Deduction of $M(Sigmapi)$ for $Lambda(1405)$ with mixed $T_{Sigmapileftarrow{K}^{-}p}and{T}_{SigmapileftarrowSigmapi}$ from Hemingway's data

Abstract

We formulated the $Lambda(1405)$ (abbreviated as $Lambd{a}^{\ast }$) $rightarrow(Sigmapi{)}^0$ invariant-mass spectra produced in the $K^{-}+prightarrowSigm{a}^{+}(1660)+p{i}^{-}$, followed by $Sigm{a}^{+}(1660)rightarrowLambda(1405)+p{i}^{+}rightarrowSigmapi+p{i}^{+}$, processes at $p(K^{-})=4.2$ GeV/$c$, in which both the incident channel for a quasi-bound $K^{-}p$ state and its decay process to $(Sigmapi{)}^0$ were taken into account realistically. We calculated $M(Sigmapi)$ spectral shapes using mixed transition matrices, $T_{21}=T_{Sigmapileftarrow{K}^{-}p}$ and $T_{22}=T_{SigmapileftarrowSigmapi}$, for various theoretical models involving $Lambd{a}^{\ast }$. The asymmetric spectra were compared to old experimental data of Hemingway, and it was found that the mixing of the two channels, written as $(1-f),T_{21}+f,T_{22}$, gave a better result than considering the individual channels, yielding $f=0.376_{-0.019}^{+0.021}$, $M(Lambd{a}^{\ast })=1406.6_{-3.3}^{+3.4}$ MeV/$c^2$ and $Gamma=70pm2$ MeV, nearly consistent with the 2014 PDG values.

Comments: 7 pages, 5 figures, Phys. Rev. C (2015), in press