Jet lag effect and leading hadron production

We propose a solution for the long standing puzzle of a too steeply falling fragmentation function for a quark fragmenting into a pion, calculated by Berger [1] in the Born approximation. Contrary to the simple anticipation that gluon resummation worsens the problem, we find good agreement with data. Higher quark Fock states slow down the quark, an effect which we call jet lag. It can be also expressed in terms of vacuum energy loss. As a result, the space-time development of the jet shrinks and the z-dependence becomes flatter than in the Born approximation. The space-time pattern is also of great importance for in-medium hadronization. 1 Leading hadrons in Born approximation We are interested here in the production of leading pions which carry a major fraction of the momentum of a highly virtual quark originating from a hard reaction. The Born graph for the perturbative fragmentation q → πq is shown in Fig. 1a, and the corresponding fragmentation function was calculated in [1], ∂D (Born) π/q (z) ∂k2 ∝ (1− z) k4 , (1) where k and z are the transverse and fractional longitudinal momenta of the pion. This expression is derived under the conditions 1− z ≪ 1 and k ≪ Q, where Q is the scale of the hard reaction. We neglect higher twist terms [1, 2], which are specific for deep-inelastic scattering (DIS).