Differential cross sections and spin density matrix elements for the reaction $\gamma p\to p\omega$

High-statistics differential cross sections and spin-density matrix elements for the reaction $\gamma p\to p\omega$ have been measured using the CEBAF large acceptance spectrometer (CLAS) at Jefferson Lab for center-of-mass (c.m.) energies from threshold up to $2.84$ GeV. Results are reported in $112\hspace{0.5em}10$-MeV wide c.m. energy bins, each subdivided into $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$ bins of width $0.1$. These are the most precise and extensive $\omega$ photoproduction measurements to date. A number of prominent structures are clearly present in the data. Many of these have not previously been observed due to limited statistics in earlier measurements.

Figure 1

(a) The confidence levels resulting from four-constraint kinematic fits performed on a sample of events to the hypothesis $\gamma p\to p{\pi }^{+}{\pi }^{-}$ integrated over all kinematics. The “peak” near zero consists of events that do not match the hypothesis, along with poorly measured (due to multiple scattering, etc.) signal events. Agreement with the ideal (flat) distribution for signal events is very good. (b) Example pull-distribution for the momentum of the ${\pi }^{-}$ from the same kinematic fits as in (a). Only events with a confidence level larger than $1\%$ are shown. The line represents a Gaussian fit to this distribution. For this event sample, the parameters obtained are $\mu =-0.029\pm 0.001,\sigma =1.086\pm 0.001$ (the uncertainties are purely statistical), which are in very good agreement with the ideal values $\mu =0,\sigma =1$. Both (a) and (b) are good indicators that the CLAS error matrix is well understood.

Figure 2

$\Delta {\mathrm{tof}}_{{\pi }^{+}}$(ns) versus $\Delta {\mathrm{tof}}_p$(ns): Particle identification cut for a sample of events that pass a $10\%$ confidence level cut when kinematically fit to the hypothesis $\gamma p\to p{\pi }^{+}{\pi }^{-}({\pi }^0)$. The black lines indicate the timing cuts. Note the logarithmic scale on the intensity axis.

Figure 3

(a) The $3\pi$ invariant mass distribution in the $W=2.205$ GeV bin, integrated over all kinematics, for all events (unshaded) and for events weighted by the background factors, $1-Q$ (shaded). (b) The $\lambda$ distribution of events in the same $W$ bin that satisfy $|M_{3\pi }-M_{\omega }|<25$ MeV/$c^2$ (unshaded), the same events weighted by signal factors $Q$ (red, dashed), and by background factors $1-Q$ (shaded). The line represents a fit of the signal to the function $a\lambda$.

Figure 4

The $3\pi$ invariant mass distribution in the $W=1.735$ GeV bin, integrated over all kinematics, for all events (unshaded) and for events weighted by the background factors, $1-Q$ (shaded).

Figure 5

Example fit result in the $W=2.005$ GeV bin for data (black squares), phase space accepted Monte Carlo events (blue, dashed line) and phase space accepted Monte Carlo events weighted by the fits discussed in Sec. 5 (red, solid line). The weighted Monte Carlo provides an excellent description of the data.

Figure 6

$\varphi$ versus $\cos \theta$ in the Adair frame (see Sec. 8 B) in $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$ bins: Example fit result in the $W=2.005$ GeV bin for data (top row), phase space accepted Monte Carlo events (middle row), and phase space accepted Monte Carlo events weighted by the fits discussed in Sec. 5 (bottom row). (a) shows backward angles, while (b) shows forward angles. Note that the weighted Monte Carlo provides an accurate description of the data (${\chi }^2/$degrees of freedom $~0.6$).

Figure 7

$\frac{d\sigma }{d\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }}$ $(\mu b)$ versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Differential cross-section results for bins in the energy range $1.72$ GeV $⩽W<$ $2.00$ GeV. The centroid of each $10$-MeV wide bin is printed on the plot. The lack of reported data points in the $W=1.955$ GeV bin is discussed in Sec. 6. The error bars, which do not include systematic uncertainties, are discussed in the text. The additional near-threshold background separation uncertainties, discussed in Sec. 4, are clearly visible in the first four center-of-mass energy bins. Note that the vertical scales are linear up to $W$ of $1.945$ GeV and logarithmic above that.

Figure 8

$\frac{d\sigma }{d\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }}$ ($\mu$b) versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Differential cross-section results for bins in the energy range $2.00$ GeV $⩽W<$ $2.28$ GeV. The centroid of each $10$-MeV wide bin is printed on the plot. The error bars, which do not include systematic uncertainties, are discussed in the text.

