Search for $\eta (1475)\to K_S^0{K}^{\pm }{\pi }^{\mp }$ in two-photon fusion at the CLEO detector at Cornell

We analyze $13.8\mathrm{f}{\mathrm{b}}^{-1}$ of the integrated $e^{+}{e}^{-}$ luminosity collected at 10.6 GeV center-of-mass energy with the CLEO II and CLEO II.V detectors to study exclusive two-photon production of hadrons with masses below $1.7\mathrm{GeV}/{\mathrm{c}}^2$ decaying into the $K_S^0{K}^{\pm }{\pi }^{\mp }$ final state. We observe two statistically significant enhancements in the $\eta (1475)$ mass region. These enhancements have large transverse momentum which rules them out as being due to pseudoscalar resonances but is consistent with the production of axial-vector mesons. We use tagged two-photon events to study the properties of the observed enhancements and associate them with the production of $f_1(1285)$ and $f_1(1420)$. Our nonobservation of $\eta (1475)$ is inconsistent by more than 2 standard deviations with the first observation of this resonance in two-photon collisions by the L3 experiment. We present our estimates for 90% confidence level upper limits on the products of two-photon partial widths of light pseudoscalar hadrons and their branching fractions into $K_S^0({\pi }^{+}{\pi }^{-})K^{\pm }{\pi }^{\mp }$.

Figure 1

The shapes of partial (i.e. integrated over $p_{\perp }$ bins) cross sections $\Delta \sigma (e^{+}{e}^{-}\to e^{+}{e}^{-}\mathcal{R})$ for pseudoscalar (solid line, pole-mass parameter 770 MeV) and axial-vector (dashed and dashed-dotted lines for pole-mass parameters of 770 MeV and 400 MeV, respectively) mesons in MC at generator-level. The distributions for axial-vector mesons are normalized to the same integrated luminosity. Note that a relatively small fraction of pseudoscalar events is expected in the region of $P_{\perp }$ above 100 MeV/c, where most axial-vector mesons are produced.

Figure 2

The measurements of $dE/dx$ for (a) CLEO II and (b) CLEO II.V, and (c) TOF versus charged track momentum (shown in (d) before applying the PID requirements) for untagged $K_S^0{K}^{\pm }{\pi }^{\mp }$ data event candidates with invariant masses below $1.7\mathrm{GeV}/{\mathrm{c}}^2$ after all selection requirements but PID are applied.

Figure 3

The difference between the reconstructed and the generated scalar values of the $p_{\perp }$, for $\eta (1475)\to K_S^0{K}^{\pm }{\pi }^{\mp }$ signal MC after all selection criteria but $p_{\perp }$ are applied to the untagged sample. The curve shows the result of a Gaussian fit to the core part of the distribution.

Figure 4

The distributions of the $K_S^0{K}^{\pm }{\pi }^{\mp }$ invariant mass for data events detected with (a) $p_{\perp }\le 100\mathrm{MeV}/\mathrm{c}$, (b) $100\mathrm{MeV}/\mathrm{c}\le p_{\perp }\le 200\mathrm{MeV}/\mathrm{c}$ and (c) $200\mathrm{MeV}/\mathrm{c}\le p_{\perp }\le 600\mathrm{MeV}/\mathrm{c}$ in the untagged mode, and (d) for all $p_{\perp }$ in the tagged mode. The dashed curves in (a) show the strength of the expected $\eta (1475)$ signal according to the L3 results[5]. The solid curves in (a), (c) and (d) are the results of binned maximum likelihood fits for resonances with a polynomial approximation to the noninterfering combinatorial background. For (a), only the strength of the $\eta (1475)$ resonance is fit. For (c) and (d), the strength of $f_1(1285)$ and $f_1(1420)$ are fit. For the fit shown in (a), we use the mass and full width according to L3 estimates[5]. For the fit shown in (c), we use the masses and full widths obtained from our fit to the tagged invariant mass distribution shown in (d).

Figure 5

Reconstructed invariant mass distribution for $K_S^0$ candidates from untagged $K_S^0{K}^{\pm }{\pi }^{\mp }$ data event candidates with mass below $1.7\mathrm{GeV}/{\mathrm{c}}^2$ after all selection criteria are applied. Also shown is the result of the fit with $K_S^0$ MC shape and straight-line approximation to the combinatorial background.

Figure 6

The collinearity angle (degrees) between the $K_S^0{K}^{\pm }{\pi }^{\mp }$ system and the tagging electron (or positron) in the plane perpendicular to the collision axis. The data are represented by the points with error bars. The dashed straight line approximates not fully reconstructed two-photon events. The solid histogram is a fit to the data with the signal MC shape for axial-vector meson production and the aforementioned approximation for the background. The vertical line indicates the selection criterion for tagged events.

Figure 7

The invariant mass of $K_S^0{K}_S^0$ candidates in data. Events to the left of the vertical line are accepted for calibration and efficiency studies.

Figure 8

Transverse momentum of $K_S^0{K}_S^0$ candidates from the calibration data sample (points) and MC (solid histogram) after all selection criteria but $p_{\perp }$ are applied. The MC distribution is normalized to data for $p_{\perp }$ below 100 MeV/c, which is also the selection criterion applied to our $K_S^0{K}^{\pm }{\pi }^{\mp }$ candidates in the untagged analysis.

Figure 9

90% CL upper limits (in eV) on ${\Gamma }_{\gamma \gamma }(1475)\mathcal{B}(K_S^0({\pi }^{+}{\pi }^{-})K^{\pm }{\pi }^{\mp })$ versus the mass of $\eta (1475)$ for various hypotheses for its full width assuming three-body phase-space decay to $K_S^0{K}^{\pm }{\pi }^{\mp }$.

Figure 10

90% CL upper limits (in eV) on ${\Gamma }_{\gamma \gamma }(1475)\mathcal{B}(K_S^0({\pi }^{+}{\pi }^{-})K^{\pm }{\pi }^{\mp })$ versus the mass of $\eta (1475)$ for various hypotheses for its full width assuming two-body decay to ${\overline{K}}^{*}K$ followed by the decay $K_S^0{K}^{\pm }{\pi }^{\mp }$.

Figure 11

Dalitz plot for $f_1(1420)$ candidates detected in tagged data events in the $K_S^0{K}^{\pm }{\pi }^{\mp }$ invariant mass region between $1.35\mathrm{GeV}/{\mathrm{c}}^2$ and $1.55\mathrm{GeV}/{\mathrm{c}}^2$ (a). The projections of Dalitz plot on the $K^{\pm }{\pi }^{\mp }$ (b) and $K_S^0{\pi }^{\mp }$ (c) invariant masses. The $K_S^0{K}^{\pm }{\pi }^{\mp }$ invariant mass distribution (d) for data events with at least one $K\pi$ combination in the $K^{*}$ mass region indicated by the vertical and horizontal bands in (a), (b) and (c). Solid and dashed curves show the results of the fits.