Photoproduction of the $f_2(1270)$ resonance

TL;DR

This paper models the photoproduction of the $f_2(1270)$ resonance as a $ ho$-$ ho$ molecular state using a local hidden gauge approach, successfully matching experimental data without free parameters.

Contribution

It introduces a parameter-free theoretical model for $f_2(1270)$ photoproduction based on vector meson dominance and molecular state assumptions, incorporating Regge phenomenology and $ ho NN$ coupling.

Findings

Good agreement with experimental differential cross sections.

Supports the molecular $ ho$-$ ho$ structure of $f_2(1270)$.

First baryonic reaction test of the molecular picture.

Abstract

We have performed a calculation of the $\gamma p \to \pi^+ \pi^- p$ reaction, where the two pions have been separated in $D$-wave producing the $f_2(1270)$ resonance. We use elements of the local hidden gauge approach that provides the interaction of vector mesons in which the $f_2(1270)$ resonance appears as a $\rho$-$\rho$ molecular state in $L=0$ and spin 2. The vector meson dominance, incorporated in the local hidden gauge approach converts a photon into a $\rho^0$ meson and the other meson connects the photon with the proton. The picture is simple and has no free parameters, since the parameters of the theory have been constrained in the previous study of the vector-vector states. In a second step we introduce new elements, not present in the local hidden gauge approach, adapting the $\rho$ propagator to Regge phenomenology and introducing the $\rho NN$ tensor coupling. We find that both the differential cross section as well as the $t$ dependence of the cross section are in good agreement with the experimental results and provide support for the molecular picture of the $f_2(1270)$ in the first baryonic reaction where it has been tested.