Baryonic resonances close to the $\overline{K}N$ threshold: The case of $\Lambda \left(1405\right)$ in $pp$ collisions

We present an analysis of the $\Lambda \left(1405\right)$ resonance produced in the reaction $p+p\to {\Sigma }^{\pm }+{\pi }^{\mp }+K^{+}+p$ at $3.5\mathrm{GeV}$ kinetic beam energy measured with the High Acceptance Dielectron Spectrometer (HADES) at the Gesellschaft für Schwerionenforschung (GSI). The two charged decay channels $\Lambda \left(1405\right)\to {\Sigma }^{\pm }{\pi }^{\mp }$ have been reconstructed for the first time in $p+p$ collisions. The efficiency and acceptance-corrected spectral shapes show a peak position clearly below $1400\mathrm{MeV}/{\mathrm{c}}^2$. We find a total production cross section of ${\sigma }_{\Lambda \left(1405\right)}=9.2\pm 0.9\pm 0.7_{-1.0}^{+3.3}\mu$b. The analysis of its polar angle distribution suggests that the $\Lambda \left(1405\right)$ is produced isotropically in the $p-p$ center-of-mass system (CMS).

Figure 1

Missing mass $MM(p,K^{+})$ distributions for events attributed to the ${\Sigma }^{+}{\pi }^{-}$ decay channel (a) and the ${\Sigma }^{-}{\pi }^{+}$ decay channel (b). (c) Sum of both spectra from panels (a) and (b). The gray dashed histogram shows the sum of all simulated channels if $\Lambda \left(1405\right)$ is simulated with its nominal mass of $1405\mathrm{MeV}/{\mathrm{c}}^2$. Colored histograms in the three panels indicate the contributions of the channels (1, 2, 3, 4, 5) obtained from simulations. Data and simulations are acceptance and efficiency corrected. The gray boxes indicate systematic errors.

Figure 2

Missing mass to the $p$, $\Lambda$, and $K^{+}$ particles. The colored histograms show the contributions of the simulated channels 6–9. The experimental data are uncorrected. See the text for details.

Figure 3

Differential cross-section for the different simulated reaction channels as a function of $\cos \left({\theta }_{CMS}^{MV(p,K)}\right)$ for the ${\Sigma }^{+}{\pi }^{-}$ decay channel (a) and the ${\Sigma }^{-}{\pi }^{+}$ decay channel (b). The cross-sections are obtained by integrating the simulations, which have been fitted to the experimental data. The gray boxes indicate the systematic errors. The solid histograms show the angular distribution used to fold the simulation of the reactions $p+p\to {\Sigma }^{+}+{\pi }^{-}+p+K^{+}$ and $p+p\to {\Delta }^{++}+{\Sigma }^{-}+K^{+}$, respectively.

Figure 4

Compilation of production cross-sections as a function of the excess energy $\epsilon$ for the reactions $p+p\to \Lambda +K^{+}+p$ from Ref. [20] where the proper quotations of the references listed in the legend can be found, $p+p\to \Lambda \left(1405\right)+K^{+}+p$ from ANKE [11] and this work. See the text for details.