A covariant nonlocal Lagrangian for the description of the scalar kaonic sector

TL;DR

This paper develops covariant and non-covariant nonlocal Lagrangians with form factors for meson interactions, applied specifically to the scalar kaonic sector, revealing dynamically generated companion poles through loop calculations.

Contribution

It introduces a covariant nonlocal Lagrangian framework for meson interactions, enabling more accurate loop calculations in the scalar kaonic sector.

Findings

Covariant Lagrangian guarantees Lorentz invariance.

Dynamically generated $K_0^*(800)$ pole from loops.

Disappearance of the companion pole in large-$N_c$ limit.

Abstract

Mesons are extended objects, hence their interaction can be described by utilizing form factors. At the Lagrangian level, one can use nonlocal interaction terms. Here we describe two possible nonlocal Lagrangians leading to a 3D form factor: the first one is simple but does not fulfill covariance (if one insists on a 3D cutoff), the second extension is more involved but guarantees covariance. Such form factors are useful when calculating mesonic loops. As an important example, we discuss the scalar kaonic sector, $I(J^{P})=\frac{1}{2}(0^{+})$. The Lagrangian contains a single scalar kaon (the well-establish state $K_{0}^{\ast}(1430)$), but through loops $K_{0}^{\ast}(800)$ emerges as a dynamically generated companion pole (which disappears in the large-$N_{c}$ limit).