2022 Impact factor 4.4
Particles and Fields
Eur. Phys. J. C 28, 261-278 (2003)
DOI: 10.1140/epjc/s2003-01146-0

Measuring the FSR-inclusive $\pi^+\pi^-$ cross section

J. Gluza1, 2, A. Hoefer3, S. Jadach3 and F. Jegerlehner2

1  Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland
2  DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
3  Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Krakow, Poland

(Received: 2 January 2003 / Published online: 24 March 2003 )

Final state radiation (FSR) in pion pair production cannot be calculated reliably because of the composite structure of the pions. However, FSR corrections have to be taken into account for a precise evaluation of the hadronic contribution to g-2 of the muon. The role of FSR in both energy scan and radiative return experiments is discussed. It is shown how FSR influences the pion form factor extraction from experimental data and, as a consequence, the evaluation of $a_{\mu}^{\mathrm {had}}$. In fact the $O(\alpha)$ FSR corrections should be included to reach the precision we are aiming at. We argue that for an extraction of the desired FSR-inclusive cross section $\sigma^{(\gamma)}_{\mathrm {had}}$ a photon-inclusive scan measurement of the " $e^+e^- \to \pi^+\pi^- + {\mathrm {photons}}$" cross section is needed. For exclusive scan and radiative return measurements in contrast we have to rely on ad hoc FSR models if we want to obtain either $\sigma^{(\gamma)}_{\mathrm {had}}$ or the FSR-exclusive cross section $\sigma^{(0)}_{\mathrm {had}}$. We thus advocate to consider seriously precise photon-inclusive energy scan measurements at present and future low energy e+e--facilities. Then together with radiative return measurements from DA $\Phi$NE and BABAR and forthcoming scan measurements at VEPP-2000 we have a good chance to substantially improve the evaluation of $a_{\mu}^{\mathrm {had}}$ in the future.

© Società Italiana di Fisica, Springer-Verlag 2003