Four fermion soft emission in QCD hard scattering

Abstract

We consider the radiation of two distinguishable soft quark-antiquark pairs ($\mathrm{q}\bar{\mathrm{q}}\mathrm{Q}\bar{\mathrm{Q}}$) in a generic process for multiparton hard scattering in QCD. We evaluate the corresponding soft current at tree level in terms of an independent-emission contribution and an irreducible correlation component, which includes strictly non-abelian terms and also terms with an abelian character. The squared current for soft $\mathrm{q}\bar{\mathrm{q}}\mathrm{Q}\bar{\mathrm{Q}}$ emission produces colour dipole and colour tripole interactions between the hard-scattering partons, with structures similar to soft gluon-quark-antiquark emission. The colour tripole interactions are odd under charge conjugation and lead to charge asymmetry effects. We extend our analysis by including QED interactions, the emission of two distinguishable soft lepton-antilepton pairs, and mixed quark-antiquark-lepton-antilepton soft emission.

Figures (1)

• Figure 1: QCD diagrams contributing to the ${\mathrm{q}\bar{\mathrm{q}}}{\mathrm{Q}\bar{\mathrm{Q}}}$ soft emission current. The ${\mathrm{q}\bar{\mathrm{q}}}$ pair is shown in blue and the ${\mathrm{Q}\bar{\mathrm{Q}}}$ pair in red. Diagrams from A to E correspond to soft quark emission stemming from a single gluon leg attached to a hard parton. In diagrams M and N each soft pair stems from a different gluon attached to a hard leg. The sum of diagrams of type M and N yields the symmetric product of the quark-antiquark currents $\bigl({{\hbox{\boldmath $J$}}}_{12}\, {{\hbox{\boldmath $J$}}}_{34}\bigr)_{sym}$ of Eq. \ref{['J1234']} plus the commutator of the same currents attached on the same leg, represented by diagram F. Therefore, the irreducible correlation $\boldsymbol{\Gamma}$ is given by the sum of diagrams A-F.