Search results for "singular"
showing 10 items of 589 documents
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.
Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: Comparison with the BSSN formulation in spherical symmetry
2014
We adopt a reference-metric approach to generalize a covariant and conformal version of the Z4 system of the Einstein equations. We refer to the resulting system as ``fully covariant and conformal", or fCCZ4 for short, since it is well suited for curvilinear as well as Cartesian coordinates. We implement this fCCZ4 formalism in spherical polar coordinates under the assumption of spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method and show that our code can evolve both vacuum and non-vacuum spacetimes without encountering instabilities. Our method does not require regularization of the equations to handle coordinate singularities, nor does it depend on constraint-preservi…
Trapping Horizons as inner boundary conditions for black hole spacetimes
2007
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.
Palatini $f(R)$ Black Holes in Nonlinear Electrodynamics
2011
The electrically charged Born-Infeld black holes in the Palatini formalism for $f(R)$ theories are analyzed. Specifically we study those supported by a theory $f(R)=R\pm R^2/R_P$, where $R_P$ is Planck's curvature. These black holes only differ from their General Relativity counterparts very close to the center, but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model $f(R)=R - R^2/R_P$ the singularity is shifted to a finite radius, $r_+$, and the Kretschmann scalar diverges only as $1/(r-r_+)^{2}$.
Triangle mechanism in τ → f1(1285)πντ decay
2018
Abstract We show that the τ − decay into f 1 ( 1285 ) π − ν τ is dominated by a triangle loop mechanism with K ⁎ , K ¯ ⁎ and K (or K ¯ ) as internal lines, which manifests a strong enhancement reminiscent of a nearby singularity present in the narrow K ⁎ limit and the near K ¯ ⁎ K ⁎ threshold of the internal K ⁎ propagators. The f 1 ( 1285 ) is then produced by its coupling to the K ⁎ K ¯ and K ¯ ⁎ K which is obtained from a previous model where this resonance was dynamically generated as a molecular K ⁎ K ¯ (or K ¯ ⁎ K ) state using the techniques of the chiral unitary approach. We make predictions for the f 1 π mass distribution which significantly deviates from the phase-space shape, due…
On the singular behaviour of scattering amplitudes in quantum field theory
2014
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
Triangle singularity enhancing isospin violation in ${\bar{{\rm{B}}}}_{{\rm{s}}}^{0}\to {\rm{J}}/{\rm{\psi }}{\pi }^{0}{{\rm{f}}}_{0}(980)$
2018
We perform calculations for the and reactions, showing that the first is isospin-suppressed while the second is isospin-allowed. The reaction proceeds via a triangle mechanism, with , followed by the decay K* → Kπ and a further fusion of into the or a0(980). We show that the mechanism develops a singularity around the π0 f0(980) or π0 a0(980) invariant mass of 1420 MeV, where the π0 f0 and π0 a0 decay modes are magnified and also the ratio of π0 f0 to π0 a0 production. Using experimental information for the decay, we are able to obtain absolute values for the reactions studied which fall into the experimentally accessible range. The reactions proposed and the observables evaluated, when con…