Precision Measurement of the Quasifree $pn\to d\varphi$ Reaction Close to Threshold

The quasifree $pn\to d\varphi$ reaction has been studied at the Cooler Synchrotron COSY—Jülich, using the internal proton beam incident on a deuterium cluster-jet target and detecting a fast deuteron in coincidence with the $K^{+}{K}^{-}$ decay of the $\varphi$ meson. The energy dependence of the total and differential cross sections are extracted for excess energies up to 80 MeV by determining the Fermi momentum of the target neutron on an event-by-event basis. Though these cross sections are consistent with $s$-wave production, the kaon angular distributions show the presence of $p$ waves at quite a low energy. Production on the neutron is found to be stronger than on the proton but not by as much as for the $\eta$ meson.

Figure 1

(a) Missing-mass distribution of the $pd\to d{K}^{+}{K}^{-}X$ events with lines indicating the proton selection range. (b) $K^{+}{K}^{-}$ invariant-mass distribution with lines showing the mass range of selected $\varphi$ meson events. The dashed curve shows the four-body phase-space fit to the nonresonant production, while the solid histogram is the sum of this and the $\varphi$ meson contribution. (c) Momentum distribution of the unobserved proton compared with a Monte Carlo simulation based on the spectator model. (d) Distribution in c.m. excess energy compared with the same simulation.

Figure 2

Differential cross sections for $pn\to d\varphi$ for different ranges of excess energy, with the left panels showing the dependence on the angle of the $K^{+}$ from the $\varphi$ decay in the $\varphi$ rest frame, and the right panels the dependence on the polar angle of the $\varphi$ in the overall c.m. system. Vertical error bars indicate purely statistical uncertainties, whereas the horizontal ranges reflect the bin width.

Figure 3

Total cross section for the quasifree $pn\to d\varphi$ reaction as a function of the excess energy (solid circles). In addition to the statistical error bars shown, there are overall systematic uncertainties of $\pm 10\%$. The curve represents a phase-space $\sqrt{ϵ}$ behavior. For comparison, we also show as open circles the values obtained from $pp\to pp\varphi$ [8].