Study of the $f_0{\mathrm{}\left(1500\right)/f}_2\mathrm{}\left(1565\right)\mathrm{}$ production in the exclusive annihilation $\mathrm{n̄}\overrightarrow{p}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ in flight

The spin-parity analysis of the $\mathrm{n̄}\overrightarrow{p}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ exclusive reaction in flight is presented. The main aim is to study the $\left({\pi }^{+}{\pi }^{-}\right)$ invariant mass spectrum in the region around 1500 MeV. The analysis was performed with a Breit-Wigner parametrization for all the resonant states and, for the scalar sector in the mass region below 1.2 GeV, by means of a K-matrix-like treatment. It clearly shows the need for two states, a scalar one ${(0\mathrm{}}^{++})$ with mass and width $(1522\mathrm{}\pm 25)\hspace{0.5em}\mathrm{MeV}$ and $(108\mathrm{}\pm 33)\hspace{0.5em}\mathrm{MeV}$, and a tensorial one ${(2\mathrm{}}^{++})$ with mass $(1575\mathrm{}\pm 18)\hspace{0.5em}\mathrm{MeV}$ and width $(119\mathrm{}\pm 24)\hspace{0.5em}\mathrm{MeV}$, respectively. In addition, the analysis requires the presence of a scalar state at $(1280\mathrm{}\pm 55)\hspace{0.5em}\mathrm{MeV}$, $(323\mathrm{}\pm 13)\hspace{0.5em}\mathrm{MeV}$ broad, and of a second vectorial one, in addition to the ${\rho }^0\mathrm{}\left(770\right)\mathrm{}$ signal, with mass and width $(1348\mathrm{}\pm 33)\hspace{0.5em}\mathrm{MeV}$ and $(275\mathrm{}\pm 10)\hspace{0.5em}\mathrm{MeV}$, respectively.