Figure 9

$\frac{d\sigma }{d\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }}$ ($\mu$b) versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Differential cross-section results for bins in the energy range $2.28$ GeV $⩽W<$ $2.56$ GeV. The centroid of each $10$-MeV wide bin is printed on the plot. The error bars, which do not include systematic uncertainties, are discussed in the text.

Figure 10

$\frac{d\sigma }{d\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }}$ ($\mu$b) versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Differential cross-section results for bins in the energy range $2.56$ GeV $⩽W<$ $2.84$ GeV. The centroid of each $10$-MeV wide bin is printed on the plot. The lack of reported data points in the $W=2.735$ GeV and $W=2.745$ GeV bins is discussed in Sec. 6. The error bars, which do not include systematic uncertainties, are discussed in the text.

Figure 11

${\rho }_{{\mathit{MM}}^{\text{'}}}^0$ versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Spin-density matrix element measurements, in the Adair frame, for bins in the range $1.72$ GeV $⩽W<$ $2.00$ GeV. The black squares are ${\rho }_{00}^0$, the (red) circles are ${\rho }_{1-1}^0$, and the (blue) crosses are $\mathrm{Re}({\rho }_{10}^0)$. The centroid of each $10$-MeV wide bin is printed on the plot. The error bars do not include systematic uncertainties.

Figure 12

${\rho }_{{\mathit{MM}}^{\text{'}}}^0$ versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Spin-density matrix element measurements, in the Adair frame, for bins in the range $2.00$ GeV $⩽W<$ $2.28$ GeV. The black squares are ${\rho }_{00}^0$, the (red) circles are ${\rho }_{1-1}^0$, and the (blue) crosses are $\mathrm{Re}({\rho }_{10}^0)$. The centroid of each $10$-MeV wide bin is printed on the plot. The error bars do not include systematic uncertainties.

Figure 13

${\rho }_{{\mathit{MM}}^{\text{'}}}^0$ versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Spin-density matrix element measurements, in the Adair frame, for bins in the range $2.28$ GeV $⩽W<$ $2.56$ GeV. The black squares are ${\rho }_{00}^0$, the (red) circles are ${\rho }_{1-1}^0$, and the (blue) crosses are $\mathrm{Re}({\rho }_{10}^0)$. The centroid of each $10$-MeV wide bin is printed on the plot. The error bars do not include systematic uncertainties.

Figure 14

${\rho }_{{\mathit{MM}}^{\text{'}}}^0$ versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Spin-density matrix element measurements, in the Adair frame, for bins in the range $2.56$ GeV $⩽W<$ $2.84$ GeV. The black squares are ${\rho }_{00}^0$, the (red) circles are ${\rho }_{1-1}^0$, and the (blue) crosses are $\mathrm{Re}({\rho }_{10}^0)$. The centroid of each $10$-MeV wide bin is printed on the plot. The error bars do not include systematic uncertainties.

Figure 15

A comparison of the theoretical models of Oh et al. [8] (red, dashed lines) and Laget [6, 7] (blue, dot-dashed lines) to the $W=2.805$ GeV data presented in this article (black squares).

Figure 16

$\frac{d\sigma }{d\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }}$ ($\mu$b) versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Comparison of the present CLAS results [(blue) circles] with previously published results from CLAS [4] (black open crosses, triangles, squares, and circles) and Daresbury [2, 3] [(red) open diamonds and stars] in the energy range 2.62 GeV $<W<$ 2.96 GeV. The Daresbury $(1977)$ points have no error bars; the points were extracted from a portable document format (PDF) image.

Figure 17

$\frac{d\sigma }{d\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }}$ ($\mu$b) versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Comparison of the present CLAS results [(blue) circles] with previously published results from SAPHIR [5] (black open squares).

Figure 18

${\rho }_{{\mathit{MM}}^{\text{'}}}^0$ in the Adair frame versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Comparison of the present CLAS results [(blue) circles] with previously published SAPHIR [5] results [open (red) squares and triangles]. SAPHIR extracted results independently in the Gottfried-Jackson and helicity frames—both presented here rotated to the Adair frame.

Figure 19

${\rho }_{{\mathit{MM}}^{\text{'}}}^0$ in the Adair frame versus $\cos {\theta }_{\mathrm{c}.\mathrm{m}.}^{\omega }$: Comparison of the present CLAS results [(blue) circles] with previously published Daresbury [3] [open (red) circles and triangles] and SLAC [1] (open black squares).