Photoproduction and electroproduction of $\mathrm{\Lambda }\left(1405\right)$ via ${\gamma }^{(*)}p\to K^{*+}{\pi }^0{\mathrm{\Sigma }}^0$

We study the photoproduction and electroproductions of the vector kaon off the proton, i.e., ${\gamma }^{(*)}p\to K^{*+}{\pi }^0{\mathrm{\Sigma }}^0$, and investigate the line shape of the ${\pi }^0{\mathrm{\Sigma }}^0$ invariant mass in an effective Lagrangian approach with the inclusion of a $K^{*}N{\mathrm{\Lambda }}^{*}$ interaction. Relevant electromagnetic form factors for the neutral hyperons and charged strange mesons are constructed by considering experimental and theoretical information. We find that the ${\mathrm{\Lambda }}^{*}$ peak is clearly observed for the photoproduction and electroproductions with the finite $K^{*}N{\mathrm{\Lambda }}^{*}$ interaction, whereas the clear peak signals survive only for the electroproduction, when we ignore the interaction. These different behaviors can be understood by different $Q^2$ dependencies in the $K^{*}$ electromagnetic and $K^{*}\to \gamma K$ transition form factors. We suggest a photon-polarization asymmetry $\mathrm{\Sigma }$ to extract information of the $K^{*}N{\mathrm{\Lambda }}^{*}$ interaction. It turns out that $\mathrm{\Sigma }$ near the ${\mathrm{\Lambda }}^{*}$ peak region becomes negative with a finite $K^{*}N{\mathrm{\Lambda }}^{*}$ interaction while positive without it for $Q^2=0$, because of the different naturalities of $K$ and $K^{*}$ exchanges. For $Q^2\ne 0$, we observe more obvious signals in the peak region owing to the additional contribution of the longitudinal virtual photon for ${\mathrm{\Lambda }}^{*}$.

Figure 1

Relevant Feynman diagrams for $\gamma p\to K^{*+}{\pi }^0{\mathrm{\Sigma }}^0$: (a) proton-pole diagram in the $s$ channel, (b) hyperon ground-state and resonance diagram in the $u$ channel, (c) $K^{*}$ exchange in the $t$ channel, (d) $K$ exchange in the $t$ channel, (e) and (f) background contributions from the $PB\to VB$ Kroll-Ruddermann (KR) interaction, and (g) those from the $PB\to PB$ Weinberg-Tomozawa (WT) interaction. As for the hyperons $Y^{(*)}$, we consider $\mathrm{\Lambda }(1116,1/2^{+}), {\mathrm{\Sigma }}^0(1192,1/2^{+}), H(1430,1/2^{-})$, and $L(1390,1/2^{-})$, in which $H$ and $L$ indicate the higher- and lower-pole contributions for $\mathrm{\Lambda }(1405,1/2^{-})$, respectively. See the text for details.

Figure 2

EM form factors of various neutral hyperons (a)–(d) and strange mesons (e) as functions of $Q^2$ (${\mathrm{GeV}}^2$). The solid, dashed, dotted, and dot-dashed lines indicate $\mathrm{Re}{F}_1, \mathrm{Im}{F}_1, \mathrm{Re}{F}_2$, and $\mathrm{Im}{F}_2$, respectively. Here, $F_1$ and $F_2$ stand for the Dirac and Pauli form factors for spin-$1/2$ baryons.

Figure 3

Each contribution for ${\pi }^0{\mathrm{\Sigma }}^0$-invariant-mass line shape $(d\sigma /d{M}_{{\pi }^0{\mathrm{\Sigma }}^0})$ for (a) $Q^2=0$ and (b) $Q^2=2{\mathrm{GeV}}^2$ at $\sqrt{s}=2.35\mathrm{GeV}$.

Figure 4

${\pi }^0{\mathrm{\Sigma }}^0$ invariant-mass plot $(d\sigma /d{M}_{{\pi }^0{\mathrm{\Sigma }}^0})$ for (a) $Q^2=0$, (b) $Q^2=1.0{\mathrm{GeV}}^2$, and (c) $Q^2=2.0{\mathrm{GeV}}^2$ at $\sqrt{s}=2.35\mathrm{GeV}$ for $\varphi =0$, using different choices of the parameter $g=1$ and 0, which correspond to the cases with and without the $K^{*}$-exchange contribution in the $t$ channel. The vertical dashed line corresponds to the mass of $\mathrm{\Lambda }\left(1405\right)$. See the text for the details.

Figure 5

${\pi }^0{\mathrm{\Sigma }}^0$-invariant-mass plots in the same manner as in Fig. 4 for $\varphi =\pi$. See the text for the details.

Figure 6

(a) Definition for the photon polarizations and the relevant momenta for $\mathrm{\Sigma }$, defined in Eq. (17). (b) Numerical results for $\mathrm{\Sigma }$ with $Q^2=0$ varying $g$ and $\varphi$. The vertical shaded area represents the higher-pole peak region. (c) The same with $Q^2=1{\mathrm{GeV}}^2$.