Search results for "Scattering amplitude"

The Crossing Symmetric Bethe-Salpeter Equation

1972

As you may recall from the lectures of Prof. Sand-has [1], in non-relativistic quantum theory,the scattering amplitude satisfies the Lippmann-Schwinger equation, $$T = V + V{G_o}T$$ (1) It can be explicitly shown that if V=V+, T satisfies the elastic unitarity relation, Im T=TT+.

Low Energy Behaviour of the Phase Shifts for Velocity-Dependent Potentials

1973

Study of thepd→pdηreaction

2007

A study of the pd{yields}pd{eta} reaction in the energy range where the recent data from Uppsala are available is done in the two-step model of {eta} production including the final state interaction. The {eta}-d final state interaction is incorporated through the solution of the Lippmann Schwinger equation using an elastic scattering matrix element, T{sub {eta}}{sub d{yields}}{sub {eta}}{sub d}, which is required to be half off-shell. It is written in a factorized form, with an off-shell form factor multiplying an on-shell part given by an effective range expansion up to the fourth power in momentum. The parameters of this expansion have been taken from an existing recent relativistic Fadde…

Description of thef2(1270),ρ3(1690),f4(2050),ρ5(2350), andf6(2510)resonances as multi-ρ(770)states

2010

In a previous work regarding the interaction of two $\ensuremath{\rho}(770)$ resonances, the ${f}_{2}(1270)$ (${J}^{PC}={2}^{++}$) resonance was obtained dynamically as a two-$\ensuremath{\rho}$ molecule with a very strong binding energy, 135 MeV per $\ensuremath{\rho}$ particle. In the present work we use the $\ensuremath{\rho}\ensuremath{\rho}$ interaction in spin 2 and isospin 0 channel to show that the resonances ${\ensuremath{\rho}}_{3}(1690)$ (${3}^{--}$), ${f}_{4}(2050)$ (${4}^{++}$), ${\ensuremath{\rho}}_{5}(2350)$ (${5}^{--}$), and ${f}_{6}(2510)$ (${6}^{++}$) are basically molecules of increasing number of $\ensuremath{\rho}(770)$ particles. We use the fixed center approximation o…

Scattering of unstable particles in a finite volume: The case ofπρscattering and thea1(1260)resonance

2012

We present a way to evaluate the scattering of unstable particles quantized in a finite volume with the aim of extracting physical observables for infinite volume from lattice data. We illustrate the method with the $\ensuremath{\pi}\ensuremath{\rho}$ scattering which generates dynamically the axial-vector ${a}_{1}(1260)$ resonance. Energy levels in a finite box are evaluated both considering the $\ensuremath{\rho}$ as a stable and unstable resonance and we find significant differences between both cases. We discuss how to solve the problem to get the physical scattering amplitudes in the infinite volume, and hence phase shifts, from possible lattice results on energy levels quantized insid…

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude

2015

In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the spectrum to a non-standard infinite-volume quantity, denoted ${\cal K}_{{\rm df},3}$. Here we present the relation between ${\cal K}_{{\rm df},3}$ and ${\cal M}_3$. We then discuss briefly how our now completed formalism can be practically implemented to extract ${\cal M}_3$ from the finite-volume energy spectrum.

Inverse amplitude method in pi pi scattering in chiral perturbation theory to two loops

2002

The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.

Chiral dynamics of thepwave inK−pand coupled states

2002

We perform an evaluation of the p-wave amplitudes of meson-baryon scattering in the strangeness $S=\ensuremath{-}1$ sector starting from the lowest order chiral Lagrangians and introducing explicitly the ${\ensuremath{\Sigma}}^{*}$ field with couplings to the meson-baryon states obtained using SU(6) symmetry. The $N/D$ method of unitarization is used, equivalent, in practice, to the use of the Bethe-Salpeter equation with a cutoff. The procedure leaves no freedom for the p-waves once the s-waves are fixed and thus one obtains genuine predictions for the p-wave scattering amplitudes, which are in good agreement with experimental results for differential cross sections, as well as for the wid…

The threshold behaviour of partial wave scattering amplitudes and theN/D-method

1964

It is shown that in partial wave dispersion relations the weight function on the unphysical cut must have a certain number of zeros in order to permit the correct threshold behaviour of the amplitude. Assuming a solution — not necessarily with correct threshold behaviour — of the once-subtractedN/D-equations to exist, the role of the subtraction parameters in repeatedly subtractedN/D equations is studied with particular reference to the threshold behaviour.

EXTRACTION OF THE Λ(1405) POLES FROM π0Σ0 PHOTOPRODUCTION DATA

2014

In this contribution we review a work where we showed how to extract the position of the two Λ(1405) poles from experimental photoproduction data which have been measured recently in the γp → K+π0Σ0 reaction at Jefferson Lab. Using a potential motivated by chiral dynamics but with free parameters, we solve the Bethe Salpeter equation in the coupled channels [Formula: see text] and πΣ in isospin I=0 and parameterize the amplitude for the photonuclear reaction in terms of a linear combination of the πΣ → πΣ and [Formula: see text] scattering amplitudes in I=0, with a different linear combination for each energy. Good fits to the data are obtained which lead to two poles at 1385 - 68i MeV and…