J. A. Oller

Chiral dynamics in the presence of bound states: kaon–nucleon interactions revisited

Abstract We study the S-wave kaon–nucleon interactions for strangeness S =−1 in a novel relativistic chiral unitary approach based on coupled channels. Dispersion relations are used to perform the necessary resummation of the lowest order relativistic chiral Lagrangian. A good description of the data in the K − p , πΣ and πΛ channels is obtained. We show how this method can be systematically extended to higher orders, emphasizing its applicability to any scenario of strong self-interactions where the perturbative series diverges even at low energies. Discussions about the differences to existing approaches employing pseudo-potentials in a regulated Lippmann–Schwinger equation are included. Finally, we describe the resonance content of our meson–baryon amplitudes and discuss its nature.

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a nonperturbative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangians. 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 \sigma,f_0 and a_0 resonances. The \pi\pi-->\pi\pi, \pi\pi-->K\bar{K} phase shifts and inelasticities in the T=0 scalar channel are well reproduced as well as the \pi^-\eta and K^-K^0 mass distributions in the T=1 channel. Furthermore, the total and partial decay widths of the f_0 and a_0 resonances are properly reproduced including also the decay into the \gamma\gamma channel. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below \sqrt(s)=1.2 GeV.We use a non-perturbative 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 strong decay widths of the f0 and a0 resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below s ≃ 1.2 GeV.

Chiral dynamics of the two Lambda(1405) states

Using a chiral unitary approach for the meson--baryon interactions, we show that two octets of J^{\pi}=1/2^- baryon states, which are degenerate in the limit of exact SU(3) symmetry, and a singlet are generated dynamically. The SU(3) breaking produces the splitting of the two octets, resulting in the case of strangeness S=-1 in two poles of the scattering matrix close to the nominal \Lambda(1405) resonance. These poles are combinations of the singlet state and the octets. We show how actual experiments see just one effective resonance shape, but with properties which change from one reaction to another.

N/D description of two meson amplitudes and chiral symmetry

The most general structure of an elastic partial wave amplitude when the unphysical cuts are neglected is deduced in terms of the N/D method. This result is then matched to lowest order,

The chiral representation of the

{\mathcal{O}}(p^2)

\pi N

, Chiral Perturbation Theory(

scattering amplitude and the pion-nucleon sigma term

\chi

Nonperturbative approach to effective chiral Lagrangians and meson interactions

PT) and to the exchange (consistent with chiral symmetry) of resonances in the s-channel. The extension of the method to coupled channels is also given. Making use of the former formalism, the

Chiral unitary approach to meson meson and meson - baryon interactions and nuclear applications

\pi\pi

S-wave Kπ scattering in chiral perturbation theory with resonances

and