Next-to-leading logarithms in the high-energy asymptotics of the quark form factor and the jet cross section

Abstract

The logarithms ∼ α s n ln 2 n ( Q 2/ μ 2) and ∼ α s n ln 2 n−1 ( Q 2/ μ 2) in the asymptotics of the quark form factor in the Sudakov region Q 2 = | q 2|>| p 2| = | p′ 2| = μ 2 are summed. We get the simple result S(Q 2, μ 23) = exp − α s(μ 2 2φ C F 1n 2 Q 2 μ 2 + 3α s(μ 2)C F 4φ 1n Q 2 μ 2 The same expression S( Q 2, M 2) describes the jet cross section in the e + e −→ q q process where the jet is defined as a set of particles whose total invariant mass does not exceed M 2. The QCD predictions are compared with the experimental data available and the jets observed are shown to be much broader than QCD predicts.