Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space

For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q^2. At JLab domain (Q^2=10 GeV^2/c^2), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.Comment: 8 pages, 7 figures, to be published in Eur. Phys. J. A; Reference [15] is adde

Masses and widths of scalar-isoscalar multi-channel resonances from data analysis

Peculiarities of obtaining parameters for broad multi-channel resonances from data are discussed analyzing the experimental data on processes $\pi\pi\to\pi\pi,K\bar{K}$ in the $I^GJ^{PC}=0^+0^{++}$ channel in a model-independent approach based on analyticity and unitarity and using an uniformization procedure. We show that it is possible to obtain a good description of the $\pi\pi$ scattering data from the threshold to 1.89 GeV with parameters of resonances cited in the PDG tables as preferred. However, in this case, first, representation of the $\pi\pi$ background is unsatisfactory; second, the data on the coupled process $\pi\pi\to K\bar{K}$ are not well described even qualitatively above 1.15 GeV when using the resonance parameters from the only $\pi\pi$ scattering analysis. The combined analysis of these coupled processes is needed, which is carried out satisfactorily. Then both above-indicated flaws, related to the analysis of solely the $\pi\pi$-scattering, are cured. The most remarkable change of parameters with respect to the values of only $\pi\pi$ scattering analysis appears for the mass of the $f_0 (600)$ which is now in some accordance with the Weinberg prediction on the basis of mended symmetry and with an analysis using the large-$N_c$ consistency conditions between the unitarization and resonance saturation. The obtained $\pi\pi$-scattering length $a_0^0$ in case when we restrict to the analysis of the $\pi\pi$ scattering or consider so-called A-solution (with a lower mass and width of $f_0(600)$ meson) agrees well with prediction of chiral perturbation theory (ChPT) and with data extracted at CERN by the NA48/2 Collaboration from the analysis of the $K_{e4}$ decay and by the DIRAC Collaboration from the measurement of the $\pi^+\pi^-$ lifetime.Comment: 21 pages, 3 figures, 6 table

The Field Theory of Gravitation and The Rest Mass of Particles

It is shown in this work that all free physical fields should have a nonzero rest mass according to the field theory of gravitation.Comment: 4 page

Estimates of the optimal density and kissing number of sphere packings in high dimensions

The problem of finding the asymptotic behavior of the maximal density of sphere packings in high Euclidean dimensions is one of the most fascinating and challenging problems in discrete geometry. One century ago, Minkowski obtained a rigorous lower bound that is controlled asymptotically by $1/2^d$, where $d$ is the Euclidean space dimension. An indication of the difficulty of the problem can be garnered from the fact that exponential improvement of Minkowski's bound has proved to be elusive, even though existing upper bounds suggest that such improvement should be possible. Using a statistical-mechanical procedure to optimize the density associated with a "test" pair correlation function and a conjecture concerning the existence of disordered sphere packings [S. Torquato and F. H. Stillinger, Experimental Math. {\bf 15}, 307 (2006)], the putative exponential improvement was found with an asymptotic behavior controlled by $1/2^{(0.77865...)d}$. Using the same methods, we investigate whether this exponential improvement can be further improved by exploring other test pair correlation functions correponding to disordered packings. We demonstrate that there are simpler test functions that lead to the same asymptotic result. More importantly, we show that there is a wide class of test functions that lead to precisely the same exponential improvement and therefore the asymptotic form $1/2^{(0.77865...)d}$ is much more general than previously surmised.Comment: 23 pages, 4 figures, submitted to Phys. Rev.

