# Standard Model

## Mathias Jamin

## The Standard Model of particle interactions is one of the major achievements of fundamental science. Within this framework a wide range of phenomena can be described to an impressive degree of accuracy. As a matter of fact, few are the branches of Physics where the predictive power of a theory has been tested to such a level of precision.

## Introduction

## STRONG COUPLING FROM electronic hadron production BELOW CHARM

Ever since the beginning of Quantum Chromodynamics (QCD), experimental data on the process $e^+e^-\to{hadrons}$ has been very instrumental in our understanding of the dynamics of quarks and gluons. With the help of a new compilation of this data, members of the Theory Division (S. Peris) together with D. Boito (Brazil), M. Golterman (USA), A. Keshavarzi (UK), K. Maltman (Canada), D. Nomura (Japan) and T. Teubner (UK) conducted a new analysis to determine the strong coupling, $\alpha_{s}$, which is the fundamental parameter governing the strength of the QCD interaction.

In this analysis use was made of all the $e^+e^-\to{hadrons}$ data from threshold to a center-of-mass energy of 2~GeV by employing finite-energy sum rules. The advantage of these sum rules is that, based on fundamental properties of Field Theory such as analyticity and unitarity, they allow us to consider the experimental data from threshold up to an arbitrary higher energy, which in our case was $4~\mathrm{GeV}^2$. Since the threshold is located at very low energy (in fact, the pion mass), the non-perturbative character of QCD would make the analysis impossible without the help of these sum rules. Data above $4~\mathrm{GeV}^2$ is also available but has less accuracy and does not provide much additional constraint. However, it is fully consistent with the values for $\alpha_s$ we obtain. We choose to quote our results at the $\tau$ mass to facilitate comparison with the results from analogous analyses of hadronic $\tau$-decay data, and obtained $\alpha(m_\tau^2)=0.298\pm 0.016\pm 0.006$ in fixed-order perturbation theory, and $\alpha_{s}(m_\tau^2)=0.304\pm 0.018\pm 0.006$ in contour-improved perturbation theory, where the first error is statistical, and the second error reflects our estimate of various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic $\t$ decays also carried out by our group.