Electroproduction of $\varphi (1020)$ mesons at $1.4⩽Q^2⩽3.8$ GeV${}^2$ measured with the CLAS spectrometer

Electroproduction of exclusive ϕ vector mesons has been studied with the CLAS detector in the kinematic range $1.4⩽Q^2⩽3.8$ GeV${}^2,0.0⩽t^{\text{'}}⩽3.6$ GeV${}^2$, and $2.0⩽W⩽3.0$ GeV. The scaling exponent for the total cross section as $1/(Q^2+M_{\varphi }^2){}^n$ was determined to be $n=2.49\pm 0.33$. The slope of the four-momentum transfer $t^{\text{'}}$ distribution is $b_{\varphi }=0.98\pm 0.17$ GeV${}^{-2}$. Under the assumption of $s$-channel helicity conservation, we determine the ratio of longitudinal to transverse cross sections to be $R=0.86\pm 0.24$. A two-gluon exchange model is able to reproduce the main features of the data.

Figure 1

Graphical representation of ϕ-meson electroproduction. Shown from left to right then above are the electron scattering plane, the hadron production plane, and helicity rest frame of the $\varphi ,$ respectively.

Figure 2

Energy deposited by the electron candidates in the electromagnetic calorimeter vs momentum. The lines show the selection cuts for good electrons as described in the text.

Figure 3

Mass computed from the flight time vs momentum for positive particles. The top band corresponds to protons, the middle band corresponds to $K^{+}$'s, and the lower enhancement at 1.5 GeV/$c$ momentum is due to pion contamination.

Figure 4

Distribution of ${\mathrm{epK}}^{+}X$ missing mass. The vertical lines indicate the cuts placed to select events with a missing $K^{-}$.

Figure 5

$K^{+}{K}^{-}$ invariant mass including all data cuts and a fit to ϕ peak with Eq. (3).

Figure 6

Sketch of exclusive $\varphi (1020)$ production via Pomeron exchange and of excited hyperon production, of which $\Lambda (1520)$ is an example. This is the primary physics background for $\varphi (1020)$ production.

Figure 7

Dalitz plot of $M_{\mathit{pK}}^2$ vs $M_{\mathit{KK}}^2$. The well-defined horizontal strip is the $\Lambda (1520)$ band. The vertical strip is the $\varphi (1020)$ band.

Figure 8

2-D acceptance in $Q^2$ and $t$, as well as the 1-D acceptance in $Q^2,W$, and $-t$. Error bars are not shown; the lines are present to guide the eye. The axes in the 2-D plot in (a) have the same range as that of the axis of the two 1-D plots in (b) and (d).

Figure 9

2-D acceptance in $\cos {\theta }_H$ and ψ, as well as the 1-D acceptance in $\cos {\theta }_H,\Phi$, and ψ. Error bars are not shown; the lines are present to guide the eye. The axes in the 2-D plot in (a) have the same range as that of the axis of the two 1-D plots in (b) and (c).

Figure 10

Radiative correction $F_{\mathrm{rad}}$ as a function of Φ for assorted values of $W$ from 2.0 to 3.0 GeV. The correction for each $W$ value was computed for $\langle Q^2\rangle =2.47$ GeV${}^2$ and $\langle \cos {\theta }_{c.m.}\rangle =0.345$.

Figure 11

Plot of $d\sigma /{\mathit{dt}}^{\text{'}}$ along with an exponential fit.

Figure 12

$d\sigma /d\Phi$ vs Φ. The curve shows a fit to Eq. (11) which is used to determine ${\sigma }_{\mathit{TT}}$ and ${\sigma }_{\mathit{LT}}$. The dotted line is a fit to a constant function which is expected from SCHC.

Figure 13

Unnormalized polar angular decay distribution of the $K^{+}$ integrated over all $Q^2$ values plus a fit to Eq. (20). Also shown is the extracted $r_{00}^{04}$ parameter.

Figure 14

Unnormalized azimuthal angular distribution extracted for all $Q^2$ values plus a fit to Eq. (22). The value of $r_{1-1}^1$ can also be used to determine $R$.

Figure 15

Total cross sections as a function of $Q^2$ for our data (red full circles), previous JLab data (open circles) [22], Cornell data (stars) for $W$ between 2 and 3.7 GeV [21], HERMES data (triangles) for $W$ between 4 and 6 GeV [23], and HERA data (squares) at high $W$ [26]. The curves show the predictions of the JML model at $W=2.9$, 2.45, and 2.1 GeV (top to bottom).

Figure 16

Fit to the cross section as a function of $Q^2$ distribution to determine scaling using data from the present experiment and CLAS data from Ref. [22].

Figure 17

Exponential slope $b_{\varphi }$ plotted as a function of the fluctuation parameters $c\Delta \tau$ for the world data. The data at high $W$ measure an asymptotic slope corresponding to long fluctuation times. At low $W$ and relatively large $Q^2$, the fluctuation times becomes small and constrain the size of the interaction volume.

Figure 18

$d\sigma /\mathit{dt}$ vs $-t$ for the entire $Q^2$ range, and the JML predictions for $W=2.5$ GeV at five values of $Q^2=1.6,2.1,2.6,3.8$, and 5 GeV${}^2$, top to bottom.

Figure 19

$R={\sigma }_L/{\sigma }_T$ vs $Q^2$ for our data (solid circles), previous CLAS result (open circle), HERMES results (triangles), Cornell data (stars), ZEUS data (open diamonds), and HERA data (squares). The two determinations from the present analysis are separated for ease of viewing about the actual $Q^2$ value of 2.21 GeV${}^2$.