A Study in Depth of f0(1370)

TL;DR

This paper provides comprehensive evidence confirming the existence of the f0(1370) resonance through multiple datasets and advanced fitting techniques, addressing previous claims of its non-existence.

Contribution

It introduces a detailed refitting of data including dispersive effects and sigma -> 4pi amplitudes, conclusively demonstrating f0(1370)'s existence and analyzing its properties.

Findings

f0(1370) signals detected at over 32 standard deviations in pbar-p annihilation

Consistent mass and width measurements across different experiments

Fitted pi-pi scattering data with mixing models involving sigma, f0(1370), and f0(1500)

Abstract

Claims have been made that f0(1370) does not exist. The five primary sets of data requiring its existence are refitted. Major dispersive effects due to the opening of the 4pi threshold are included for the first time; the sigma -> 4pi amplitude plays a strong role. Crystal Barrel data on pbar-p -> 3pizero at rest require f0(1370) signals of at least 32 and 33 standard deviations in 1S0 and 3P1 annihilation respectively. Furthermore, they agree within 5 MeV for mass and width. Data on pbar-p -> eta-eta-pizero agree and require at least a 19 standard deviation contribution. This alone is sufficient to demonstrate the existence of f0(1370). BES II data for J/Psi -> phi-pi-pi contain a visible f0(1370) signal > 8 standard devations. In all cases, a resonant phase variation is required. The possibility of a second pole in the sigma amplitude due to the opening of the 4pi channel is excluded. Cern-Munich data for pi-pi elastic scattering are fitted well with the inclusion of some mixing between sigma, f0(1370) and f0(1500). The pi-pi widths for f2(1565), rho3(1690), rho3(1990) and f4(2040) are determined.