Abstract (data abstract)

We have measured the cross section of the radiative process $e^+e^- \to \pi^+\pi^-\gamma$ with the KLOE detector at the Frascati $\phi$-factory DA$\Phi$NE, from events taken at a CM energy W=1 GeV. Initial state radiation allows us to obtain the cross section for $e^+e^- \to \pi^+\pi^-$, the pion form factor $|F_\pi|^2$ and the dipion contribution to the muon magnetic moment anomaly, $\Delta a_\mu^{\pi\pi} = (478.5\pm2.0_{stat}\pm5.0_{syst}\pm4.5_{th}) \times 10^{-10}$ in the range $0.1 < M_{\pi\pi}^2 < 0.85$ GeV$^2$, where the theoretical error includes a SU(3) ChPT estimate of the uncertainty on photon radiation from the final pions. The discrepancy between the Standard Model evaluation of $a_\mu$ and the value measured by the Muon g-2 collaboration at BNL is confirmed.

Differential cross section

Data from Fig. 3, Left and Table 2

10.17182/hepdata.96268.v1/t1

Differential cross section for $e^+e^-\rightarrow\pi^+\pi^-\gamma$, with $50^o<\theta_\gamma<130^o$
Differential cross-section statistical covariance

Data from https://www.lnf.infn.it/kloe/ppg/ppg_2010/ppg_2010.html

10.17182/hepdata.96268.v1/t2

Statistical covariance matrix for differential cross section for $e^+e^-\rightarrow\pi^+\pi^-\gamma$, with $50^o<\theta_\gamma<130^o$
Differential cross-section, inverse of statistical covariance

Data from https://www.lnf.infn.it/kloe/ppg/ppg_2010/ppg_2010.html

10.17182/hepdata.96268.v1/t3

Inverse statistical covariance matrix for differential cross section for $e^+e^-\rightarrow\pi^+\pi^-\gamma$, with $50^o<\theta_\gamma<130^o$
Differential cross-section systematic uncertainties

Table 7 in additional documentation KLOE Note 225 (http://www.lnf.infn.it/kloe/ppg/ppg_2010/kn225.pdf)

10.17182/hepdata.96268.v1/t4

Breakdown of syst. uncertainties (fully bin-by-bin correlated) for differential cross section for $e^+e^-\rightarrow\pi^+\pi^-\gamma$, with $50^o<\theta_\gamma<130^o$
Bare cross-section

Data from Fig. 3, Right and Table 2

10.17182/hepdata.96268.v1/t5

Bare cross section for $e^+e^-\rightarrow\pi^+\pi^-$
Bare cross-section statistical covariance

Data from https://www.lnf.infn.it/kloe/ppg/ppg_2010/ppg_2010.html

10.17182/hepdata.96268.v1/t6

Statistical covariance matrix for bare cross section for $e^+e^-\rightarrow\pi^+\pi^-$
Bare cross-section, inverse of statistical covariance

Data from https://www.lnf.infn.it/kloe/ppg/ppg_2010/ppg_2010.html

10.17182/hepdata.96268.v1/t7

Inverse statistical covariance matrix for bare cross section for $e^+e^-\rightarrow\pi^+\pi$
Bare cross-section systematic uncertainties

Table 7 in additional documentation KLOE Note 225 (http://www.lnf.infn.it/kloe/ppg/ppg_2010/kn225.pdf)

10.17182/hepdata.96268.v1/t8

Breakdown of syst. uncertainties (fully bin-by-bin correlated) for the cross section for $e^+e^-\rightarrow\pi^+\pi^-$
Pion form factor

Data from Fig. 4 and Table 2

10.17182/hepdata.96268.v1/t9

Pion form factor $|F_\pi|^2$
Pion form factor statistical covariance

Data from https://www.lnf.infn.it/kloe/ppg/ppg_2010/ppg_2010.html

10.17182/hepdata.96268.v1/t10

Statistical covariance matrix for pion form factor $|F_\pi|^2$
Pion form factor, inverse of statistical covariance

Data from https://www.lnf.infn.it/kloe/ppg/ppg_2010/ppg_2010.html

10.17182/hepdata.96268.v1/t11

Inverse statistical covariance matrix $|F_\pi|^2$
Pion form factor systematic uncertainties

Table 7 in additional documentation KLOE Note 225 (http://www.lnf.infn.it/kloe/ppg/ppg_2010/kn225.pdf)

10.17182/hepdata.96268.v1/t12

Breakdown of syst. uncertainties (fully bin-by-bin correlated) for the pion form factor $|F_\pi|^2$
Vacuum polarisation correction

Data from Figure 71 in additional documentation KLOE Note 225

10.17182/hepdata.96268.v1/t13

Vacuum polarisation correction $\delta_{VP}(s)=(\frac{\alpha_{em}(s)}{\alpha_{em}(0)})^2$, with $\sigma^{bare} = \sigma^{dressed}/\delta$ - calculated using the routine from F.Jegerlehner: https://web.archive.org/web/20170828074416/http://www-com.physik.hu-berlin.de/~fjeger/alphaQEDn.uu (2003, archived on August...
Final State Radiation correction

FSR correction in equation (4)

10.17182/hepdata.96268.v1/t14

Final State Radiation correction $(1.+\eta_{FSR}(s))$, evaluated using the formula in Eur. Phys. J. C 24, 51-69 (2002)
ISR radiator function

Data from Figure 66 in additional documentation KLOE Note 225

10.17182/hepdata.96268.v1/t15

The differential radiator function cross section $H(M_{\pi\pi}^2,s)\cdot \frac{\pi \alpha^2 \beta_\pi^3}{3 M_{\pi\pi}^2 s}$, inclusive in $\theta_\gamma$, in bins of 0.01 GeV$^2$...

Differential cross section

Differential cross-section statistical covariance

Differential cross-section, inverse of statistical covariance

Differential cross-section systematic uncertainties

Bare cross-section

Bare cross-section statistical covariance

Bare cross-section, inverse of statistical covariance

Bare cross-section systematic uncertainties

Pion form factor

Pion form factor statistical covariance

Pion form factor, inverse of statistical covariance

Pion form factor systematic uncertainties

Vacuum polarisation correction

Final State Radiation correction

ISR radiator function

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