Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0$ cross section using initial-state radiation at BABAR

The process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}2{\pi }^0\gamma$ is investigated by means of the initial-state radiation technique, where a photon is emitted from the incoming electron or positron. Using $454.3{\mathrm{fb}}^{-1}$ of data collected around a center-of-mass energy of $\sqrt{s}=10.58\mathrm{GeV}$ by the BABAR experiment at SLAC, approximately 150000 signal events are obtained. The corresponding nonradiative cross section is measured with a relative uncertainty of 3.6% in the energy region around 1.5 GeV, surpassing all existing measurements in precision. Using this new result, the channel’s contribution to the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon is calculated as $(g_{\mu }^{{\pi }^{+}{\pi }^{-}2{\pi }^0}-2)/2=(17.9\pm {0.1}_{\mathrm{stat}}\pm {0.6}_{\mathrm{syst}})\times {10}^{-10}$ in the energy range $0.85\mathrm{GeV}<E_{\mathrm{CM}}<1.8\mathrm{GeV}$. In the same energy range, the impact on the running of the fine-structure constant at the $Z^0$-pole is determined as $\mathrm{\Delta }{\alpha }^{{\pi }^{+}{\pi }^{-}2{\pi }^0}(M_{\mathrm{Z}}^2)=(4.44\pm {0.02}_{\mathrm{stat}}\pm {0.14}_{\mathrm{syst}})\times {10}^{-4}$. Furthermore, intermediate resonances are studied and especially the cross section of the process $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^{+}{\pi }^{-}2{\pi }^0$ is measured.

Figure 1

The ${\chi }_{{\pi }^{+}{\pi }^{-}2{\pi }^0\gamma }^2$ distributions after full selection for data (black points) and the AfkQed generator (red crosses, normalized to the same area as data in the range ${\chi }_{{\pi }^{+}{\pi }^{-}2{\pi }^0\gamma }^2<10$). The vertical lines indicate the signal (${\chi }_{{\pi }^{+}{\pi }^{-}2{\pi }^0\gamma }^2<30$) and sideband ($30<{\chi }_{{\pi }^{+}{\pi }^{-}2{\pi }^0\gamma }^2<60$) regions used for background subtraction.

Figure 2

The ${\pi }^{+}{\pi }^{-}2{\pi }^0\gamma$ data (black points) compared to simulated backgrounds after selection: uds continuum (red crosses), ${\pi }^{+}{\pi }^{-}3{\pi }^0\gamma$ (blue solid circles), $K_{\mathrm{s}}{K}^{\pm }{\pi }^{\mp }\gamma$ (turquoise open squares), $K^{+}{K}^{-}2{\pi }^0\gamma$ (yellow open triangles), ${\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ (pink solid triangles), $2({\pi }^{+}{\pi }^{-}{\pi }^0)\gamma$ (black solid squares), and ${\tau }^{+}{\tau }^{-}$ (green solid stars) as a function of $M({\pi }^{+}{\pi }^{-}2{\pi }^0)$.

Figure 3

Measured $M({\pi }^{+}{\pi }^{-}3{\pi }^0)$ distribution of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}3{\pi }^0\gamma$ background channel in data.

Figure 4

Plot of the mass spectrum of the measured signal event rate (black points) before subtracting the background (blue crosses) using the sideband procedure.

Figure 5

Ratio of the cross sections measured by adopting a background removal procedure based on simulation and on the sideband subtraction method. The horizontal lines indicate the systematic uncertainties for the subtraction of ISR backgrounds.

Figure 6

The simulated efficiency as a function of the ${\pi }^{+}{\pi }^{-}2{\pi }^0$ invariant mass.

Figure 7

The ${\chi }_{{\pi }^{+}{\pi }^{-}2{\pi }^0\gamma }^2$ distributions in the clean sample for data (black points) and the AfkQed generator (red crosses, normalized to the same area as data in the range ${\chi }_{{\pi }^{+}{\pi }^{-}2{\pi }^0\gamma }^2<10$).

Figure 8

Ratio of the simulated mass distributions including $\mathrm{FSR}+\mathrm{ISR}$ and ISR only. The black line depicts a phenomenological fit function.

Figure 9

The measured dressed ${\pi }^{+}{\pi }^{-}2{\pi }^0$ cross section (statistical uncertainties only).

Figure 10

The previously published ${\pi }^{+}{\pi }^{-}2{\pi }^0$ cross section data in addition to this analysis (statistical uncertainties only).

Figure 11

The low-energy part of the vacuum polarization corrected measured undressed cross section (points with statistical uncertainties) compared to the theoretical prediction (line) from Ref. [36].

Figure 12

The measured $\omega$ data peak in the complete $M({\pi }^{+}{\pi }^{-}2{\pi }^0)$ range after selection and efficiency correction.

Figure 13

The measured $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^{+}{\pi }^{-}2{\pi }^0$ cross sections from different experiments [41, 42, 43, 44] as a function of $E_{\mathrm{CM}}$ with statistical uncertainties. Data measured in other decays than $\omega \to {\pi }^{+}{\pi }^{-}{\pi }^0$ are scaled by the appropriate branching ratio.

Figure 14

The $M({\pi }^0{\pi }^0)$ vs $M({\pi }^{+}{\pi }^{-})$ two-dimensional plot of data in the invariant mass interval $1.7\mathrm{GeV}/c^2<M({\pi }^{+}{\pi }^{-}2{\pi }^0)<2.3\mathrm{GeV}/c^2$ after selection without efficiency correction and background subtraction. The black ellipse indicates the region used to select ${\rho }^0{f}_0$ events.

Figure 15

The $M({\pi }^{+}{\pi }^{-})$ distribution in the invariant mass interval $1.7\mathrm{GeV}/c^2<M({\pi }^{+}{\pi }^{-}2{\pi }^0)<2.3\mathrm{GeV}/c^2$ for data after selection and efficiency correction.

Figure 16

The $M({\pi }^0{\pi }^0)$ distribution in the invariant mass interval $1.7\mathrm{GeV}/c^2<M({\pi }^{+}{\pi }^{-}2{\pi }^0)<2.3\mathrm{GeV}/c^2$ for data after selection and efficiency correction.

Figure 17

The $M({\pi }^0{\pi }^0)$ distribution excluding the ${\rho }^0$ mass range in $M({\pi }^{+}{\pi }^{-})$ in the invariant mass interval $1.7\mathrm{GeV}/c^2<M({\pi }^{+}{\pi }^{-}2{\pi }^0)<2.3\mathrm{GeV}/c^2$ for data after selection and efficiency correction.

Figure 18

The $M({\pi }^{+}{\pi }^0)$ vs $M({\pi }^{-}{\pi }^0)$ two-dimensional plot of data after selection without efficiency correction and background subtraction. The black circle indicates the region used to select ${\rho }^{+}{\rho }^{-}$ events.

Figure 19

The $M({\pi }^{\pm }{\pi }^0)$ distribution in data after selection and efficiency correction.

Figure 20

The mass spectra of ${\pi }^{+}{\pi }^{-}2{\pi }^0$ events (after background subtraction and efficiency correction) from data in the ${\rho }^{+}{\rho }^{-}$ (red squares), ${\rho }^0{f}_0$ regions (blue circles), and in the full range (black points).

Figure 21

The measured $J/\psi$ peak in the ${\pi }^{+}{\pi }^{-}2{\pi }^0$ cross section without background subtraction.