${\Theta }^{+}$ formation in inclusive $\gamma D\to {\mathit{pK}}^{-}X$

We analyze the possibility of producing an intermediate ${\Theta }^{+}$ via a $\mathit{KN}\to {\Theta }^{+}$ formation process in $\gamma D\to {\mathit{pK}}^{-}X(X={\mathit{nK}}^{+},{\mathit{pK}}^0)$ reactions at some specific kinematical conditions, in which a ${\mathit{pK}}^{-}$ pair is knocked out in the forward direction and its invariant mass is close to the mass of ${\Lambda }^{*}[{\Lambda }^{*}\equiv \Lambda (1520)]$. The ${\Theta }^{+}$ signal may appear in the $[\gamma D,{\mathit{pK}}^{-}]$ missing mass distribution. The ratio of the signal (cross section at the ${\Theta }^{+}$ peak position) to the smooth background processes varies from 0.7 to 2.5 depending on the spin and parity of ${\Theta }^{+}$, and it decreases correspondingly if the ${\mathit{pK}}^{-}$ invariant mass is outside of the ${\Lambda }^{*}$-resonance region. We analyze the recent CLAS search for the ${\Theta }^{+}$ in the $\gamma D\to {\mathit{pK}}^{-}{\mathit{nK}}^{+}$ reaction and show that the conditions of this experiment greatly reduce the ${\Theta }^{+}$ formation process making it difficult to extract a ${\Theta }^{+}$ peak from the data.

Figure 1

Tree-level diagrams for the reaction $\gamma D\to {\Lambda }^{*}{\Theta }^{+}$. The exchange of charged and neutral kaons is shown in (a) and (b), respectively.

Figure 2

Reaction $\gamma D\to {\mathit{pNK}}^{-}K$.

Figure 3

Tree-level diagrams for the reaction $\gamma N\to {\Lambda }^{*}K\to \mathit{NK}\overline{K}$.

Figure 4

The total cross section of the reaction $\gamma p\to {\Lambda }^{*}{K}^{+}$ as a function of the photon energy. The experimental data are taken from Ref. [14]. The dot-dashed curve is a fit to this data by $\sigma \simeq 0.7(\mu$b)$\hspace{1em}[2.9(\mathrm{GeV})/E_{\gamma }]{}^{2.1}$. The long-dashed curve represents the cross section for a constant amplitude $\left|T_0\right|=5.95$ GeV${}^{-1}$ (see discussion above Eq. (4) below). The solid curve corresponds to a solution in the low- and high-energy regimes. The dashed curve describes the extrapolation of the effective Lagrangian model to the high energy region. See Ref. [13] for more details.

Figure 5

The differential cross section of the reactions $\gamma p\to {\Lambda }^{*}{K}^{+}$ (a) and $\gamma n\to {\Lambda }^{*}{K}^0$ (b) as a function of the kaon photoproduction angle in $\gamma N$ c.m. system at $E_{\gamma }=1.8,2.1$, and 2.3 GeV.

Figure 6

The differential cross section for the $\gamma p\to {\Lambda }^{*}{K}^{+}{E}_{\gamma }=2.1$ and 3.8 GeV. Experimental data from Ref. [14].

Figure 7

The differential cross section of ϕ meson photoproduction based on the model of Ref. [18]. Data from Refs. [19, 20, 21, 22].

Figure 8

The total cross section of the $\gamma p\to p{K}^{+}{K}^{-}$ reaction as a function of the photon energy. Thin solid curve is the contribution of ${\Lambda }^{*}$ excitation, the dashed curve depicts the contribution of the vector-meson decay, all other sources denoted as ${\mathrm{BG}}_Y$ are shown by the short-dashed curve. The solid curve is the sum of all processes. Experimental data from Ref. [23].

Figure 9

Diagrammatic representation of cutting (indicated by crosses) the loop diagrams.

Figure 10

The average momenta $\langle \langle p_{\alpha }\rangle \rangle$ and $\langle \langle p_{\beta }\rangle \rangle$ in the loop diagrams shown in Figs. 9 [(α) and (β), respectively] as a function of the ${\mathit{pK}}^{-}$ photoproduction angle.

Figure 11

The angular distribution of the differential cross section $d\sigma /d\Omega {\mathit{dM}}_X$ at $M_X=M_{{\Theta }^{+}}=1.53$ GeV, $E_{\gamma }=2.1$ GeV, and $M_0=M_{{\Lambda }^{*}}=1.52$ and 1.62 (GeV), shown in (a) and (b), respectively. The solid and dashed curves correspond to resonant and coherent background contributions.

Figure 12

Diagrammatic representation of the associated nonresonant ${\mathit{pK}}^{-}{\Theta }^{+}$ photoproduction.

