Extracting the pomeron-pomeron-$f_{2}(1270)$ coupling in the $p p \to p p \pi^{+} \pi^{-}$ reaction through angular distributions of the pions

We discuss how to extract the pomeron-pomeron-$f_2(1270)$ ($\mathbb{P} \mathbb{P} f_2(1270)$) coupling within the tensor-pomeron model. The general $\mathbb{P} \mathbb{P} f_2(1270)$ coupling is a combination of seven basic couplings (tensorial structures). To study these tensorial structures we propose to measure the central-exclusive production of a $\pi^+ \pi^-$ pair in the invariant mass region of the $f_2(1270)$ meson. An analysis of angular distributions in the $\pi^+ \pi^-$ rest system, using the Collins-Soper (CS) and the Gottfried-Jackson (GJ) frames, turns out to be particularly relevant for our purpose. For both frames the $\cos\theta_{\pi^{+}}$ and $\phi_{\pi^{+}}$ distributions are discussed. We find that the azimuthal angle distributions in these frames are fairly sensitive to the choice of the $\mathbb{P} \mathbb{P} f_2$ coupling. We show results for the resonance case alone as well as when the dipion continuum is included. We show the influence of the experimental cuts on the angular distributions in the context of dedicated experimental studies at RHIC and LHC energies. Absorption corrections are included for our final distributions.