Abstract
We consider the radiation of two or more soft partons in QCD hard-scattering at one-loop order. The corresponding scattering amplitude is singular, and the singular behaviour is controlled by a process-independent soft current. Using regularization in d=4 - 2epsilon space-time dimensions, we explicitly evaluate the ultraviolet and infrared divergent (epsilon -pole) terms of the one-loop soft current for emission of an arbitrary number of soft partons in a generic hard-scattering process. Then we consider the specific case of soft quark–antiquark (q{{bar{q}}}) emission and we compute the one-loop current by including the finite terms. We find that the one-loop soft-q{{bar{q}}} current exhibits a new type of transverse-momentum singularity, which has a quantum (absorptive) origin and a purely non-abelian character. At the squared amplitude (cross section) level, this transverse-momentum singularity produces contributions to multijet production processes in hadron collisions. The one-loop squared current also leads to charge asymmetry terms, which are a distinctive features of soft-q{{bar{q}}} radiation. We also extend these results to the cases of QED and mixed QCDtimes QED radiative corrections for soft fermion–antifermion emission.
Highlights
The physics program carried out at the large hadron collider (LHC) has already produced an impressive amount of highprecision data, and similar data will be obtained in the runs of the LHC
At one-loop order the soft current contains IR and ultraviolet (UV) divergent contributions that we explicitly evaluate for the emission of an arbitrary number of soft partons
We have considered the radiation of two or more soft partons in QCD hard scattering
Summary
The physics program carried out at the large hadron collider (LHC) has already produced an impressive amount of highprecision data, and similar data will be obtained in the runs of the LHC. An important feature of QCD scattering amplitudes is the presence of singularities in soft and collinear regions of the phase space, and the corresponding presence of infrared (IR) divergences in virtual contributions at the loop level. In the computation of physical observables for hardscattering processes, phase space soft/collinear singularities and virtual IR divergences cancel between themselves. Soft/collinear factorization formulae can be used to organize and greatly simplify the cancellation mechanism of the IR divergences in fixed-oder calculations. The cancellation mechanism of the IR divergences leaves residual effects in the form of large logarithmic contributions. Soft/collinear factorization formulae and the corresponding singular factors are the basic ingredients for the explicit computation and resummation of these large logarithmic contributions
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