Mass and width of sigma(750) scalar meson from measurements of piN->pi(-)pi(+)N on polarized targets

Abstract

The measurements of reactions ${\pi }^{-}{p}_{\uparrow }\to {\pi }^{-}{\pi }^{+}n$ at 17.2 GeV/c and ${\pi }^{+}{n}_{\uparrow }\to {\pi }^{+}{\pi }^{-}p$ at 5.98 and 11.85 GeV/c made at CERN with polarized targets provide a model-independent and solution-independent evidence for a narrow scalar state sigma(750). The original chi^2 minimization method and the recent Monte Carlo method for amplitude analysis of data at 17.2 GeV/c are in excellent agreement. Both methods find that the mass distribution of the measured amplitude $|\overline{S}{|}^2\Sigma$ with recoil transversity ``up'' resonates near 750 MeV while the amplitude $|S{|}^2\Sigma$ with recoil transversity ``down'' is large and nonresonating. The amplitude $|S{|}^2\Sigma$ contributes as a strong background to S-wave intensity I_S = (|S|^2 + |\overline S |^2)\Sigma$anddistortsthedeterminationsof$\sigma$resonanceparametersfrom$I_S$.ToavoidthisproblemweperformaseriesofBreit-Wignerfitsdirectlytothemeasureddistribution$|\overline S |^2\Sigma$.Theinclusionofvariousbackgroundscausesthewidthofsigma(750)tobecomeverynarrow.Ourbestfitwith$t$-averagedcoherentbackgroundyields$m_\sigma = 753 \pm 19$MeVand$\Gamma_\sigma = 108 \pm 53$MeV.ThesevaluesareinexcellentagreementwithEllis-Laniktheoremforthewidthofscalargluonium.Thegluoniuminterpretationof$\sigma(750)$isalsosupportedbytheabsenceof$\sigma(750)$inreactions$\gamma\gamma \to \pi\pi$.Wealsoshowhowdataonpolarizedtargetinvalidateessentialassumptionsofpastdeterminationsof$\pi\pi$ phase shifts .

Comments: 77 pages