Unsubtractions at NNLO

Abstract

Computations in perturbative quantum field theory (pQFT) feature several aspects that, although intrinsically non-physical, are traditionally successfully eluded by modifying the dimen- sions of space–time. Closed loops in pQFT implicitly extrapolate the validity of the Standard Model (SM) to infinite energies—equivalent to zero distance—much above the Planck scale. We should expect this to be a legitimate procedure if the loop scattering amplitudes that contribute to the physical observables are either suppressed at very high energies, or if there is a way to suppress or renormalise their contribution in this limit. In gauge theories like QCD, massless particles can be emitted with zero energy, and pQFT treats the quantum state with N external partons as different from the quantum state with emission of extra massless particles at zero energy, while these two states are physically identical. In addition, partons can be emitted in exactly the same direction, or, in other words, at zero distance. All these unphysical features have a price and lead to the emergence of infinities in the four dimensions of space–time.