A new fracture function approach to QCD initial state radiation

Ordinary fracture functions, describing the deep inelastic scattering target fragmentation region, are generalized to account for the production of hadrons in arbitrary number, thus offering a new framework for dealing with QCD initial state radiation. We propose further a new jet-like observable which measures beam remnants and low-p⊥ scattering fragments and derive its QCD evolution equations by using jet calculus formalism. Applications to semi-inclusive deep inelastic scattering and hadron-hadron collisions are shortly discussed.