Photoproduction of ${\pi }^{+}{\pi }^{-}$ meson pairs on the proton

The exclusive reaction $\gamma p\to p{\pi }^{+}{\pi }^{-}$ was studied in the photon energy range 3.0–3.8 GeV and the momentum transfer range $0.4<-t<1.0{\mathrm{GeV}}^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. In this kinematic range, the integrated luminosity was about $20{\mathrm{pb}}^{-1}$. The reaction was isolated by detecting the ${\pi }^{+}$ and proton in CLAS, and reconstructing the ${\pi }^{-}$ via the missing-mass technique. Moments of the di-pion decay angular distributions were derived from the experimental data. Differential cross sections for the $S$, $P$, and $D$-waves, in the $M_{{\pi }^{+}{\pi }^{-}}$ mass range 0.4–1.4 GeV, were derived performing a partial wave expansion of the extracted moments. Beside the dominant contribution of the $\rho (770)$ meson in the $P$-wave, evidence for the $f_0(980)$ and the $f_2(1270)$ mesons was found in the $S$ and $D$-waves, respectively. The differential production cross sections $d\sigma /dt$ for individual waves in the mass range of the above-mentioned mesons were extracted. This is the first time the $f_0(980)$ has been measured in a photoproduction experiment.

Figure 1

Missing mass squared for the reaction $\gamma p\to p{\pi }^{+}X$ and the ${\pi }^{-}$ peak. The shaded area indicates the retained events.

Figure 2

Two dimensional plot of the invariant masses obtained combining pairs of particles of the exclusive reaction $\gamma p\to p{\pi }^{+}{\pi }^{-}$.

Figure 3

Invariant masses obtained combining pairs of particles of the exclusive reaction $\gamma p\to p{\pi }^{+}{\pi }^{-}$. Upper panel $M_{{\pi }^{+}{\pi }^{-}}$; lower panel left $M_{p{\pi }^{+}}$; lower panel right $M_{p{\pi }^{-}}$. Spectra are not corrected for the detector acceptance.

Figure 4

Moments of the di-pion angular distribution in $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $-t=0.45\pm 0.05{\mathrm{GeV}}^2$ (black dots), $-t=0.65\pm 0.05{\mathrm{GeV}}^2$ (red squares) and $-t=0.95\pm 0.05{\mathrm{GeV}}^2$ (blue trianges). The error bars include both the statistical and systematic uncertainties as explained in the text.

Figure 5

Moments of the di-pion angular distribution in $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $-t=0.45\pm 0.05{\mathrm{GeV}}^2$ (black dots), $-t=0.65\pm 0.05{\mathrm{GeV}}^2$ (red squares) and $-t=0.95\pm 0.05{\mathrm{GeV}}^2$ (blue triangles). The error bars include both the statistical and systematic uncertainties as explained in the text.

Figure 6

Moments of the di-pion angular distribution in $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $-t=0.45\pm 0.05{\mathrm{GeV}}^2$ (black dots), $-t=0.65\pm 0.05{\mathrm{GeV}}^2$ (red squares) and $-t=0.95\pm 0.05{\mathrm{GeV}}^2$ (blue triangles). The error bars include both the statistical and systematic uncertainties as explained in the text.

Figure 7

Moments of the di-pion angular distribution in $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $-t=0.45\pm 0.05{\mathrm{GeV}}^2$ (black dots), $-t=0.65\pm 0.05{\mathrm{GeV}}^2$ (red squares) and $-t=0.95\pm 0.05{\mathrm{GeV}}^2$ (blue triangles). The error bars include both the statistical and systematic uncertainties as explained in the text.

Figure 8

Fit result (black line) of the final experimental moments (red dots) for $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$. The systematic uncertainty and fit uncertainty are added in quadrature and are shown by the gray band.

Figure 9

Fit result (black line) of the final experimental moments (red dots) for $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$. The systematic uncertainty and fit uncertainty are added in quadrature and are shown by the gray band.

Figure 10

Fit result (black line) of the final experimental moments (red dots) for $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$. The systematic uncertainty and fit uncertainty are added in quadrature and are shown by the gray band.

