Abstract
We calculate the two-loop and one-loop/one-emission contributions required for soft gluon evolution at the next-to-leading order. The colour structures are expressed in the colour flow basis, and the kinematic dependence and loop integrals are expressed in terms of multiple cuts and phase-space-like integrals. This directly allows to use them in the resummation of non-global observables and improved parton shower algorithms beyond the leading order and beyond the leading colour limit. Within the colour flow basis it becomes apparent that correlations beyond a dipole picture emerge even in colour-diagonal elements of the virtual corrections.
Highlights
Theoretical framework which allows to systematically construct parton shower algorithms beyond the currently adopted approximations [6, 7], and with the highest level of control over their accuracy
The same formalism allows to analyze approaches to improve existing parton showers beyond the leading-N limit [16,17,18] in order to show which colour suppressed contributions are taken into account [19], highlighting the fact that amplitude level evolution will go beyond a probabilistic approach in the sense that unitarity cannot be naively employed anymore
We establish methodology in order to systematically obtain the virtual corrections required at this order in a representation of phase-space type integrals, which is complementary to approaches which perform the actual integrals and make the divergencies explicit in terms of poles of the dimensional regularisation parameter, see e.g. results on one, two- and three-loop divergencies [21,22,23], as well as the one-loop corrections to the emission of a soft gluon [24]
Summary
Amplitude evolution algorithms like the approach outlined in [7], and the resummation of non-global logarithms [3], proceed through evolution equations in colour space which govern the contribution to the cross section originating from n hard partons. The remaining (artificial) ultraviolet divergences in the one-loop and one-emission cross section stemming from the soft gluon approximation are absorbed to all orders into a renormalisation of the hard and soft functions, giving rise to the evolution equation stated in eq (2.1). More details of such an approach will be discussed in upcoming work. The purpose of the present work is to investigate in detail the structure of the Feynman diagrams contributing to the evolution at the next-to-leading order in colour space, as well as to explore strategies how these contributions can be manipulated to allow for the appropriate subtractions at the level of phase-space-type integrals This will enable us to address the observable dependence in a most differential way. To make the connection between the two clear we will review the one-loop case and we will outline our approach to the loop integrals involved
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
