Abstract
The three precision measurements of the cross section σ(e+e− → π+π−γ(γ)) using initial state radiation by the KLOE collaboration provide an important input for the prediction of the hadronic contribution to the anomalous magnetic moment of the muon. These measurements are correlated for both statistical and systematic uncertainties and, therefore, the simultaneous use of these measurements requires covariance matrices that fully describe the correlations. We present the construction of these covariance matrices and use them to determine a combined KLOE measurement for σ(e+e− → π+π−γ(γ)). We find, from this combination, a two-pion contribution to the muon magnetic anomaly in the energy range 0.10 < s < 0.95 GeV2 of {a}_{mu}^{pi^{+}{pi}^{-}}=left(489.8pm {1.7}_{mathrm{stat}}pm {4.8}_{mathrm{sys}}right)times {10}^{-10} .Data vectors and covariance matrices are available at http://www.lnf.infn.it/kloe/ppg/ppg_2017/ppg_2017.html.
Highlights
The μ+μ− cross section was measured for the analysis, whereas the KLOE08 π+π− data were used as the input into equation (2.3), with the KLOE12 measurement having an identical binning and energy range to KLOE08
Other than those that exist as part of the individual analyses for the KLOE08, KLOE10 and KLOE12 diagonal sub-matrices in the statistical 195 × 195 combination covariance matrix depicted in figure 2, the only statistical correlations that are present are those due to the two-pion data that are shared between KLOE08 and KLOE12
While the statistical uncertainty of aπμ+π− from the combination is dominated by KLOE08, the combination mean value of aπμ+π− is closest to that obtained with the KLOE12 data alone, which has the smallest systematic and, the smallest total error of the three
Summary
The experimental analysis of each KLOE measurement of σ e+e− → π+π−γ(γ) has been reviewed and, in some cases, updated in order to ensure a more precise and consistent combination of the three measurements. We find, using the updated data for KLOE08, a contribution to the anomalous magnetic moment of the muon of aπμ+π−(KLOE08, 0.35 < s < 0.95 GeV2) = (386.6 ± 0.4stat ± 3.3sys) × 10−10, (2.5). The KLOE10 cross section has been updated in the same way as KLOE08, with the application of the improved VP correction [36, 37], the non-rounded data and improved parameter precision resulting in aπμ+π−(KLOE10, 0.10 < s < 0.85 GeV2) = (477.9 ± 2.0stat ± 6.7sys) × 10−10, (2.6). The μ+μ− cross section was measured for the analysis, whereas the KLOE08 π+π− data were used as the input into equation (2.3), with the KLOE12 measurement having an identical binning and energy range to KLOE08. The KLOE12 cross section has been updated with respect to the use of non-rounded data and input parameter precision. The error has reduced since [5], where a flaw in the previous error calculation resulted in an overestimation of the published systematic uncertainty and, as a result, there have been necessary changes to the KLOE12 systematic matrix construction. The updated KLOE12 data are available from [41]
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