Results on R from PEP, PETRA, TRISTAN, and SLC

Abstract

We discuss the determination of the Standard Model parameters α s , M z , and sin2 θw from the total hadronic cross section in e + e - annihilation at centre of mass energies between 7 and 93 GeV. At the highest TRISTAN energies, the tail of the Z 0 resonance does increase R by 50%. Such a sizeable increase allows a direct measurement of M z . However, this measurement turns out to be somewhat below the direct value measured at SLC at energies around the Z 0-resonance. This has led to speculation about possible new physics, although statistically the effect is not too significant (less than 2 standard deviations). We study in detail if other effects, like normalization errors or higher order radiative corrections could reduce the difference. The radiative corrections at TRISTAN energies can be calculated more precisely with the new knowledge of the Z 0- mass and the correspondingly improved value for the top mass (120±35±20 GeV/c2), resulting from the combination with the value of sin2 θ w from low energy measurements.If third order QCD contributions are taken into account, one finds \( {\Lambda _{\overline {MS} }} = 0.26_{ - 0.13}^{ + 0.16} \) GeV, which corresponds to αs (34 GeV) = 0.144 ± 0.015 and αs(91 GeV) = 0.122 ± 0.011. From the combined R measurements one finds that near the Z 0-resonance the infinite QCD series 1 + α s /π +.. is 1.046±0.006. We study the effect of changing the renormalization scale of a, and find that the third order QCD corrections, which are larger than the second order ones for the usual scale Q = \( \sqrt s \) are smaller than the second order contributions at other scales.