Mass and width of theσ(750) scalar meson from measurements ofπN→π−π+Non polarized targets

Abstract

The measurements of reactions ${\ensuremath{\pi}}^{\ensuremath{-}}{p}_{\ensuremath{\uparrow}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n$ at 17.2 GeV/$c$ and ${\ensuremath{\pi}}^{+}{n}_{\ensuremath{\uparrow}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}p$ at 5.98 and 11.85 GeV/$c$ on polarized targets at CERN provide model-independent and solution-independent evidence for a narrow scalar state $\ensuremath{\sigma}(750).$ The original ${\ensuremath{\chi}}^{2}$ minimization method and the recent Monte Carlo method for the amplitude analysis of data at 17.2 GeV/$c$ are in excellent agreement. Both methods find that the mass distribution of the measured amplitude $|\mathrm{S\ifmmode\bar\else\textasciimacron\fi{}}{|}^{2}\ensuremath{\Sigma}$ with recoil transversity ``up'' resonates near 750 MeV while the amplitude $|S{|}^{2}\ensuremath{\Sigma}$ with recoil transversity ``down'' is large and nonresonating. The amplitude $|S{|}^{2}\ensuremath{\Sigma}$ contributes as a strong background to $S$-wave intensity ${I}_{S}=(|S{|}^{2}+|\mathrm{S\ifmmode\bar\else\textasciimacron\fi{}}{|}^{2})\ensuremath{\Sigma}$ and distorts the determinations of $\ensuremath{\sigma}$ resonance parameters from ${I}_{S}.$ To avoid this problem we perform a series of Breit-Wigner fits directly to the measured distribution $|\mathrm{S\ifmmode\bar\else\textasciimacron\fi{}}{|}^{2}\ensuremath{\Sigma}.$ The inclusion of various backgrounds causes the width of $\ensuremath{\sigma}(750)$ to become very narrow. Our best fit with a $t$-averaged coherent background yields ${m}_{\ensuremath{\sigma}}=753\ifmmode\pm\else\textpm\fi{}19\mathrm{MeV}$ and ${\ensuremath{\Gamma}}_{\ensuremath{\sigma}}=108\ifmmode\pm\else\textpm\fi{}53\mathrm{MeV}.$ These values are in excellent agreement with the Ellis-Lanik theorem for the width of scalar gluonium. The gluonium interpretation of $\ensuremath{\sigma}(750)$ is also supported by the absence of $\ensuremath{\sigma}(750)$ in reactions $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}.$ We also show how data on polarized target invalidate essential assumptions of past determinations of $\ensuremath{\pi}\ensuremath{\pi}$ phase shifts which explains the absence of $\ensuremath{\sigma}(750)$ in the conventional phase shift ${\ensuremath{\delta}}_{0}^{0}.$ We examine the interference of $\ensuremath{\sigma}(750)$ with ${f}_{0}(980)$ and find it has only a very small effect on the determination of the $\ensuremath{\sigma}(750)$ mass and width. The data on the amplitude $|\mathrm{S\ifmmode\bar\else\textasciimacron\fi{}}{|}^{2}\ensuremath{\Sigma}$ in the mass range of 1120--1520 MeV show the existence of a scalar resonance ${f}_{0}(1300)$ with a mass of $1280\ifmmode\pm\else\textpm\fi{}12\mathrm{MeV}$ and a width of $192\ifmmode\pm\else\textpm\fi{}26\mathrm{MeV}.$ Our results emphasize the need for a systematic study of production processes on the level of spin amplitudes measured in experiments with polarized targets.