Combination of KLOE σ (e+e− → π+π−γ(γ)) measurements and determination of $$ {a}_{\mu}^{\pi^{+}{\pi}^{-}} $$ in the energy range 0.10 < s < 0.95 GeV2

Abstract

A bstract 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 &lt; s &lt; 0 . 95 GeV 2 of $$ {a}_{\mu}^{\pi^{+}{\pi}^{-}}=\left(489.8\pm {1.7}_{\mathrm{stat}}\pm {4.8}_{\mathrm{sys}}\right)\times {10}^{-10} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mrow> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>489.8</mml:mn> <mml:mo>±</mml:mo> <mml:msub> <mml:mn>1.7</mml:mn> <mml:mi>stat</mml:mi> </mml:msub> <mml:mo>±</mml:mo> <mml:msub> <mml:mn>4.8</mml:mn> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>y</mml:mi> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Data vectors and covariance matrices are available at http://www.lnf.infn.it/kloe/ppg/ ppg_2017/ppg_2017.html .