First observation of the $\Lambda \left(1405\right)$ line shape in electroproduction

We report the first observation of the line shape of the $\Lambda \left(1405\right)$ from electroproduction, and show that it is not a simple Breit-Wigner resonance. Electroproduction of $K^{+}\Lambda \left(1405\right)$ off the proton was studied by using data from CLAS at Jefferson Lab in the range $1.0<Q^2<3.0$ (GeV/$c$)${}^2$. The analysis utilized the decay channels ${\Sigma }^{+}{\pi }^{-}$ of the $\Lambda \left(1405\right)$ and $p{\pi }^0$ of the ${\Sigma }^{+}$. Neither the standard Particle Data Group resonance parameters, nor free parameters fitting to a single Breit-Wigner resonance represent the line shape. In our fits, the line shape corresponds approximately to predictions of a two-pole meson-baryon picture of the $\Lambda \left(1405\right)$, with a lower mass pole near 1368 MeV/$c^2$ and a higher mass pole near 1423 MeV/$c^2$. Furthermore, with increasing photon virtuality the mass distribution shifts toward the higher mass pole.

Figure 1

The presumed primary diagram for electroproduction of the $\Lambda \left(1405\right)$ at the kinematics of the present experiment.

Figure 2

Missing mass of $e^{-}{K}^{+}p{\pi }^{-}$ versus missing mass of $e^{-}{K}^{+}{\pi }^{-}$ from data. The strong central peak contains the ${\Sigma }^{+}{\pi }^0$ events selected for analysis.

Figure 3

Number of counts plotted versus the missing mass of $e^{-}{K}^{+}$ without either acceptance corrections or background subtraction for (a) $1.0\le Q^2\le 1.5$ (GeV/$c$)${}^2$, and (b) $1.5\le Q^2\le 3.0$ (GeV/$c$)${}^2$.

Figure 4

Invariant mass squared of $K^{+}{\pi }^{-}$. Points with error bars are measured data, the matching (red) line is the total fit to the data with two background simulations. The (green) line at the bottom is the simulation of $K^{*0}{\Sigma }^{+}$, and the upper (blue) line is simulation of $K^{+}{\Sigma }^{+}{\pi }^{-}$.

Figure 5

Estimated rescaled yield of the ${\Sigma }^{*0}$ contamination shown in red (lower points) and missing mass of $e^{-}{K}^{+}$ in black (upper points). The upper points are the sum of the yields from Fig. 3. The histogram is on a log scale to make the ${\Sigma }^{*0}$ contribution visible.

Figure 6

Acceptance-corrected yield versus the missing mass of $e^{-}{K}^{+}$ for (a) $1.0\le Q^2\le 1.5$, and (b) $1.5\le Q^2\le 3.0$ (GeV/$c$)${}^2$.

Figure 7

Fits of the missing mass of $e^{-}{K}^{+}$ for $1.5<Q^2<3.0$ (GeV/$c$)${}^2$. Points with error bars are measured data, solid (red) lines are overall fits, dash-dotted (green) lines around 1.52 GeV/$c^2$ are from the $\Lambda \left(1520\right)$ simulation. The dashed (blue) lines are from the $\Lambda \left(1405\right)$ simulation parametrized by PDG values (a), by one relativistic Breit-Wigner function (b), and by two relativistic Breit-Wigner functions (c). The dotted (purple) lines show the summed background contributions. The shadowed histograms at the bottom show the estimated systematic uncertainty.

Figure 8

Overall fit of the acceptance-corrected missing mass of $e^{-}{K}^{+}$ with simulated background, simulated production of the $\Lambda \left(1520\right)$, and two relativistic Breit-Wigner functions in the ranges $Q_{\min }^2\le Q^2\le 3.0$ (GeV/$c$)${}^2$, where $Q_{\min }^2$ is (a) 1.0 (GeV/$c$)${}^2$, (b) 1.2 (GeV/$c$)${}^2$, (c) 1.4 (GeV/$c$)${}^2$, (d) 1.6 (GeV/$c$)${}^2$, (e) 1.8 (GeV/$c$)${}^2$, (f) 2.0 (GeV/$c$)${}^2$, and (g) 2.2 (GeV/$c$)${}^2$. The fit takes the statistical uncertainties (error bars on points) into account. The shadowed histograms show the estimated systematic uncertainties.