Large-$N_c$ pole trajectories of the vector kaon $K^{\ast }(892)$ and of the scalar kaons $K_0^{\ast }(800)$ and $K_0^{\ast }(1430)$

Abstract

We study the spectral functions, the poles and their trajectories for increasing $N_c$ of the vector kaon state $K^{\ast }(892),$ characterized by $I(J^P)=\frac{1}{2}(1^{-})$, and of the scalar kaons $K_0^{\ast }(800)$ and $K_0^{\ast }(1430),$ characterized by $I(J^P)=\frac{1}{2}(0^{+})$. To this end, we use relativistic QFT's Lagrangians with both derivative and non-derivative terms. In the vector kaonic sector the spectral function is well approximated by a Breit-Wigner function: there is one single peak and, correspondingly, a single pole in the complex plane. On the contrary, in the scalar sector, although the Lagrangian contains only one scalar kaonic field, we find two poles, one corresponding to a standard quark-antiquark ,,seed\textquotedblright\ state $K_0^{\ast }(1430),$ and one to a \textquotedblleft companion\textquotedblright\ dynamically generate pole $K_0^{\ast }(800)$. The latter does not correspond to any peak in the scalar kaonic spectral function, but only to an enhancement in the low-energy regime.

Comments: Presented at XI Workshop on Particle Correlations and Femtoscopy, 3-7/11/2015, Warsaw, Poland. 4 pages, 2 figures