Productions of $f_{1}(1420)$ in pion and kaon induced reactions

TL;DR

This study investigates the production mechanisms of the $f_{1}(1420)$ meson in pion and kaon induced reactions on protons using effective Lagrangian models, comparing Feynman and Regge approaches to predict cross sections and angular distributions.

Contribution

It introduces a comparative analysis of Feynman and Regge models for $f_{1}(1420)$ production, providing predictions for kaon-induced reactions with limited experimental data.

Findings

Both models reproduce pion-induced total cross section data.

Predicted kaon-induced cross sections are of similar magnitude to pion-induced ones.

Regge model shows sharp forward-angle increase in differential cross sections.

Abstract

The $f_{1}(1420)$ productions via pion and kaon induced reactions on a proton target are investigated in an effective Lagrangian approach. Two treatments of the $t$-channel Born term, the Feynman model and the Regge model, are introduced to calculate the total and differential cross sections of the $\pi^{-}p\rightarrow f_{1}(1420)n$ and $K^{-}p\rightarrow f_{1}(1420)\Lambda $ reactions. The numerical results indicate that the experimental data of the total cross section of the $\pi ^{-}p\rightarrow f_{1}(1420)n$ reaction can be reproduced in both the Feynman and the Regge models. Based on the parameters determined in the pion induced reaction, the cross sections of the $K^{-}p\rightarrow f_{1}(1420)\Lambda $ reaction, about which there is little data found in the literature, are predicted in the same beam momentum range. It is found that the line shapes of the total cross section obtained in a kaon induced reaction with two treatments are quite different. The cross sections for both reactions are at an order of magnitude of $\mu$b, or larger, at a beam momenta up to 10 GeV/c. The differential cross sections for both pion and kaon induced reactions are also present. It is found that in the Regge model, the $t$ channel provides a sharp increase at extreme forward angles. The results suggest that the experimental study of the $f_1(1420)$ in the kaon induced reaction on a proton target is as promising as in the pion induced reaction. Such an experimental measurement is also very helpful to clarify the production mechanism of the $f_1(1420)$.