TRIPLE (AND QUADRUPLE) SOFT-PARTON RADIATION IN QCD HARD SCATTERING

We compute the tree-level current for triple soft-gluon emission from both massless and massive hard partons. The three-gluon current is expressed in terms of the maximally non-Abelian irreducible correlations. We compute the soft behaviour of squared amplitudes and the colour correlations produced by the squared current. The radiation of one and two soft gluons leads to colour dipole correlations. Triple soft-gluon radiation produces, in addition, colour quadrupole correlations between the hard partons. We examine the soft and collinear singularities of the squared current in various energy-ordered and angular-ordered regions. Considering triple soft-gluon radiation from three hard partons, colour quadrupole interactions break the Casimir scaling symmetry between quarks and gluons. We also present some results on the radiation of four soft gluons from two hard partons, and we discuss the colour monster contribution and its relation with the violation (and generalization) of Casimir scaling. We also compute the first correction of (1/Nc2) to the eikonal formula for multiple soft-gluon radiation with strong energy ordering from two hard gluons. Finally, we compute also the tree-level current and its squared modulus for emission of soft quark–antiquark–gluon states.