KKbar molecules with momentum-dependent interactions

TL;DR

This paper investigates momentum-dependent kaon-antikaon interactions derived from vector meson exchange, incorporating them into a non-relativistic Bethe-Salpeter framework to analyze the properties of KKbar molecules and related bound states.

Contribution

It introduces a method to include non-local, momentum-dependent interactions into a non-relativistic wave equation for KKbar systems, providing new estimates for meson masses and decay widths.

Findings

Estimated masses and decay widths of f_0(980) and a_0(980) as KKbar molecules.

Analyzed K+K- atomic bound states (kaonium).

Argued the difficulty in distinguishing molecular from elementary models without better form factor data.

Abstract

It is shown that the momentum-dependent kaon-antikaon interactions generated via vector meson exchange from the standard SU_V(3) x SU_A(3) interaction Lagrangian lead to a non-local potential in coordinate space that can be incorporated without approximation into a non-relativistic version of the Bethe-Salpeter wave equation containing a radial-dependent effective kaon mass appearing in a fully symmetrized kinetic energy operator, in addition to a local potential. Estimates of the mass and decay widths of f_0(980) and a_0(980), considered as KKbar molecules of isospin 0 and 1, as well as for K^+K^- atomic bound states (kaonium) are presented, and compared with previous studies of a similar nature. It is argued that without a better knowledge of hadronic form factors it is not possible to distinguish between the molecular versus elementary particle models for the structure of the light scalar mesons.