Analytical approach to chiral symmetry breaking in Minkowsky space

The mass gap equation for spontaneous chiral symmetry breaking is studied directly in Minkowsky space. In hadronic physics, spontaneous chiral symmetry breaking is crucial to generate a constituent mass for the quarks, and to produce the Partially Conserved Axial Current theorems, including a small mass for the pion. Here a class of finite kernels is used, expanded in Yukawa interactions. The Schwinger-Dyson equation is solved with an analytical approach. This improves the state of the art of solving the mass gap equation, which is usually solved with the equal-time approximation or with the Euclidean approximation. The mapping from the Euclidean space to the Minkowsky space is also illustrated.Comment: 7 pages, 3 figure

Weak-field approximation of effective gravitational theory with local Galilean invariance

We examine the weak-field approximation of locally Galilean invariant gravitational theories with general covariance in a $(4+1)$-dimensional Galilean framework. The additional degrees of freedom allow us to obtain Poisson, diffusion, and Schr\"odinger equations for the fluctuation field. An advantage of this approach over the usual $(3+1)$-dimensional General Relativity is that it allows us to choose an ansatz for the fluctuation field that can accommodate the field equations of the Lagrangian approach to MOdified Newtonian Dynamics (MOND) known as AQUAdratic Lagrangian (AQUAL). We investigate a wave solution for the Schr\"odinger equations.Comment: 15 page

Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galilean particle interacting with an external electric field.Comment: 23 pages, 2 table

Path-integral quantization of Galilean Fermi fields

The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. Firstly, we review the five-dimensional approach to the Galilean Dirac equation, which leads to the Levy-Leblond equations, and define the Galilean generating functional and Green's functions for positive- and negative-energy/mass solutions. Then, as an example of interactions, we consider the quartic self-interacting potential ${\lambda} (\bar{\Psi} {\Psi})^2$, and we derive expressions for the 2- and 4-point Green's functions. Our results are compatible with those found in the literature on non-relativistic many-body systems. The extended manifold allows for compact expressions of the contributions in $(3+1)$ space-time. This is particularly apparent when we represent the results with diagrams in the extended $(4+1)$ manifold, since they usually encompass more diagrams in Galilean $(3+1)$ space-time.Comment: LATEX file, 27 pages, 8 figures; typos in the journal version are removed, equation (1) in Introduction is correcte

αs\alpha_s from τ\tau decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion

We consider the determination of $\alpha_s$ from $\tau$ hadronic decays, by investigating the contour-improved (CI) and the fixed-order (FO) renormalization group summations in the frame of a new perturbation expansion of QCD, which incorporates in a systematic way the available information about the divergent character of the series. The new expansion functions, which replace the powers of the coupling, are defined by the analytic continuation in the Borel complex plane, achieved through an optimal conformal mapping. Using a physical model recently discussed by Beneke and Jamin, we show that the new CIPT approaches the true results with great precision when the perturbative order is increased, while the new FOPT gives a less accurate description in the regions where the imaginary logarithms present in the expansion of the running coupling are large. With the new expansions, the discrepancy of 0.024 in $\alpha_s(m_\tau^2)$ between the standard CI and FO summations is reduced to only 0.009. From the new CIPT we predict $\alpha_s(m_\tau^2)= 0.320 ^{+0.011}_{-0.009}$, which practically coincides with the result of the standard FOPT, but has a more solid theoretical basis

On the QCD perturbative expansion for e^+ e^- --> hadrons

We study the perturbative QCD series for the hadronic width of the Z boson. We sum a class of large ``pi^2 terms'' and reorganize the series so as to minimize ``renormalon'' effects. We also consider the renormalization scheme-scale ambiguity of the perturbative results. We find that, with three nontrivial known terms in the perturbative expansion, the treatment of the pi^2 terms is quite important, while renormalon effects are less important. The measured hadronic width of the Z is often used to determine the value of alpha_s(M_Z^2). A standard method is to use the perturbative expansion for the width truncated at order alpha_s^3 in the MS-bar scheme with scale mu = M_Z. We estimate that the determined value of alpha_s(M_Z^2) should be increased by 0.6% compared to the value extracted with this standard method. After this adjustment for pi^2 and renormalon effects, we estimate that the uncertainty in alpha_s(M_Z^2) arising from QCD theory is about 0.4%. This is, of course, much less than the experimental uncertainty of about 5%.Comment: 23 pages, REVTEX3.0, uses epsf.tex to insert figures; with 6 figures in encapsulated postscript for

