Search results for "SINGULARITY"
showing 10 items of 352 documents
Critical properties and finite-size effects of the five-dimensional Ising model
1985
Monte Carlo calculations of the thermodynamic properties (energy, specific heat, magnetization suceptibility, renormalized coupling) of the nearest-neighbour Ising ferromagnet on a five-dimensional hypercubic lattice are presented and analyzed. Lattices of linear dimensionsL=3, 4, 5, 6, 7 with periodic boundary conditions are studied, and a finite size scaling analysis is performed, further confirming the recent suggestion thatL does not scale with the correlation length ξ (the temperature variation of which near the critical temperatureT c is ξ∝|1-T/T c |−1/2), but rather with a “thermodynamic length”l (withl∝|1-T/T c |−2/d ,d=5 here). The susceptibility (extrapolated to the thermodynamic …
A covariant constituent-quark formalism for mesons
2014
Using the framework of the Covariant Spectator Theory (CST) [1] we are developing a covariant model formulated in Minkowski space to study mesonic structure and spectra. Treating mesons as effective $q\bar{q}$ states, we focused in [2] on the nonrelativistic bound-state problem in momentum space with a linear confining potential. Although integrable, this kernel has singularities which are difficult to handle numerically. In [2] we reformulate it into a form in which all singularities are explicitely removed. The resulting equations are then easier to solve and yield accurate and stable solutions. In the present work, the same method is applied to the relativistic case, improving upon the r…
Electronic States in Mesoscopic Systems
1992
Abstract Electronic states in disordered systems are studied within the Anderson model of localization. By means of the Green's function technique we derive the transmission coefficient for electronic states through mesoscopic samples. The transmission coefficient is shown to be not self-averaging due to strong spatial fluctuations of the amplitude of the eigenstates, which are obtained by direct diagonalization of the respective secular matrices. The wave functions display a multifractal behaviour, characterized by the set of generalized fractal dimensions and the singularity spectrum of the fractal measure.
Power law singularities inn-vector models
2012
Power law singularities and critical exponents in n-vector models are considered within a theoretical approach called GFD (grouping of Feynman diagrams) theory. It is discussed how possible values of the critical exponents can be related to specific n-vector models in this approach. A good agreement with the estimates of the perturbative renormalization group (RG) theory can be obtained. Predictions for corrections to scaling of the perturbative RG and GFD approaches are different. A nonperturbative proof is provided, supporting corrections to scaling of the GFD theory. Highly accurate experimental data very close to the λ-transition point in liquid helium, as well as the Goldstone mode sin…
Erratum to: “Processes with a t-channel singularity in the physical region: finite beam sizes make cross sections finite”
2003
This affects the normalization of the “non-standard” cross-section, increasing it by thesame factor of two. As a consequence, Eq. (47), Fig. 3 and the estimate of the number ofneutrinos after Eq. (47) is modified accordingly.We are grateful to C. Dams and R. Kleiss for correspondencethat helped to uncoverthiserror.
Search for the Σ⁎ state in Λc+→π+π0π−Σ+ decay by triangle singularity
2019
Abstract A Σ ⁎ resonance with spin-parity J P = 1 / 2 − and mass in the vicinity of the K ¯ N threshold has been predicted in the unitary chiral approach and inferred from the analysis of CLAS data on the γ p → K + π 0 Σ 0 reaction. In this work, based on the dominant Cabibbo favored weak decay mechanism, we perform a study of Λ c + → π + π 0 Σ ⁎ with the possible Σ ⁎ state decaying into π − Σ + through a triangle diagram. This process is initiated by Λ c + → π + K ¯ ⁎ N , then the K ¯ ⁎ decays into K ¯ π and K ¯ N produce the Σ ⁎ through a triangle loop containing K ¯ ⁎ N K ¯ which develops a triangle singularity. We show that the π − Σ + state is generated from final state interaction of …
Linear confinement in momentum space: singularity-free bound-state equations
2014
Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs not only in the relativistic case but also in the nonrelativistic Schr\"odinger equation where this problem can be studied more easily. For the linear confining interaction the singularity reduces to one of Cauchy principal value form. Although this singularity is integrable, it still makes accurate numerical solutions difficult. We show that this principal value singularity can be eliminated by means of a subtraction method. The resulting equation is much…
On the chiral covariant approach to ρρ scattering
2017
We examine in detail a recent work (D.~G\"ulmez, U.-G.~Mei\ss ner and J.~A.~Oller, Eur. Phys. J. C 77:460 (2017)), where improvements to make $\rho\rho$ scattering relativistically covariant are made. The paper has the remarkable conclusion that the $J=2$ state disappears with a potential which is much more attractive than for $J=0$, where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full $\rho$ propagators, and we show that they do not develop singula…
The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory
2008
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into account, the results of dispersion theory and effective field theory are not inconsistent.
The two-loop three-point functions. General massive cases
1992
Abstract We present a calculation of the two-loop three-point scalar functions for the two overlapping topologies. These are the master functions for the ladder and the crossed ladder graphs. We also present a method for the extraction of possible (on-shell) mass singularities.