Investigation of the $\Lambda \left(1405\right)$ line shape observed in $pp$ collisions

In this work we investigate different possible interpretations of the $\Lambda \left(1405\right)$ signal associated with the production of the $\Lambda \left(1405\right)$ in $p+p$ reactions at 3.5 GeV beam kinetic energy measured by the HADES collaboration. We study the influence of interference effects between the $\Lambda \left(1405\right)$ resonance and the nonresonant background. The two poles nature of the $\Lambda \left(1405\right)$, which is supported by most of the theoretical models, is also discussed with emphasis on the relative contributions of the two complex poles to the formation of the resonance in $p+p$ reactions.

Figure 1

Comparison between the HADES data and the data of [11] and [12], measured in ${\pi }^{-}+p$ reactions. All three spectra show the sum of the ${\Sigma }^{+}{\pi }^{-}$ and ${\Sigma }^{-}{\pi }^{+}$ data samples.

Figure 2

The $\Lambda \left(1405\right)$ spectral shape calculated in [8] (gray histogram). The spectrum is fitted with equation (1). The two phase space modified Breit-Wigner functions $C_{\mathrm{p}.\mathrm{s}.}\left(m\right){\left|B{W}_1\left(m\right)\right|}^2{q}_{\mathrm{c}.\mathrm{m}.}$ and $C_{\mathrm{p}.\mathrm{s}.}\left(m\right){\left|B{W}_2\left(m\right)\right|}^2{q}_{\mathrm{c}.\mathrm{m}.}$ are shown in the dotted and dashed lines.

Figure 3

Missing mass spectrum to proton and $K^{+}$. The black data points are the measurements of [1], for the $\Lambda \left(1405\right)$ in the ${\Sigma }^{+}{\pi }^{-}$ (a) and ${\Sigma }^{-}{\pi }^{+}$ (b) decay channel. (c) shows the summed spectrum of (a) and (b). The black lines in (a) and (b) are the results from the simultaneous fit with Eqs. (2) and (3), the gray line represents the sum of all fitted functions. In (c) the fit functions corresponding to the ${\Sigma }^{+}{\pi }^{-}$ and ${\Sigma }^{-}{\pi }^{+}$ channels respectively are shown in gray and the sum of both functions is shown in the black line.

Figure 4

Same as Fig. 3 but now the data are fitted with Eqs. (5) and (6). See text for details.

Figure 5

$\Lambda \left(1405\right)$ signal (black line) obtained by fitting Eqs. (5) and (6) to the experimental data in Fig. 4. The dotted and dashed lines show the contributions of $C_{\mathrm{p}.\mathrm{s}.}\left(m\right){\left|B{W}_1\left(m\right)\right|}^2{q}_{\mathrm{c}.\mathrm{m}.}$ and $C_{\mathrm{p}.\mathrm{s}.}\left(m\right){\left|B{W}_2\left(m\right)\right|}^2{q}_{\mathrm{c}.\mathrm{m}.}$.

Figure 6

Same as Fig. 4 but the mass and width constraints for the two $\Lambda \left(1405\right)$ poles are taken from [25]. See text for details.

Figure 7

Same as Fig. 5 but the constraints of [25] for the mass and width values of the two $\Lambda \left(1405\right)$ poles were used in the fits. See text for details.