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.Comment: 13 pages, 1 figure, submitted to Phys. Rev.

Constructing the fermion-boson vertex in QED3

We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive QED3 through its one loop evaluation in an arbitrary covariant gauge. Written in a particular form, these constraints naturally lead us to the first non-perturbative construction of the vertex, which is in complete agreement with its one loop expansion in all momentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgoing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.Comment: 13 pages, 2 figure

Maternal pregnancy vitamin D supplementation increases offspring bone formation in response to mechanical loading : findings from a MAVIDOS trial sub-study

The Maternal Vitamin D Osteoporosis (MAVIDOS) trial reported higher total body bone mineral content in winter-born infants of mothers receiving vitamin D supplementation [1000 IU/day cholecalciferol] compared with placebo from 14 weeks gestation until delivery. This sub-study aimed to determine whether antenatal vitamin D supplementation altered postnatal bone formation in response to mechanical stimulation. Thirty-one children born to MAVIDOS participants randomised to either placebo (n=19) or cholecalciferol (n=12) were recruited at age 4-5 years. Children received whole body vibration (WBV) for 10 minutes on 5 consecutive days. Fasting blood samples for bone homeostasis, 25 hydroxyvitamin D (25OHD), parathyroid hormone (PTH), and bone turnover markers (Pro-collagen Type 1 N-terminal propeptide, P1NP; Cross-linked C-telopeptide of Type I Collagen, CTX) were collected pre-WBV and on day 8 (D8). Mean changes (D) in P1NP (ng/ml) between baseline and D8 in the vitamin-D intervention and placebo groups were 40.6 and -92.6 respectively and mean changes (Δ) in CTX (ng/ml) were 0.034 (intervention) and -0.084 (placebo) respectively. Between-group DP1NP difference was 133.2ng/ml [95% CI 0.4, 266.0; p=0.049] and ΔCTX 0.05ng/ml (95% CI -0.159, 0.26ng/mL; p=0.62). Antenatal vitamin-D supplementation resulted in increased P1NP in response to WBV, suggesting early life vitamin D supplementation increases the anabolic response of bone to mechanical loading in children

Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory

The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived from the (standard, second order) functional formalism. It is shown how these identities form closed sets from which one can in principle fully determine the Green's functions involving the temporal component of the gauge field without approximation, given appropriate input.Comment: 20 pages, no figure

Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics

We study the gauge covariance of the massive fermion propagator in three as well as four dimensional Quantum Electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a non-perturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one loop results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.Comment: 9 pages, no figures, uses revte

Three point SUSY Ward identities without Ghosts

We utilise a non-local gauge transform which renders the entire action of SUSY QED invariant and respects the SUSY algebra modulo the gauge-fixing condition, to derive two- and three-point ghost-free SUSY Ward identities in SUSY QED. We use the cluster decomposition principle to find the Green's function Ward identities and then takes linear combinations of the latter to derive identities for the proper functions.Comment: 20 pages, no figures, typos correcte

Longitudinal and transverse fermion-boson vertex in QED at finite temperature in the HTL approximation

We evaluate the fermion-photon vertex in QED at the one loop level in Hard Thermal Loop approximation and write it in covariant form. The complete vertex can be expanded in terms of 32 basis vectors. As is well known, the fermion-photon vertex and the fermion propagator are related through a Ward-Takahashi Identity (WTI). This relation splits the vertex into two parts: longitudinal (Gamma_L) and transverse (Gamma_T). Gamma_L is fixed by the WTI. The description of the longitudinal part consumes 8 of the basis vectors. The remaining piece Gamma_T is then written in terms of 24 spin amplitudes. Extending the work of Ball and Chiu and Kizilersu et. al., we propose a set of basis vectors T^mu_i(P_1,P_2) at finite temperature such that each of these is transverse to the photon four-momentum and also satisfies T^mu_i(P,P)=0, in accordance with the Ward Identity, with their corresponding coefficients being free of kinematic singularities. This basis reduces to the form proposed by Kizilersu et. al. at zero temperature. We also evaluate explicitly the coefficient of each of these vectors at the above-mentioned level of approximation.Comment: 13 pages, uses RevTe

The Quark-Photon Vertex and the Pion Charge Radius

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study the low-momentum behavior of the pion electromagnetic form factor. With model gluon parameters previously fixed by the pion mass and decay constant, the pion charge radius $r_\pi$ is found to be in excellent agreement with the data. When the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex directly from the quark propagator, less than half of $r_\pi^2$ is generated. The remainder of $r^2_\pi$ is seen to be attributable to the presence of the $\rho$-pole in the solution of the ladder Bethe-Salpeter equation.Comment: 21 pages, 9 figure

Regularization-independent study of renormalized non-perturbative quenched QED

A recently proposed regularization-independent method is used for the first time to solve the renormalized fermion Schwinger-Dyson equation numerically in quenched QED$_4$. The Curtis-Pennington vertex is used to illustrate the technique and to facilitate comparison with previous calculations which used the alternative regularization schemes of modified ultraviolet cut-off and dimensional regularization. Our new results are in excellent numerical agreement with these, and so we can now conclude with confidence that there is no residual regularization dependence in these results. Moreover, from a computational point of view the regularization independent method has enormous advantages, since all integrals are absolutely convergent by construction, and so do not mix small and arbitrarily large momentum scales. We analytically predict power law behaviour in the asymptotic region, which is confirmed numerically with high precision. The successful demonstration of this efficient new technique opens the way for studies of unquenched QED to be undertaken in the near future.Comment: 20 pages,5 figure

The JCMT Legacy Survey of the Gould Belt: a first look at Orion B with HARP

‘The definitive version is available at www3.interscience.wiley.com '. Copyright Royal Astronomical Society.The Gould Belt Legacy Survey will survey nearby star-forming regions (within 500 pc), using Heterodyne Array Receiver Programme (HARP), Submillimetre Common-User Bolometer Array 2 and Polarimeter 2 on the James Clerk Maxwell Telescope. This paper describes the initial data obtained using HARP to observe 12CO, 13CO and C18O J= 3 → 2 towards two regions in Orion B, NGC 2024 and NGC 2071. We describe the physical characteristics of the two clouds, calculating temperatures and opacities utilizing all the three isotopologues. We find good agreement between temperatures calculated from CO and from dust emission in the dense, energetic regions. We determine the mass and energetics of the clouds, and of the high-velocity material seen in 12CO emission, and compare the relative energetics of the high- and low-velocity material in the two clouds. We present a clumpfind analysis of the 13CO condensations. The slope of the condensation mass functions, at the high-mass ends, is similar to the slope of the initial mass function.Peer reviewe