Search results for "Lippmann–Schwinger equation"
showing 6 items of 6 documents
Couplings in coupled channels versus wave functions in the case of resonances: Application to the twoΛ(1405)states
2011
In this paper we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on-shell approach for the scattering matrix, commonly used, is also obtained in quantum mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coupled channel approach, as bound states of one bound channel, which decays into open ones. It also pr…
Doubly charmed exotic mesons: A gift of nature?
2011
Article history: We study doubly charmed exotic states by solving the scattering problem of two D mesons. Our results point to the existence of a stable isoscalar doubly charmed meson with quantum numbers (I) J P = (0)1 + . We perform a thorough comparison to the results obtained within the hyperspherical harmonic formalism. Such exotic states could be measured at LHC and RHIC. Their experimental observation would,
Study of meson production in nuclei near threshold
2009
We present a study of the η production at low energies in pd collision with 3He and pd nuclear systems in the final state. The η production mechanism is described by a two-step model and the final state interactions are included fully. The η - d and η - 3He final state interactions are incorporated through the solution of the Lippmann Schwinger equation for a half off-shell η - AT-matrix. For η - d this t -matrix is written in a factorized form, with an off-shell form factor multiplying an on-shell part having the scattering length representation. The p - d final state interaction is included by multiplying the production matrix element by the inverse of the Jost function which includes th…
Two pion decay of the Roper resonance
2002
We evaluate the two pion decay of the Roper resonance in a model where explicit re-scattering of the two final pions is accounted for by the use of unitarized chiral perturbation theory. Our model does not include an explicit $\epsilon$ or $\sigma$ scalar-isoscalar meson decay mode, instead it generates it dynamically by means of the pion re-scattering. The two ways, explicit or dynamically generated, of introducing this decay channel have very different amplitudes. Nevertheless, through interference with the other terms of the model we are able to reproduce the same phenomenology as models with explicit consideration of the $\epsilon$ meson.
Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f[sub 0](980), a[sub 0](980) scalar mesons
1998
We use a nonperturbative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f0 and a0 resonances. The ππ→ππ, ππ→KK phase shifts and inelasticities in the T=0 scalar channel are well reproduced as well as the π0η and KK mass distributions in the T=1 channel. Furthermore, the total and partial decay widths of the f0 and a0 resonances are properly reproduced. The results seem to indicate that chiral symmetry constraint…
Relativistic scattering theory of charged spinless particles
1986
In the context of a relativistic quantum mechanics we discuss the scattering of two and three charged spinless particles. The corresponding transition operators are shown to satisfy four-dimensional Lippmann-Schwinger and eight-dimensional Faddeev-type equations, respectively. A simplified model of two particles with Coulomb interaction can be solved exactly. We calculate: (i) The partial waveS-matrix from which we extract the bound state spectrum. The latter agrees with a fourth-order result of Schwinger, (ii) The full scattering amplitude which in the weakfield limit coincides with the expression derived by Fried et al. from eikonalized QED.