Figure 13

The same as in Fig. 11 but for different $E_{\gamma }$. (a) and (b) correspond to the dependence on the ${\Lambda }^{*}$ photoproduction angle in the c.m. system and the laboratory frame, respectively.

Figure 14

The same as in Fig. 13a, but for different ${\Theta }^{+}$ spin and parities. $E_{\gamma }=2.1$ GeV and $M_0=1.52$ GeV.

Figure 15

Diagrammatic representation of background spectator channels. [(a) and (b)] Quasifree ${\Lambda }^{*}K$ photoproduction; [(c) and (d)] quasifree nonresonant ${\mathit{pK}}^{-}K$ photoproduction.

Figure 16

Background contributions to the missing-mass distribution in the $\gamma D\to {\mathit{pK}}^{-}X$ reaction at $E_{\gamma }=2.1$ GeV for quasifree ${\Lambda }^{*}$ photoproduction, vector-meson, and hyperon excitations (spectator mechanism), and rescattering channels shown by solid, dot-dashed, long-dashed, and dashed curves, respectively. (a) and (b) correspond to $M_0=1.52$ and 1.62 GeV, respectively.

Figure 17

Rescattering of the proton (a and b) and $K^{-}$ meson (c and d) in the ${\mathit{pK}}^{-}\mathit{NK}$ photoproduction from the deuteron.

Figure 18

The $\mathit{pN}$ and $K^{-}N$ rescattering channels in $\gamma D\to {\mathit{pK}}^{-}X$ reaction at $E_{\gamma }=2.1$ GeV for $M_0=1.52$ and 1.62 GeV shown in (a) and (b), respectively.

Figure 19

The angular dependence of the missing mass distribution for the associated ${\Lambda }^{*}{\Theta }^{+}$ (solid curve) photoproduction and the background spectator processes (dashed curve) at $M_X=1.53$ GeV, $M_0=1.52$ GeV, and $E_{\gamma }=2.1$ GeV.

Figure 20

The $[\gamma D,{\mathit{pK}}^{-}]$ missing mass distribution in the $\gamma D\to {\mathit{pK}}^{-}X$ reaction together with the partial contributions of different background channels at $M_0=1.52$ GeV and $E_{\gamma }=1.7\text{−}2.3$ GeV. The contributions from the ${\Theta }^{+}$ signal, spectator and rescattering processes are shown by the thin, long dashed, and dashed curves, respectively. (a) and (b) correspond to calculations without and with the angular cut ${\theta }_{{\mathit{pK}}^{-}}\le {22}^{°}$, respectively.

Figure 21

The same as in Fig. 20b but for $M_0=1.62$ GeV.

Figure 22

Missing mass distribution in the $\gamma D\to {\mathit{pK}}^{-}X$ reaction at $E_{\gamma }=1.7\text{−}2.3$ GeV and $M_0=1.52$ GeV for different ${\Theta }^{+}$ spin and parity: (a), (b), (c) and (d) correspond to the ${\Theta }^{+}$ spin and parity $J^P={\frac{1}{2}}^{-},{\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$, and ${\frac{3}{2}}^{-}$, respectively.

Figure 23

The missing mass distribution for $\gamma D\to {\mathit{pK}}^{-}\mathit{NK}$ at $E_{\gamma }=1.7\text{−}2.3$ GeV and $M_0=1.52$ GeV and for different ${\Theta }^{+}$ spin and parity, folded with a Gaussian resolution function.

Figure 24

The nonresonant background structure of the ${\mathit{nK}}^{+}$ invariant mass distribution in $\gamma D\to {\mathit{pK}}^{-}\mathit{NK}$ at $E_{\gamma }=1.7\text{−}3.5$ GeV and for CLAS conditions.

Figure 25

The ${\mathit{nK}}^{+}$ invariant mass distribution in $\gamma D\to {\mathit{pK}}^{-}\mathit{NK}$ at $E_{\gamma }=1.7\text{−}3.5$ GeV and for conditions (i)–(v).

Figure 26

(Left) Missing mass distribution in inclusive $\gamma D\to {\mathit{pK}}^{-}X$ at $E_{\gamma }=1.7\text{−}2.3$ GeV and the ${\mathit{pK}}^{-}$ photoproduction angular cut (${\theta }_{{\mathit{pK}}^{-}}<{22}^{°}$ (c.m.s.)) and ϕ-meson cut. (Right) ${\mathit{nK}}^{+}$ invariant mass distribution in exclusive $\gamma D\to {\mathit{pK}}^{-}{\mathit{nK}}^{+}$ at $E_{\gamma }=1.7\text{−}3.5$ GeV and for CLAS experimental conditions (i)–(v). Experimental data from Ref. [7]. In both cases, $J_{\Theta }^P=3/2^{-}$ and the ${\Theta }^{+}$ signal is folded with a Gaussian resolution function with a width of 3 MeV.