Search results for "singular"
showing 10 items of 589 documents
Triangle Singularity as the Origin of the a1(1420)
2021
The COMPASS Collaboration experiment recently discovered a new isovector resonancelike signal with axial-vector quantum numbers, the a 1 ( 1420 ) , decaying to f 0 ( 980 ) π . With a mass too close to and a width smaller than the axial-vector ground state a 1 ( 1260 ) , it was immediately interpreted as a new light exotic meson, similar to the X , Y , Z states in the hidden-charm sector. We show that a resonancelike signal fully matching the experimental data is produced by the decay of the a 1 ( 1260 ) resonance into K * ( → K π ) K ¯ and subsequent rescattering through a triangle singularity into the coupled f 0 ( 980 ) π channel. The amplitude for this process is calculated using a new a…
All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order
2019
We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in D space-time dimensions. These integrals evaluate to Q-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless 2→3 scattering process, thereby opening up a ne…
Fluctuations in mesoscopic systems
1992
Abstract Electronic wavefunctions in weakly disordered systems have been studied within the Anderson model of localization. The eigenstates calculated by means of the Lanczos diagonalization algorithm display characteristic spatial fluctuations that can be described by a multifractal analysis. For increasing disorder or energy the observed curdling of the wavefunction reflects the stronger localization, but no exponential decay can be observed. This is reflected in the set of generalized fractal dimensions and the singularity spectrum of the fractal measure.
Disentangling boson peaks and Van Hove singularities in a model glass
2018
Using the example of a two-dimensional macroscopic model glass in which the interparticle forces can be precisely measured, we obtain strong hints for resolving a controversy concerning the origin of the anomalous enhancement of the vibrational spectrum in glasses (boson peak). Whereas many authors attribute this anomaly to the structural disorder, some other authors claim that the short-range order, leading to washed-out Van Hove singularities, would cause the boson-peak anomaly. As in our model system, the disorder-induced and shortrange--order-induced features can be completely separated, we are able to discuss the controversy about the boson peak in real glasses in a new light. Our find…
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 …