Figure 11

Fit result (black line) of the final experimental moments (red dots) for $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$. The systematic uncertainty and fit uncertainty are added in quadrature and are shown by the gray band.

Figure 12

$S$-wave cross section derived by the fit in the $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$ bin. The systematic and the fit uncertainties are added in quadrature and are shown by the gray band.

Figure 13

$P$-wave cross section derived by the fit in the $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$ bin. Bottom plots: the same amplitudes for the three possible values of ${\lambda }_{\pi \pi }$ (from left to right $-1$, 0, and $+1$). The systematic and fit uncertainties are added in quadrature and are shown by the gray band.

Figure 14

As Fig. 13 for $D$-wave.

Figure 15

As Fig. 13 for $F$-wave.

Figure 16

Pion angles in the ${\pi }^{+}{\pi }^{-}$ helicity rest frame for $M_{\pi \pi }$ in the $f_0(980)$ mass region ($M_{\pi \pi }=0.985\pm 0.01\mathrm{GeV}$). The experimental data are plotted in black (large dots) and the fit results in red (small dots).

Figure 17

$M_{p{\pi }^{+}}$ distribution in three different $M_{\pi \pi }$ mass regions (bottom: $M_{\pi \pi }=0.475\pm 0.01\mathrm{GeV}$, middle: $M_{\pi \pi }=0.775\pm 0.01\mathrm{GeV}$, top: $M_{\pi \pi }=1.295\pm 0.01\mathrm{GeV}$). The experimental data are plotted in black (large dots) and the fit results in red (small dots).

Figure 18

$S$-, $P$- and $D$-wave cross sections in the $3.4<E_{\gamma }<3.6\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$ bin. The gray (filled area) and red (cross hatched) bands show the results of the standard fit and the fit performed adding a second-order polynomial to the partial wave expansion of the moments to account for the baryon resonance contributions. The width of the bands represents the fit uncertainties only. The fit results are shown for a specific parametrization of the moments (second method, see Sec. 3b3).

Figure 19

Spin density matrix elements for the $P$-wave in the $3.0<E_{\gamma }<3.2\mathrm{GeV}$ and $0.4<-t<0.5{\mathrm{GeV}}^2$ bin. The black dots are data points from Ref. [9], taken in a similar kinematic bin ($E_{\gamma }\sim 2.8\mathrm{GeV}$ and $0.02<-t<0.4{\mathrm{GeV}}^2$).

Figure 20

Spin density matrix elements for the $P$-wave in the $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$ bin.

Figure 21

Spin density matrix elements for the interference between $S$- and $P$-waves in the $3.2<E_{\gamma }<3.4\mathrm{GeV}$ and $0.5<-t<0.6{\mathrm{GeV}}^2$ bin.

Figure 22

Differential cross section $d\sigma /dt$ for the $S$-wave in the $M_{\pi \pi }$ range $0.98\pm 0.04\mathrm{GeV}$ and photon energy range $E_{\gamma }=3.0–3.8\mathrm{GeV}$. The solid line corresponds to an exponential fit $A{e}^{Bt}$, with $A=(0.6\pm 0.1)$ $\mu b/{\mathrm{GeV}}^2$, and $B=(3.7\pm 0.4){\mathrm{GeV}}^{-2}$.

Figure 23

Differential cross section $d\sigma /dt$ for the $P$-wave in the $M_{\pi \pi }$ range 0.4–1.2 GeV and photon energy range $E_{\gamma }=3.0–3.8\mathrm{GeV}$. The solid line corresponds to an exponential fit $A{e}^{Bt}$, with $A=(30.0\pm 5.0)$ $\mu b/{\mathrm{GeV}}^2$, and $B=(4.0\pm 0.3){\mathrm{GeV}}^{-2}$.

Figure 24

Differential cross section $d\sigma /dt$ for the $D$-wave in the $M_{\pi \pi }$ range $1.275\pm 0.185\mathrm{GeV}$ and photon energy range $E_{\gamma }=3.0–3.8\mathrm{GeV}$. The solid line corresponds to an exponential fit, $A{e}^{Bt}$, with $A=(0.8\pm 0.3)$ $\mu b/{\mathrm{GeV}}^2$, and $B=(1.8\pm 0.6){\mathrm{GeV}}^{-2}$.