The $\sigma K$ coupling in the chiral unitary approach and the isoscalar $\bar{K}N$, $\bar{K}A$ interaction

Abstract

We evaluate the "$\sigma$" exchange contribution to the $\bar{K}N\to \bar{K}N$ scattering within a chiral unitary approach. We show that the chiral transition potentials for $\pi \pi \to K\bar{K}$ in the $t$-channel lead to a "$\sigma$" contribution that vanishes in the $\bar{K}$ forward direction and, hence, would produce a null "$\sigma$" exchange contribution to the $K^{-}$ optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading order chiral Lagrangian gives an I=0 $\pi \pi \to K\bar{K}$ amplitude proportional to the squared momentum transfer, $q^2$. This finding poses questions on the meaning or the origin of "$\sigma$" exchange potentials used in relativistic mean field approaches to the $K^{-}$ nuclear selfenergy. This elementary "$\sigma$" exchange potential in $\bar{K}N\to \bar{K}N$ is compared to the Weinberg-Tomozawa term and is found to be smaller than present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data.

arXiv commentnew channels and higher order contributions included. Published version

References in corpus (49)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Chiral dynamics in the presence of bound states: kaon-nucleon interactions revisited
• Non perturbative chiral approach to s-wave \bar{K}N interactions
• ππscattering
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• Chiral Dynamics of the Two Λ(1405) States
• Chiral Dynamics and the Low Energy Kaon-Nucleon Interaction
• Meson-Meson interaction in a non-perturbative chiral approach
• N/D Description of Two Meson Amplitudes and Chiral Symmetry
• Mass and width of the lowest resonance in QCD
• Roy equation analysis of pi pi scattering
• Dynamically Generated Open and Hidden Charm Meson Systems
• The properties of \bar{K} in the nuclear medium
• Low lying S=-1 excited baryons and chiral symmetry
• Effective Kbar N interaction based on chiral SU(3) dynamics
• Peripheral NN-Scattering: Role of Delta-Excitation, Correlated Two-Pion and Vector Meson Exchange
• Nuclear kaon dynamics
• Quark mass dependence of s-wave baryon resonances
• $S=-1$ Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory and the $S_{01}-$ $\Lambda$(1405) and $-\Lambda$(1670) Resonances
• K^- p scattering length from scattering experiments
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Evidence for the two pole structure of the Lambda(1405) resonance
• Flavor SU(3) breaking effects in the chiral unitary model for meson-baryon scatterings
• Extended-soft-core Baryon-Baryon Model II. Hyperon-Nucleon Interaction
• Chiral dynamics of kaon-nucleon interactions, revisited
• On the Strangeness -1 S-wave Meson-Baryon Scattering
• Medium Modified Cross Sections, Temperature and Finite Momentum Effects for Antikaon Production in Heavy-Ion Collisions
• Study of chirally motivated low-energy $K^{-}$ optical potentials
• $\bar{K}$ nuclear bound states in a dynamical model
• Surprises in threshold antikaon-nucleon physics
• $K^{-}$ - nucleus relativistic mean field potentials consistent with kaonic atoms
• Deeply bound levels in kaonic atoms
• $\sigma$ Exchange in the NN Interaction within the Chiral Unitary Approach
• SU(6) Extension of the Weinberg-Tomozawa Meson-Baryon Lagrangian
• The radiative decay phi - gamma pi pi in a coupled channel model and the structure of f0(980)
• Meson exchange in the weak decay of Lambda hypernuclei and the Gamma_n/Gamma_p ratio
• Pion-Nucleon Sigma Term in Lattice QCD
• Strange tribaryons as Kbar-mediated dense nuclear systems
• A critical analysis on deeply bound kaonic states in nuclei
• Widths of $\bar{K}$-nuclear deeply bound states in a dynamical model
• Finite size effects on kaonic pasta structures
• Interplay between kaon condensation and hyperons in highly dense matter
• CHIRAL SYMMETRY CONSTRAINTS ON THE $K^{+}$ INTERACTION WITH THE NUCLEAR PION CLOUD
• The properties of kaonic nuclei in relativistic mean-field theory
• Scalar Lambda N and Lambda Lambda interaction in a chiral unitary approach
• On the momentum-dependence of $K^{-}$-nuclear potentials
• Further considerations concerning claims for deeply bound kaon atoms and reply to criticisms
• Pasta structures in compact stars

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