Chiral two-loop pion-pion scattering parameters from crossing-symmetric constraints

Constraints on the parameters in the one- and two-loop pion-pion scattering amplitudes of standard chiral perturbation theory are obtained from explicitly crossing-symmetric sum rules. These constraints are based on a matching of the chiral amplitudes and the physical amplitudes at the symmetry point of the Mandelstam plane. The integrals over absorptive parts appearing in the sum rules are decomposed into crossing-symmetric low- and high-energy components and the chiral parameters are finally related to high-energy absorptive parts. A first application uses a simple model of these absorptive parts. The sensitivity of the results to the choice of the energy separating high and low energies is examined with care. Weak dependence on this energy is obtained as long as it stays below ~560 MeV. Reliable predictions are obtained for three two-loop parameters.Comment: 23 pages, 4 figures in .eps files, Latex (RevTex), our version of RevTex runs under Latex2.09, submitted to Phys. Rev. D,minor typographical corrections including the number at the end of the abstract, two sentences added at the end of Section 5 in answer to a referee's remar

One-channel Roy equations revisited

The Roy equation in the single channel case is a nonlinear, singular integral equation for the phase shift in the low-energy region. We first investigate the infinitesimal neighborhood of a given solution, and then present explicit expressions for amplitudes that satisfy the nonlinear equation exactly. These amplitudes contain free parameters that render the non-uniqueness of the solution manifest. They display, however, an unphysical singularity at the upper end of the interval considered. This singularity disappears and uniqueness is achieved if one uses analyticity properties of the amplitudes that are not encoded in the Roy equation.Comment: 36 pages (LaTex), 9 figures embedded with epsfig.st

On The Linearity of The Black Hole - Bulge Mass Relation in Active and in Nearby Galaxies

Analysis of PG quasar observations suggests a nonlinear relation between the black hole mass, M_BH, and the bulge mass, M_bulge, although a linear relation, as proposed for nearby galaxies, cannot be ruled out. New M_BH values for nearby galaxies from Gebhardt et al., and L_bulge measurements for Seyfert 1 galaxies from Virani et al., are used here to obtain a more accurate value for the slope of the M_BH-M_bulge relation. The combined sample of 40 active and non-active galaxies suggests a significantly nonlinear relation, M_BH\propto M_bulge^{1.53\pm 0.14}. Further support for a nonlinear relation is provided by the slope of the M_BH-stellar velocity dispersion relation found recently, and by the low M_BH found in late type spiral galaxies. The mean M_BH/M_bulge ratio is therefore not a universal constant, but rather drops from ~0.5% in bright (M_V ~ -22) ellipticals, to ~0.05% in low luminosity (M_V ~ -18) bulges. Hubble Space Telescope determinations of M_BH in late type spirals, and of the bulge magnitude in narrow line Seyfert 1 galaxies (both predicted to have low M_BH), can further test the validity of the nonlinear M_BH-M_bulge relation.Comment: Accepted for publication in ApJ, 9 pages inc. 2 figure

Characterization of the human omega-oxidation pathway for omega-hydroxy-very-long-chain fatty acids

Very-long-chain fatty acids (VLCFAs) have long been known to be degraded exclusively in peroxisomes via beta-oxidation. A defect in peroxisomal beta-oxidation results in elevated levels of VLCFAs and is associated with the most frequent inherited disorder of the central nervous system white matter, X-linked adrenoleukodystrophy. Recently, we demonstrated that VLCFAs can also undergo omega-oxidation, which may provide an alternative route for the breakdown of VLCFAs. The omega-oxidation of VLCFA is initiated by CYP4F2 and CYP4F3B, which produce omega-hydroxy-VLCFAs. In this article, we characterized the enzymes involved in the formation of very-long-chain dicarboxylic acids from omega-hydroxy-VLCFAs. We demonstrate that very-long-chain dicarboxylic acids are produced via two independent pathways. The first is mediated by an as yet unidentified, microsomal NAD(+)-dependent alcohol dehydrogenase and fatty aldehyde dehydrogenase, which is encoded by the ALDH3A2 gene and is deficient in patients with Sjogren-Larsson syndrome. The second pathway involves the NADPH-dependent hydroxylation of omega-hydroxy-VLCFAs by CYP4F2, CYP4F3B, or CYP4F3A. Enzyme kinetic studies show that oxidation of omega-hydroxy-VLCFAs occurs predominantly via the NAD(+)-dependent route. Overall, our data demonstrate that in humans all enzymes are present for the complete conversion of VLCFAs to their corresponding very-long-chain dicarboxylic acids

