$\varphi$-meson photoproduction on hydrogen in the neutral decay mode

We report the first measurement of the photoproduction cross section of the $\varphi$ meson in its neutral decay mode in the reaction $\gamma p\to p\varphi \left(K_S{K}_L\right)$. The experiment was performed with a tagged photon beam of energy $1.6\le E_{\gamma }\le 3.6$ GeV incident on a liquid hydrogen target of the CLAS spectrometer at the Thomas Jefferson National Accelerator Facility. The $p\varphi$ final state is identified via reconstruction of $K_S$ in the invariant mass of two oppositely charged pions and by requiring the missing particle in the reaction $\gamma p\to p{K}_{S}X$ to be $K_L$. The presented results significantly enlarge the existing data on $\varphi$ photoproduction. These data, combined with the data from the charged decay mode, will help to constrain different mechanisms of $\varphi$ photoproduction.

Figure 1

Measured $\varphi$ photoproduction cross section for the charged kaon decay channel $(d\sigma /dt)$, extrapolated to $t=t_{\text{min}}$, as a function of incident photon energy $E_{\gamma }$ [22]. The dashed line shows the cross section calculated according to the model of Titov and Lee [16].

Figure 2

Difference between the time of the Start Counter hit closest to the event start time and the time of the tagger hits. A $\pm$2-ns cut was used to select good photons.

Figure 3

Invariant mass of the ${\pi }^{+}{\pi }^{-}$ system from the $\gamma p\to p{\pi }^{+}{\pi }^{-}$ reaction: (a) with a cut on the mass of the missing $K_L$ from the $\gamma p\to p{\pi }^{+}{\pi }^{-}X$ reaction $|M_X-M_{K_L}|<0.1$ GeV; (b) with a cut on the mass of the missing $K_L$ from the $\gamma p\to p{\pi }^{+}{\pi }^{-}X$ reaction $|M_X-M_{K_L}|<0.015$ GeV; (c) with the previous cut and an additional cut on the missing mass of $\gamma p\to pX$, $|M_X-M_{\varphi }|<0.02$ GeV.

Figure 4

Missing mass of the $\gamma p\to p{\pi }^{+}{\pi }^{-}X$ reaction: (a) with a cut on the invariant mass of the ${\pi }^{+}{\pi }^{-}$ system in the $\gamma p\to p{\pi }^{+}{\pi }^{-}$ reaction $|M\left({\pi }^{+}{\pi }^{-}\right)-M_{K_S}|<0.035$ GeV; (b) with a cut on the invariant mass of ${\pi }^{+}{\pi }^{-}$ $|M\left({\pi }^{+}{\pi }^{-}\right)-M_{K_S}|<0.008$ GeV; (c) with the previous cut and an additional cut on the missing mass of $\gamma p\to pX$, $|M_X-M_{\varphi }|<0.02$ GeV.

Figure 5

The missing mass of the $\gamma p\to pX$ reaction: (a) with cuts on the invariant mass of ${\pi }^{+}{\pi }^{-}$ $|M\left({\pi }^{+}{\pi }^{-}\right)-M_{K_S}|<0.035$ GeV and on the mass of the missing $K_L$ from the $\gamma p\to p{\pi }^{+}{\pi }^{-}X$ reaction $|M_X-M_{K_L}|<0.1$ GeV; (b) with a cut on the invariant mass of ${\pi }^{+}{\pi }^{-}$ $|M\left({\pi }^{+}{\pi }^{-}\right)-M_{K_S}|<0.008$ GeV; (c) with the previous cut and an additional cut on the mass of the missing $K_L$ from the $\gamma p\to p{\pi }^{+}{\pi }^{-}X$ reaction $|M_X-M_{K_L}|<0.015$ GeV.

Figure 6

Signal and background separation for $1.8\le E_{\gamma }<2.0$ GeV and different $cos{\theta }_{\text{c.m.}}$ bins. The histograms (black) are the unweighted distributions from data. The dash-dotted line (blue) shows the signal from the fit. The dashed line (magenta) shows the background from the fit. The solid line (green) shows the overall fit of the mass distribution.

Figure 7

Differential cross section $d\sigma /dt$ plotted versus $|t-t_{\text{min}}|$ for different photon energy bins in the $1.6\le E_{\gamma }<2.8$ GeV range. The solid downward triangles (black) are the results of the current CLAS(2013) analysis for the neutral decay mode of the $\varphi$. The open circles (red) are the SAPHIR [21] data for the charged-mode topology. The open squares (blue) are the LEPS [22] data for the charged-mode topology. The solid lines (cyan) show the fit function. The dashed lines (black) show the MC distribution.

Figure 8

Differential cross section $d\sigma /dt$ plotted versus $|t-t_{\text{min}}|$ for different photon energy bins in the $2.8\le E_{\gamma }\le 3.6$ GeV range. The solid triangles (black) are the results of the current CLAS(2013) analysis for the neutral decay mode of the $\varphi$. The open crosses (magenta) are the DARESBURY [23] data for the charged mode. The open stars (red) represent the CLAS(2000) [27] results for charged decay mode of the $\varphi$ meson. The solid lines (cyan) show the fit function. The dashed lines (black) show the MC distribution.

Figure 9

The $cos{\theta }_{\text{c.m.}}$ dependence of the $\varphi$ meson differential cross section $d\sigma /dcos{\theta }_{\text{c.m.}}$ for different photon beam energy bins $1.6\le E_{\gamma }<2.8$ GeV. The $cos{\theta }_{\text{c.m.}}$ bin size is 0.1. The dashed lines (black) show the MC distribution.

Figure 10

The $cos{\theta }_{\text{c.m.}}$ dependence of the $\varphi$ meson differential cross section $d\sigma /dcos{\theta }_{\text{c.m.}}$ for different photon beam energy bins $2.8\le E_{\gamma }\le 3.6$ GeV. The $cos{\theta }_{\text{c.m.}}$ bin size is 0.1. The dashed lines (black) show the MC distribution.

Figure 11

The $E_{\gamma }$ dependence of the $\varphi$ meson differential cross section $d\sigma /dt$ in different $cos{\theta }_{\text{c.m.}}$ bins for $-0.45\le cos{\theta }_{\text{c.m.}}<0.35$.

Figure 12

The $E_{\gamma }$ dependence of the $\varphi$ meson differential cross section $d\sigma /dt$ in different $cos{\theta }_{\text{c.m.}}$ bins for $0.35\le cos{\theta }_{\text{c.m.}}<0.95$.

Figure 13

(a) Differential cross section $d\sigma /dt$ at $t=t_{\text{min}}$ and (b) $\varphi$ meson photoproduction slope $B$ for the neutral decay mode plotted as a function of the photon beam energy $E_{\gamma }$. The error bars represent the statistical uncertainties. The solid circles (red) are the current CLAS (2013) data in the neutral mode. For the charged decay mode, the open circles (black) are the SAPHIR [21] results, the open squares (blue) are the LEPS [22] results, the open crosses (magenta) are the DARESBURY [23] data, the stars (black) are the SLAC [24] data, the open upward triangles (black) are the BONN [25] data, and the solid squares (cyan) are the DESY [26] data. The dashed curve represents the prediction of a model including the Pomeron trajectory, $\pi$, and $\eta$ exchange processes [16].