Experimental study of the $\mathit{pd}\to$${}^3\mathrm{He}$ $K^{+}{K}^{-}$ and $\mathit{pd}\to$${}^3\mathrm{He}$ $\varphi$ reactions close to threshold

Two-kaon production in proton-deuteron collisions has been studied at three energies close to threshold using a calibrated magnetic spectrograph to measure the final ${}^3\mathrm{He}$ and a vertex detector to measure the $K^{+}{K}^{-}$ pair. Differential and total cross sections are presented for the production of ϕ-mesons, decaying through $\varphi \to K^{+}{K}^{-}$, as well as for prompt $K^{+}{K}^{-}$ production. The prompt production seems to follow phase space in both its differential distributions and in its energy dependence. The amplitude for the $\mathit{pd}\to {}^3\mathrm{He}\varphi$ reaction varies little for excess energies below 22 MeV and the value is consistent with that obtained from a threshold measurement. The angular distribution of the $K^{+}{K}^{-}$ decay pair shows that near threshold the ϕ-mesons are dominantly produced with polarization $m=0$ along the initial proton direction. No conclusive evidence for $f_0(980)$ production is found in the data.

Figure 1

Energy loss in the first scintillation layer in the focal plane of the spectrograph as a function of the time of flight between the two scintillation hodoscopes, both in arbitrary units. The well-separated groups of different particles show up very clearly.

Figure 2

Front view to the MOMO vertex detector with the indication of a typical event. Both the primary beam and the recoil ${}^3\mathrm{He}$ detected in Big Karl pass through the central hole. The numbers denote the different layers and the three boxes at the end of each read-out symbolize the phototubes. The support stand is visible in the lower part of the figure.

Figure 3

Monte Carlo simulation estimates of the acceptance of the setup as a function of the excitation energy $Q_{\mathit{KK}}$ at (a) ${\varepsilon }_{\mathit{KK}}=35.1\hspace{1em}$MeV, (b) 40.6 MeV, and 55.2 MeV. The differing luminosities for the various spectrograph settings were taken into account.

Figure 4

The excitation energy in the $\mathit{KK}$ system obtained in the ${\varepsilon }_{\mathit{KK}}=40.6$ MeV run, evaluated I from the invariant $\mathit{KK}$ mass, and II from the missing mass of the ${}^3\mathrm{He}$ measured with Big Karl.

Figure 5

Cross section for the reaction $\mathit{pd}\to$${}^3\mathrm{He}$ $K^{+}{K}^{-}$ as a function of the excitation energy $Q_{\mathit{KK}}$ of the two kaons at overall excess energies of (a) ${\varepsilon }_{\mathit{KK}}=35.1\hspace{1em}$MeV, (b) 40.6 MeV, and 55.2 MeV. The events are binned in equally spaced intervals. The curves are fits to the $Q_{\mathit{KK}}$ distributions in terms of phase space coming from prompt $K^{+}{K}^{-}$ production (dashed line), proceeding via ϕ-meson formation (chain), and their sum (solid line).

Figure 6

Same as Fig. 5 but as a function of the excitation energy $Q_{K\mathrm{He}}$ in the $K{}^3\mathrm{He}$ system. The consequences of the fits shown in Fig. 5 for the $Q_{K\mathrm{He}}$ distributions are shown, though the deviations from simple three-body phase space are here relatively minor. This is due in part to the averaging over the $K^{-}{}^3\mathrm{He}$ and $K^{+}{}^3\mathrm{He}$ distributions by the MOMO apparatus.

Figure 7

Distribution in the cosine of the opening angle ${\theta }_{\mathit{KK}}$ at (a) ${\varepsilon }_{\mathit{KK}}=35.1$ MeV, (b) 40.6 MeV, and 55.2 MeV. The dashed line represents the phase-space contribution arising from prompt $K^{+}{K}^{-}$ production, whereas the chain corresponds to the ϕ component and the solid line the sum thereof.

Figure 8

Same as Fig. 7 but for the distribution in the angle between an outgoing kaon and the incident proton in the overall c.m. system. For prompt production of $S$-wave kaon pairs, this distribution is expected to be isotropic. However, a variation with angle can be generated through a polarization dependence of ϕ production.

Figure 9

Angular distributions of the kaons as a function of the helicity angle for the lowest energy of ${\varepsilon }_{\mathit{KK}}=35.1$ MeV. The data are consistent with the average value indicated.

Figure 10

Angular distributions of the kaons as a function of the Jackson angle for the lowest energy of ${\varepsilon }_{\mathit{KK}}=35.1$ MeV. The data are divided into those with $Q_{\mathit{KK}}<28$ MeV (closed circles) and $Q_{\mathit{KK}}>28$ MeV (open circles). In order to show clearly the difference in slopes, the data have been arbitrarily scaled so that they have similar values at the origin. The straight lines shown here are predictions based on the fits to Fig. 5, assuming that the ϕ are produced only with $m=0$ along the proton beam direction.

Figure 11

Shape of the cross section expected for the reaction $\mathit{pd}\to$${}^3\mathrm{He}$$f_0(980)$, with the subsequent decay $f_0(980)\to K^{+}{K}^{-}$, for the excess energies indicated. All predictions have been normalized to unity.

Figure 12

The variation of the amplitude-square for ϕ production, as defined by Eq. (2), with ${\varepsilon }_{\varphi }$. The open circle at ${\varepsilon }_{\varphi }=0.3$ MeV is taken from the SPESIV measurement [8]. The results are all consistent with $\left|f\right|{}^2$ being constant, as indicated.

Figure 13

Total cross section for prompt two-kaon production divided by a phase-space factor of ${\varepsilon }_{\mathit{KK}}^2$ as a function of ${\varepsilon }_{\mathit{KK}}$. The average value is also indicated.