Measurement of initial-state–final-state radiation interference in the processes e^+e^− → μ^+μ^−γ and e^+e^− → π^+π^−γ
Charge asymmetry in the processes e^+e^− → μ^+μ^−γ and e^+e− → π^+π^−γ is measured using 232 fb^(−1 of data collected with the BABAR detector at eþe− center-of-mass energies near 10.58 GeV. An observable is introduced and shown to be very robust against detector asymmetries while keeping a large sensitivity to the physical charge asymmetry that results from the interference between initial- and final-state radiation (FSR). The asymmetry is determined as a function of the invariant mass of the final-state tracks from production threshold to a few GeV=c^2. It is compared to the expectation from QED for e^+e^− → μ^+μ^−γ, and from theoretical models for e^+e^− → π^+π^−γ. A clear interference pattern is observed in e^+e^− → π^+π^−γ, particularly in the vicinity of the f_2(1270) resonance. The inferred rate of lowest-order FSR production is consistent with the QED expectation for e^+e^− → μ^+μ^−γ, and is negligibly small for e^+e^− → π^+π^−γ.
Additional Information© 2015 American Physical Society. Received 1 September 2015; published 28 October 2015. We gratefully acknowledge useful discussions on theoretical issues with H. Czyż, Zhun Lu and B. Pire, and clarifications by A. B. Arbuzov, S. J. Brodsky, R. Gastmans, and R. Kleiss. We thank Henryk Czyż for providing tests with phokhara-V9. We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them. This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat à l'Energie Atomique and Institut National de Physique Nucléaire et de Physique des Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Economía y Competitividad (Spain), the Science and Technology Facilities Council (United Kingdom), and the Binational Science Foundation (U.S.-Israel). Individuals have received support from the Marie-Curie IEF program (European Union) and the A. P. Sloan Foundation (USA).
Published - PhysRevD.92.072015.pdf