Atypical hemolytic uremic syndrome : update on the complement system and what is new

Atypical hemolytic uremic syndrome (aHUS) is a rare disease of microangiopathic hemolytic anemia, thrombocytopenia, and predominant renal impairment. It is characterized by the absence of Shiga toxin-producing bacteria as a triggering factor. During the last decade, aHUS has been demonstrated to be a disorder of the complement alternative pathway dysregulation, as there is a growing list of mutations and polymorphisms in the genes encoding the complement regulatory proteins that alone or in combination may lead to aHUS. Approximately 60% of aHUS patients have so-called 'loss-of-function' mutations in the genes encoding the complement regulatory proteins, which normally protect host cells from complement activation: complement factor H (CFH), factor I (CFI) and membrane cofactor protein (MCP or CD46), or have 'gain-of-function' mutations in the genes encoding the complement factor B or C3. In addition, approximately 10% of aHUS patients have a functional CFH deficiency due to anti-CFH antibodies. Recent advances in understanding the pathogenesis of aHUS have led to a revised classification of the syndrome. Normal plasma levels of CFH and CFI do not preclude the presence of a mutation in these genes. Further, genotype-phenotype correlations of aHUS have clinical significance in predicting renal recovery and transplant outcome. Therefore, it is important to make a comprehensive analysis and perform genetic screening of the complement system in patients with aHUS to allow a more precise approach, especially before transplantation. This may also provide opportunities for more specific treatments in the near future, as complement inhibition could represent a therapeutic target in these patients who have a considerably poor prognosis in terms of both mortality and progression to end-stage renal disease and a great risk of disease recurrence after transplantation

The Red Queen visits Minkowski Space

When Alice went `Through the Looking Glass' [1], she found herself in a situation where she had to run as fast as she could in order to stay still. In accordance with the dictum that truth is stranger than fiction, we will see that it is possible to find a situation in special relativity where running towards one's target is actually counter-productive. Although the situation is easily analysed algebraically, the qualitative properties of the analysis are greatly illuminated by the use of space-time diagrams

An X-ray absorption analysis of the high-velocity system in NGC 1275

We present an X-ray absorption analysis of the high-velocity system (HVS) in NGC 1275 using results from a deep 200 ks Chandra observation. We are able to describe the morphology of the HVS in more detail than ever before. We present an HST image for comparison, and note close correspondence between the deepest X-ray absorption and the optical absorption. A column density map of the HVS shows an average column density NH of 1x10^21 cm^-2 with a range from ~5x10^20 to 5x10^21 cm^-2. From the NH map we calculate a total mass for the absorbing gas in the HVS of (1.32+-0.05)x10^9 solar masses at solar abundance. 75 per cent of the absorbing mass is contained in the four regions of deepest absorption. We examine temperature maps produced by spectral fitting and find no direct evidence for shocked gas in the HVS. Using deprojection methods and the depth of the observed absorption, we are able to put a lower limit on the distance of the HVS from the nucleus of 57 kpc, showing that the HVS is quite separate from the body of NGC 1275.Comment: 6 pages, 5 colour figures, accepted by MNRA

Stable quark stars beyond neutran stars : can they account for the missing matter ?

The structure of a spherically symmetric stable dark 'star' is discussed, at zero temperature, containing 1) a core of quarks in the deconfined phase and antileptons 2) a shell of hadrons in particular $n$, $p$, $\Lambda$ and $\Sigma^-$ and leptons or antileptons and 3) a shell of hydrogen in the superfluid phase. If the superfluid hydrogen phase goes over into the electromagnetic plasma phase at densities well below one atom / $(10 fm)^{3}$, as is usually assumed, the hydrogen shell is insignificant for the mass and the radius of the 'star'. These quantities are then determined approximatively : mass = 1.8 solar masses and radius = 9.2 km. On the contrary if densities of the order of one atom / $(10 fm)^{3}$ do form a stable hydrogen superfluid phase, we find a large range of possible masses from 1.8 to 375 solar masses. The radii vary accordingly from 9 to 1200 km.Comment: 5 pages, 2 figures, contribution to Strange Quark Matter conference, Frankfurt, Germany, Sept. 200

A Potential Foundation for Emergent Space-Time

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.Comment: The paper was originally titled "The Physics of Events: A Potential Foundation for Emergent Space-Time". We changed the title (and abstract) to be more direct when the paper was accepted for publication at the Journal of Mathematical Physics. 24 pages, 15 figure