2020 Impact factor 4.590
Particles and Fields

Eur. Phys. J. C 19, 681-691
DOI: 10.1007/s100520100598

Improving $\alpha_{\rm QED} (M_Z^2)$ and the charm mass by analytic continuation

A.D. Martin1, J. Outhwaite1 and M.G. Ryskin1, 2

1  Department of Physics and Institute for Particle Physics Phenomenology, University of Durham, Durham, DH1 3LE
2  Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg, 188300, Russia

(Received: 19 December 2000 / Published online: 6 April 2001 -© Springer-Verlag 2001 )

The standard determination of the QED coupling on the Z pole is performed using the latest available data for R. The direct application of analytic continuation techniques is found not to improve the accuracy of the value of $\alpha (M_Z^2)$. However they help to resolve an ambiguity in the values of R in the energy region $\sqrt{s} \lesssim
2 {\rm GeV}$, which, in turn, reduces the uncertainty in $\alpha (M_Z^2)$. Moreover, they provide a sensitive determination of the mass of the charm quark. The favoured solution, which uses the inclusive data for R for $\sqrt{s} \lesssim
2 {\rm GeV}$, has a pole mass $m_c = 1.33-1.40 {\rm GeV}$ and $\alpha^{-1} (M_Z^2) =
128.972 \pm 0.026$; whereas if the sum of the exclusive channels is used to determine R in this region, we find $\alpha^{-1} (M_Z^2) = 128.941 \pm 0.029$.

© Società Italiana di Fisica, Springer-Verlag 2001