Central exclusive diffractive production of $\pi^{+}\pi^{-}$ continuum, scalar and tensor resonances in $pp$ and $p \bar{p}$ scattering within tensor pomeron approach

TL;DR

This paper models central exclusive dipion production in high-energy proton-proton and proton-antiproton collisions using a tensor pomeron approach, providing new formulae and comparing with experimental data to understand resonance contributions and experimental cut effects.

Contribution

It introduces the first formulae for dipion continuum and tensor meson production within the tensor pomeron model, enhancing theoretical understanding of these processes.

Findings

Resonant $f_2(1270)$ and dipion continuum contributions vary with experimental cuts.

The model explains past ISR experiment discrepancies.

Proposes experimental analyses to determine pomeron-pomeron-$f_{2}$ coupling.

Abstract

We consider central exclusive diffractive dipion production in the reactions $pp \to pp \pi^{+} \pi^{-}$ and $p\bar{p} \to p\bar{p} \pi^{+} \pi^{-}$ at high energies. We include the dipion continuum, the dominant scalar $f_{0}(500)$, $f_{0}(980)$, and tensor $f_{2}(1270)$ resonances decaying into the $\pi^{+} \pi^{-}$ pairs. The calculation is based on a tensor pomeron model and the amplitudes for the processes are formulated in terms of vertices respecting the standard crossing and charge-conjugation relations of Quantum Field Theory. The formulae for the dipion continuum and tensor meson production are given here for the first time. The theoretical results are compared with existing STAR, CDF, CMS experimental data and predictions for planned or being carried out experiments (ALICE, ATLAS) are presented. We show the influence of the experimental cuts on the integrated cross section and on various differential distributions for outgoing particles. Distributions in rapidities and transverse momenta of outgoing protons and pions as well as correlations in azimuthal angle between them are presented. We find that the relative contribution of resonant $f_2(1270)$ and dipion continuum strongly depends on the cut on proton transverse momenta or four-momentum transfer squared $t_{1,2}$ which may explain some controversial observations made by different ISR experiments in the past. The cuts may play then the role of a $\pi \pi$ resonance filter. We suggest some experimental analyses to fix model parameters related to the pomeron-pomeron-$f_{2}$ coupling.