Photoproduction of the $f_1\left(1285\right)$ meson

The $f_1\left(1285\right)$ meson with mass $1281.0\pm 0.8$ MeV/$c^2$ and width $18.4\pm 1.4$ MeV (full width at half maximum) was measured for the first time in photoproduction from a proton target using CLAS at Jefferson Lab. Differential cross sections were obtained via the $\eta {\pi }^{+}{\pi }^{-},K^{+}{\overline{K}}^0{\pi }^{-}$, and $K^{-}{K}^0{\pi }^{+}$ decay channels from threshold up to a center-of-mass energy of 2.8 GeV. The mass, width, and an amplitude analysis of the $\eta {\pi }^{+}{\pi }^{-}$ final-state Dalitz distribution are consistent with the axial-vector $J^P=1^{+} f_1\left(1285\right)$ identity, rather than the pseudoscalar $0^{-} \eta \left(1295\right)$. The production mechanism is more consistent with $s$-channel decay of a high-mass $N^{*}$ state and not with $t$-channel meson exchange. Decays to $\eta \pi \pi$ go dominantly via the intermediate $a_0^{\pm }\left(980\right){\pi }^{\mp }$ states, with the branching ratio $\mathrm{\Gamma }\left[a_0\pi \text{(no}\overline{K}K\text{)}\right]/\mathrm{\Gamma }\left[\eta \pi \pi \text{(all)}\right]=0.74\pm 0.09$. The branching ratios $\mathrm{\Gamma }\left(K\overline{K}\pi \right)/\mathrm{\Gamma }\left(\eta \pi \pi \right)=0.216\pm 0.033$ and $\mathrm{\Gamma }\left(\gamma {\rho }^0\right)/\mathrm{\Gamma }\left(\eta \pi \pi \right)=0.047\pm 0.018$ were also obtained. The first is in agreement with previous data for the $f_1\left(1285\right)$, while the latter is lower than the world average.

Figure 1

Missing mass off the proton for the $\eta {\pi }^{+}{\pi }^{-}p$ final state summed over the full kinematic range. The ${\eta }^{\prime }\left(958\right)$ and $f_1\left(1285\right)$ mesons are visible. The $f_1\left(1285\right)$ is seen atop a substantial multipion background.

Figure 2

Example fits for two methods of treating spectra of missing mass off the proton for $\gamma p\to p\eta {\pi }^{+}{\pi }^{-}$ in the same bin $W=2.35$ GeV and $cos{\mathrm{\Theta }}^{\text{c.m.}}=-0.7$. (a) Voigtian signal plus polynomial background (solid red line) and background only (dashed red line); (b) Monte Carlo template method with smoothed 4-MeV-wide bins. The $f_1\left(1285\right)$ signal is the lowest histogram (red), with the $p\rho \pi \pi$ background (green), the $f\left(1370\right)p$ background (brown), the sum of the three simulated spectra (blue), and the data (gray). The fit range was 1.20 to 1.35 GeV for both methods.

Figure 3

Missing mass off the proton for (a) $\gamma p\to p{\pi }^{-}{K}^{+}\left({\overline{K}}^0\right)$ and (b) $\gamma p\to p{\pi }^{+}{K}^{-}\left(K^0\right)$. The small bumps at 1.28 GeV show the meson of interest. These spectra are summed over the full kinematic domain.

Figure 4

Summed data for the reactions $\gamma p\to p{\pi }^{-}{K}^{+}\left({\overline{K}}^0\right)$ and $\gamma p\to p{\pi }^{+}{K}^{-}\left(K^0\right)$ in the kinematic bin $W=2.45$ GeV and $-0.2<cos{\mathrm{\Theta }}^{\text{c.m.}}<0.0$. The Voigtian-plus-polynomial fit (total is the solid red line; polynomial is the dashed line) gives the yield of $f_1\left(1285\right)$ events.

Figure 5

Missing mass off the proton for $\gamma p\to p{\pi }^{+}{\pi }^{-}\left(\gamma \right)$ events after kinematic fitting and confidence level cut for one run (open histogram). A strong signal for $\omega /{\rho }^0$ near $800 \mathrm{MeV}/c^2$ remains, as well as the ${\eta }^{\prime }\left(958\right)$ and a slight hint of the broad $a_2\left(1320\right)$. The solid histogram shows the effect of a minimum missing transverse momentum in reducing background. No significant $f_1\left(1285\right)$ signal is seen at this stage.

Figure 6

(a) Missing mass off the proton for $\gamma p\to p{\pi }^{+}{\pi }^{-}\left(\gamma \right)$ fitted with a Voigtian signal shape plus a polynomial background. (b) Spectrum after background subtraction using the polynomial parameters from the fit.

