Abstract

We have measured the running of the effective QED coupling constant $\alpha(s)$ in the time-like region $0.6<\sqrt s< 0.975$ GeV with the KLOE detector at DA$\Phi$NE using the Initial State Radiation process $e^+e^-\to\mu^+ \mu^-\gamma$. It represents the first measurement of the running of $\alpha(s)$ in this energy region. Our results show a more than 5$\sigma$ significance of the hadronic contribution to the running of $\alpha(s)$, which is the strongest direct evidence both in time- and space-like regions achieved in a single measurement. By using the $e^+e^-\to\pi^+\pi^-$ cross section measured by KLOE, the real and imaginary part of the shift $\Delta\alpha(s)$ has been extracted. By a fit of the real part of $\Delta\alpha(s)$ and assuming the lepton universality the branching ratio $BR(\omega\to\mu^+\mu^-) = (6.6\pm1.4_{stat}\pm1.7_{syst})\cdot 10^{-5} $ has been determined.

Highlights

  • Precision tests of the Standard Model (SM) require an appropriate inclusion of higher-order effects and the very precise knowledge of input parameters [1]

  • The QED coupling constant is predicted and observed [4,5] to increase with rising momentum transfer, which can be understood as a result of the screening of the bare charge caused by the polarized cloud of virtual particles

  • We have measured the hadronic contribution to the running ocrfotshseseecffteiocntivdeσQ(eE+De−co→uplμin+gμc−oγns)t/adn√t sαi(ns)thuesinreggitohne differe√ntial 0.6 < s

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Summary

Introduction

Precision tests of the Standard Model (SM) require an appropriate inclusion of higher-order effects and the very precise knowledge of input parameters [1]. The shift of the fine-structure constant from the Thomson limit to high energy involves low energy non-perturbative hadronic effects which affect the precision. These effects represent the largest uncertainty (and the main limitation) for the electroweak precision tests as the determination of sin θW at the Z pole or the SM prediction of the muon g − 2 [3]. In the Eq (2) Im α related to the imaginary part of the VP function γ is completely neglected, which is a good approximation in the continuum as the contributions from the imaginary part are suppressed This approximation is not sufficient in the presence of resonances like the ρ meson, where the accuracy of the cross section measurements reaches the order of (or even less than) 1%, and the imaginary part should be taken into account. The analysis has been performed by using the data collected with the KLOE detector at DA NE [10], the e+e− collider running at the φ meson mass, with a total integrated luminosity of 1.7 fb−1

The KLOE detector
Event selection
Measurement of the μμγ cross section
Efficiencies and systematic errors
Luminosity and radiative corrections
Measurement of the running of α
Conclusions
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