratic divergence in the vacuum polarization. We discuss how this can be avoided in numerical studies of the Schwinger-Dyson equations.

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