Perceived thickness and creaminess modulates the short-term satiating effects of high protein drinks

Previous research suggests that increasing beverage protein content enhances subsequent satiety, but whether this effect is entirely attributable to post-ingestive effects of protein or is partly caused by the distinct sensory characteristics imparted by the presence of protein remains unclear. To try and discriminate nutritive from sensory effects of added protein, we contrasted effects of three higher energy (c. 1.2MJ) and one lower energy (LE: 0.35MJ) drink preloads on subsequent appetite and lunch intake. Two higher energy drinks had 44% of energy from protein, one with the sensory characteristics of a juice drink (HP-) and the second thicker and more creamy (HP+). The high-carbohydrate preload (HC+) was matched for thickness and creaminess to the HP+ drink. Participants (healthy male volunteers, n=26) consumed significantly less at lunch after the HP+ (566g) and HC+ (572g) than after HP- (623g) and LE (668g) drinks, although the compensation for drink energy accounted for only 50% of extra energy at best. Appetite ratings indicated that participants felt significantly less hungry and more full immediately before lunch in HP+ and HC+ compared to LE, with HP- intermediate. The finding that protein generated stronger satiety in the context of a thicker creamier drink (HP+ but not HP-), and that an isoenergetic carbohydrate drink (HC+) matched in thickness and creaminess to the HP+ drink generated the same pattern of satiety as HP+ both suggest an important role for these sensory cues in the development of protein-based satiety

Long-chain 3-hydroxyacyl-CoA dehydrogenase deficiency

A new case of 3-hydroxyacyl-CoA dehydrogenase deficiency is described with a relatively benign course

A general introduction to the biochemistry of mitochondrial fatty acid β-oxidation

Over the years, the mitochondrial fatty acid β-oxidation (FAO) pathway has been characterised at the biochemical level as well as the molecular biological level. FAO plays a pivotal role in energy homoeostasis, but it competes with glucose as the primary oxidative substrate. The mechanisms behind this so-called glucose–fatty acid cycle operate at the hormonal, transcriptional and biochemical levels. Inherited defects for most of the FAO enzymes have been identified and characterised and are currently included in neonatal screening programmes. Symptoms range from hypoketotic hypoglycaemia to skeletal and cardiac myopathies. The pathophysiology of these diseases is still not completely understood, hampering optimal treatment. Studies of patients and mouse models will contribute to our understanding of the pathogenesis and will ultimately lead to better treatment

Magnetic Confinement, MHD Waves, and Smooth Line Profiles in AGN

In this paper, we show that if the broad line region clouds are in approximate energy equipartition between the magnetic field and gravity, as hypothesized by Rees, there will be a significant effect on the shape and smoothness of broad emission line profiles in active galactic nuclei. Line widths of contributing clouds or flow elements are much wider than their thermal widths, due to the presence of non-dissipative MHD waves, and their collective contribution produce emission line profiles broader and smoother than would be expected if a magnetic field were not present. As an illustration, a simple model of isotropically emitting clouds, normally distributed in velocity, is used to show that smoothness can be achieved for less than 80,000 clouds and may even be as low as a few hundred. We conclude that magnetic confinement has far reaching consequences for observing and modeling active galactic nuclei.Comment: to appear in MNRA

Determination of SU(2) Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters

We determine the values of the one- and two-loop low energy constants appearing in the SU(2) Chiral Perturbation Theory calculation of pion-pion scattering. For this we use a recent and precise sum rule determination of some scattering lengths and slopes that appear in the effective range expansion. In addition we provide sum rules for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the S, P, D and F waves are consistent with previous determinations, but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion.Comment: 16 pages. Version published in Phys. Rev. D. Enlarged discussions in several sections, appendices and many references added. Results and conclusions unchange

On the precision of the theoretical predictions for pi pi scattering

In a recent paper, Pelaez and Yndurain evaluate some of the low energy observables of pi pi scattering and obtain flat disagreement with our earlier results. The authors work with unsubtracted dispersion relations, so that their results are very sensitive to the poorly known high energy behaviour of the scattering amplitude. They claim that the asymptotic representation we used is incorrect and propose an alternative one. We repeat their calculations on the basis of the standard, subtracted fixed-t dispersion relations, using their asymptotics. The outcome fully confirms our earlier findings. Moreover, we show that the Regge parametrization proposed by these authors for the region above 1.4 GeV violates crossing symmetry: Their ansatz is not consistent with the behaviour observed at low energies.Comment: Added more material, mostly in Sects. 7, 8 and 9, in support of the same conclusions. Latex, 28 pages, 3 figure