Measurement of the $e^+e^-\toηγ$ cross section near the $φ(1020)$ resonance with the SND detector

TL;DR

The paper presents a high-precision measurement of the cross section for $e^+e^- o ηγ$ in the vicinity of the φ(1020) resonance using the SND detector at VEPP-2000, focusing on the $η o 2γ$ decay mode. A two-stage event selection and detailed modeling of backgrounds enable extraction of the signal yield, which is then corrected for radiative effects and beam-energy spread. The Born cross section is described with a vector meson dominance model including multiple vector resonances and interference, yielding four viable solutions; the nominal solution (φ phase near $180^ ext{o}$) provides the product $B(φ o e^+e^-)B(φ o ηγ) = (4.30 ext{ to } 4.33) imes 10^{-6}$ with corresponding uncertainties. Compared to previous measurements, the SND results are more precise and generally higher, enhancing constraints on φ decays and related low-energy QCD dynamics.

Abstract

In the experiment with the SND detector at the VEPP-2000 $e^+e^-$ collider, the $e^+e^-\toηγ$ cross section is measured in the energy range $E = 980 - 1060$ MeV. The measurement is carried out in the $η\to 2γ$ decay mode. Data with an integrated luminosity of 73 pb$^{-1}$ collected in 2018 and 2024 are used in the analysis. The measured cross section is the most accurate to date and is higher compared to other measurements. From the fit to the cross section data with the vector meson dominance model, the value of the product of the branching fractions $B(φ\to e^+e^-)B(φ\to ηγ)$ has been obtained.

Figures (6)

• Figure 1: The distribution of $\chi^2_{3\gamma}$ at $E = 1020.055$ MeV for the data (dots with error bars) and simulation of the signal and the background processes (open histogram). The shaded histogram represents the contribution of the multiphoton hadronic background. The simulated distributions are normalized to the number of expected events. The arrow indicates the boundary of the selection condition.
• Figure 2: The $M_{\gamma\gamma}$ distribution for data events (points with error bars) at $E = 1000.039$ MeV (left), $E = 1020.055$ MeV (middle), $E = 1049.992$ MeV (right). The solid curve represents the result of the fit described in the text. The background distribution is shown as stacked histograms for $F_{bkg}^{I}$ (in light gray) and $F_{bkg}^{II}$ (in dark gray).
• Figure 3: The $x$ dependence of the detection efficiency obtained from simulation is shown by points with error bars. The solid curve is the result of approximation by a smooth function.
• Figure 4: The Born cross section for the $e^+e^- \to \eta\gamma$ process. Left panel shows the cross section measured in this work for the 2024 (blue dots) and 2018 (red crosses) energy scans. Right panel shows the cross section measured by SND in Ref. SNDetg23. The black solid, red dashed, blue dotted and green dash-dotted curves represent the result of the fit described in the text for solution 1, 2, 3, and 4, respectively. The c.m. energy is corrected by the value of the energy scale shift (see Table \ref{['FitTab']}).
• Figure 5: The relative differences between the measured $e^+e^- \to \eta\gamma$ Born cross section and the result of the fit described in the text for this work (top left), for the SND measurement using the decay channel $\eta\to3\pi^0$ in Ref. SNDetg2007 (top right), for the CMD-2 measurement in Ref. CMDetg2001 (bottom left) and for the SND measurement in Ref. SNDetg2000 (bottom right). The solid line represents the average value of the relative difference. The shaded region represents the systematic uncertainty of corresponding measurement. The c.m. energy for the measurement from this work is corrected by the value of the energy scale shift (see Table \ref{['FitTab']}).