Bilocal expansion of the Borel amplitude and the hadronic tau decay width

The singular part of Borel transform of a QCD amplitude near the infrared renormalon can be expanded in terms of higher order Wilson coefficients of the operators associated with the renormalon. In this paper we observe that this expansion gives nontrivial constraints on the Borel amplitude that can be used to improve the accuracy of the ordinary perturbative expansion of the Borel amplitude. In particular, we consider the Borel transform of the Adler function and its expansion around the first infrared renormalon due to the gluon condensate. Using the next-to-leading order Wilson coefficient of the gluon condensate operator, we obtain an exact constraint on the Borel amplitude at the first IR renormalon. We then extrapolate, using judiciously chosen conformal transformations and Pade approximants, the ordinary perturbative expansion of the Borel amplitude in such a way that this constraint is satisfied. This procedure allows us to predict the $O(\alpha_s^4)$ coefficient of the Adler function, which gives a result consistent with the estimate by Kataev and Starshenko using a completely different method. We then apply this improved Borel amplitude to the tau decay width, and obtain the strong coupling constant $\alpha_s(M_Z) =0.1193 \pm 0.0007_{exp.} \pm 0.0010_{EW+CKM} \pm 0.0009_{meth.} \pm 0.0003_{evol.}$. We then compare this result with those of other resummation methods.Comment: 30 pages, 4 eps-figures, revtex; version as appears in PRD; no major changes; more careful rounding of some number

Parametric exploration of the liver by magnetic resonance methods

MRI, as a completely noninvasive technique, can provide quantitative assessment of perfusion, diffusion, viscoelasticity and metabolism, yielding diverse information about liver function. Furthermore, pathological accumulations of iron and lipids can be quantified. Perfusion MRI with various contrast agents is commonly used for the detection and characterization of focal liver disease and the quantification of blood flow parameters. An extended new application is the evaluation of the therapeutic effect of antiangiogenic drugs on liver tumours. Novel, but already widespread, is a histologically validated relaxometry method using five gradient echo sequences for quantifying liver iron content elevation, a measure of inflammation, liver disease and cancer. Because of the high perfusion fraction in the liver, the apparent diffusion coefficients strongly depend on the gradient factors used in diffusion-weighted MRI. While complicating analysis, this offers the opportunity to study perfusion without contrast injection. Another novel method, MR elastography, has already been established as the only technique able to stage fibrosis or diagnose mild disease. Liver fat content is accurately determined with multivoxel MR spectroscopy (MRS) or by faster MRI methods that are, despite their widespread use, prone to systematic error. Focal liver disease characterisation will be of great benefit once multivoxel methods with fat suppression are implemented in proton MRS, in particular on high-field MR systems providing gains in signal-to-noise ratio and spectral resolution

Polygenic transmission disequilibrium confirms that common and rare variation act additively to create risk for autism spectrum disorders

Autism spectrum disorder (ASD) risk is influenced by common polygenic and de novo variation. We aimed to clarify the influence of polygenic risk for ASD and to identify subgroups of ASD cases, including those with strongly acting de novo variants, in which polygenic risk is relevant. Using a novel approach called the polygenic transmission disequilibrium test and data from 6,454 families with a child with ASD, we show that polygenic risk for ASD, schizophrenia, and greater educational attainment is over-transmitted to children with ASD. These findings hold independent of proband IQ. We find that polygenic variation contributes additively to risk in ASD cases who carry a strongly acting de novo variant. Lastly, we show that elements of polygenic risk are independent and differ in their relationship with phenotype. These results confirm that the genetic influences on ASD are additive and suggest that they create risk through at least partially distinct etiologic pathways