Initial-state radiation measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ cross section

We study the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}\gamma$, with a photon emitted from the initial-state electron or positron, using $454.3{\mathrm{fb}}^{-1}$ of data collected with the BABAR detector at SLAC, corresponding to approximately 260 000 signal events. We use these data to extract the nonradiative $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})$ cross section in the energy range from 0.6 to 4.5 GeV. The total uncertainty of the cross section measurement in the peak region is less than 3%, higher in precision than the corresponding results obtained from energy scan data.

Figure 1

(a,b) The ${\chi }_{4\pi }^2$ distribution for data without background subtraction (triangles) and signal MC (histogram) on a logarithmic and linear scale. (c) MC distributions of the principal backgrounds. (d) The difference between the measured and the simulated distributions from part (a,b). The dashed and solid vertical lines indicate the boundaries with the $0<{\chi }_{4\pi }^2<10$ region used for normalization and the ${\chi }_{4\pi }^2<30$ requirement, respectively.

Figure 2

(a) The ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ invariant mass distribution of ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}\gamma$ ISR events (triangles) for the main selection and the sum of simulated $K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}\gamma$, $K_S^0{K}^{\pm }{\pi }^{\mp }\gamma$, $\omega {\pi }^{+}{\pi }^{-}\gamma$ and nonradiative $uds$-continuum background (histogram). The large ${\pi }^{+}{\pi }^{-}\gamma \gamma$ and ${\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ background contribution in the threshold region ($M_{4\pi }<1.1\mathrm{GeV}/c^2$) is not included in the simulation. (b) The individual simulated background channel contributions from top to bottom as indicated in the legend.

Figure 3

(a) Invariant mass distribution under the ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ hypothesis for the data; (b) ${\pi }^{+}{\pi }^{-}$ invariant mass distribution for events with $M_{4\pi }$ in the $\psi (2S)$ mass region represented by the vertical lines in (a) (4 entries per event); (c) Same as part (a) after removing entries of the invariant ${\pi }^{+}{\pi }^{-}$-mass in the $J/\psi$ mass region represented by the vertical lines in (b).

Figure 4

${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}\gamma$ cross section in the threshold region for the data (squares) and for the data after requiring each track to satisfy a dedicated pion selection algorithm (triangles), corresponding to the method 2 selection criterion. The indicated uncertainties are statistical.

Figure 5

(a) The ${\chi }^2$ distribution for data after background subtraction (points), signal MC (histogram) and the sum of simulated background channels (hatched histogram). (b) The difference between data with background subtraction and signal MC. The dashed line indicates the boundary with the $0<{\chi }_{4\pi }^2<10$ region used for normalization.

Figure 6

The efficiency as a function of the ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ invariant mass. The vertical line at $M_{4\pi }=1.1\mathrm{GeV}/c^2$ separates the regions with and without a pion PID requirement for the reconstructed tracks. The curves on either side of the vertical line are fits based on the sum of a Gaussian and a polynomial.

Figure 7

Photon inefficiency as a function of the ISR photon polar angle for the data (circles) and signal MC (crosses). The binsize is increased to 6 mrad for ${\theta }_{\mathrm{Photon}}>2.1\mathrm{rad}$.

Figure 8

Ratio of the simulated radiative cross section with only the ISR contribution to the cross section with both ISR and FSR.

Figure 9

The $E_{\mathrm{CM}}$ dependence of the dressed $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ cross section measured from the ISR data. The uncertainties are statistical.

Figure 10

The $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ cross section in comparison to other experiments. Only statistical uncertainties are shown.

Figure 11

Invariant ${\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ and ${\pi }^{+}{\pi }^{-}$ mass combinations vs invariant ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ mass for the data without background subtraction (left) and signal MC (right).

Figure 12

Left: invariant ${\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ mass distributions (four entries per event) for different regions in $M_{4\pi }$ for the data without background subtraction (points) and signal simulation (histogram); Middle: ${\pi }^{+}{\pi }^{-}$ mass distributions (4 entries per event); Right: ${\pi }^{+}{\pi }^{-}$ mass distribution with another ${\pi }^{+}{\pi }^{-}$ mass in the $\rho (770{)}^0$ mass region.

Figure 13

(a) Invariant $4\pi$ mass $M_{4\pi }$ distribution for the data around the $J/\psi$ peak with a fit, which consists of a sum of two Gaussian and a linear distribution, describing the peak and the nonresonant ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ contribution, respectively. (b) Invariant ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ mass $M_{4\pi }$ distribution, assuming all four particles are pions, for the data around the $\psi (2S)$ peak with a fit, which consists of a sum of two Gaussian and a linear distribution, describing the peak and the nonresonant ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ contribution, respectively.

Figure 14

Invariant ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ mass distribution for the data in the invariant mass range $3.2\mathrm{GeV}/c^2<M_{4\pi }<6.0\mathrm{GeV}/c^2$ (a) and $3.75\mathrm{GeV}/c^2<M_{4\pi }<4.25\mathrm{GeV}/c^2$ (inset, b).