Figure 7

Differential cross sections $d\sigma /d\mathrm{\Omega }$ for $\gamma p\to {\eta }^{\prime }\left(958\right)p$ from the present measurement (solid blue points) compared to recent CLAS-published results from Ref. [39] (open red circles) and Ref. [47] (open green squares). Note that bins for $W=2.45$ GeV and above are on semilogarithmic scales. Data agreement in bins for $W=2.35$ GeV and above, bins used later in this analysis, is very good.

Figure 8

The mass (top row) and Lorentzian width $\mathrm{\Gamma }$ (bottom row) of the meson from fits binned in $W$ and $cos{\mathrm{\Theta }}^{\text{c.m.}}$. The width parameters were part of a Voigtian line shape using the bin-dependent experimental mass resolution. The overall weighted mean of each quantity is shown by the corresponding horizontal red lines. See the summary in Table 2.

Figure 9

Differential cross section $d\sigma /d\mathrm{\Omega }$ for $\gamma p\to f_1\left(1285\right)p$, with $f_1\left(1285\right)\to \eta {\pi }^{+}{\pi }^{-}$ as a function of the meson c.m. production angle. The vertical error bars are the statistical uncertainties from fitting and from combining two decay modes. The shaded histogram is the total point-to-point systematic uncertainty discussed in the text. Each panel shows a 100-MeV-wide bin centered at the indicated $W$.

Figure 10

Cross section comparison for $\gamma p\to f_1\left(1285\right)p\to \eta {\pi }^{+}{\pi }^{-}p$ (blue solid circles) compared to $\gamma p\to {\eta }^{\prime }\left(958\right)p\to \eta {\pi }^{+}{\pi }^{-}p$ (red open circles) at $W=2.55\mathrm{GeV}$. The $f_1\left(1285\right)$ differential cross section is not forward-peaked as is that of the ${\eta }^{\prime }$(958). Note the logarithmic vertical scale.

Figure 11

Differential cross sections $d\sigma /d\mathrm{\Omega }$ for $\gamma p\to f_1\left(1285\right)p$ and $f_1\left(1285\right)\to \eta {\pi }^{+}{\pi }^{-}$ as a function of the meson c.m. production angle for five values of the frame-invariant energy, $W$. The error bars are statistical only. The solid red line is the prediction by Kochelev et al. [21] for the $f_1\left(1285\right)$ and the dashed red line is the corresponding prediction for the $\eta \left(1295\right)$. The curves have been scaled by the PDG branching fraction for $f_1\left(1285\right)\to \eta {\pi }^{+}{\pi }^{-}$ (see text). The dotted line is the incoherent sum of both mesons.

Figure 12

Predictions from several models of $f_1\left(1285\right)$ photoproduction compared to the present results at $W=2.45$ GeV and $W=2.65$ GeV. The Kochelev et al. model prediction [21] for the $f_1\left(1285\right)$ (solid red line) is generally closest to the data, but the match is poor. The model of Domokos et al. [22] (dashed blue line) is based on $\rho$ and $\omega$ exchange using a specific model for the coupling to the $f_1\left(1285\right)$: The meson-exchange model prediction of Huang et al. [23, 51] (dotted black line) used hadronic form factors unconstrained by other reactions.

Figure 13

(a) Initial Dalitz plot for $\eta {\pi }^{+}{\pi }^{-}$ events with missing mass off the proton between 1251 and $1311 \mathrm{MeV}/c^2$, prior to sideband subtraction. (b) After subtracting weighted and scaled multipion sidebands. The result is not yet corrected for acceptance.

Figure 14

Dalitz plot boundaries for several decays to $\eta {\pi }^{+}{\pi }^{-}$. The solid red curves show the limits for decay of the ${\eta }^{\prime }$(958) and an $x\left(1280\right)$ meson. The solid blue curves mark the limits for events with missing mass off the proton in 30-MeV-wide sidebands of the meson signal shown in the inset. The dashed blue curves show the transformed boundaries of sideband events using the method discussed in the text.

Figure 15

Acceptance-corrected Dalitz plot for $\eta {\pi }^{+}{\pi }^{-}$ events with missing mass off the proton between 1251 and $1311 \mathrm{MeV}/c^2$ after subtracting the weighted and scaled sidebands.

Figure 16

Helicity system fit for the $x\to \eta {\pi }^{+}{\pi }^{-}$ Dalitz distribution. Both data and simulation events are restricted to the range of the dominant $a_0$ bands and folded on the symmetry axis (black diagonal). (a) Data; (d) amplitude-weighted Monte Carlo simulation; (b) projection onto the vertical axis; and (c) onto the horizontal axis. Blue dashed histogram, coherent $m=0$ for $L=0$ and $L=1$; green lower solid line, $m=\pm 1,L=1$; red solid upper line, sum total.