2011 QCD and High Energy Interactions - Rencontres de Moriond ...

g
q
(LO)
Z
g
q
Z
g
(NLO)
“LO type topology”
g
Z
g
(NLO)
“dijet type topology”
Figure 1: Diagrams contributing to Z+jet production at LO (left) and NLO (middle and right).
contributions. The latter is essential to cancel infra-red and collinear divergences arising from
certain configurations of Z+2j NLO result. The 2-loop contribution has however the topology of
Z+j at LO and that, as we discussed above, is strongly subleading for the observables exhibiting
giant K-factor. Therefore, even an approximate 2-loop contribution would be sufficient to get
reliable approximation of NNLO, provided that one could combine it with the tree and the
1-loop diagrams to get finite result for Z+j at the order O αewα3
s .
In this proceedings, we present a method, called LoopSim 1 , which by the use of unitarity,
estimates the missing loop contributions and allows one to obtain approximate higher order
QCD corrections for a number of processes.
2 The LoopSim method
Unitarity guarantees that soft and collinear singularities of real diagrams cancel, after phase
space integration, with singularities of loop diagrams at any order of the perturbative expansion.
That can happen since the pole structure of real and virtual contributions is the same. One
could, therefore, use a diagram with n real partons and deduce from it, for instance, the singular
terms of the corresponding diagram with n − 1 real partons and 1 loop. This is the main idea
that LoopSim 1 is based on. More precisely, the LoopSim procedure takes as an input an event
with n final state particles and returns as an output all events with n − k final state particles
(equivalently all k-loop events). The method is capable of taking as an input both tree-level and
loop diagrams. This allows one to obtain the highest possible accuracy by approximating only
those contributions that are missing (e.g. 2-loop diagrams for Z+j). To distinguish between
exact and approximate loops we denote our results as ¯n p N r LO which corresponds to diagrams
with exact contributions up to r loops and approximate constitutions for loops from r + 1 to p.
So for example, Z+j at ¯nNLO corresponds to exact 1-loop and approximate 2-loop diagrams.
In more detail, the procedure consists of the following steps. First, an input (“original”) event
is clustered with the Cambridge/Aachen algorithm with radius RLS and an emission sequence
of particles is attributed to the event. This is done by reinterpreting clustering of particles i
and j into k as splitting k → ij. In the next step one identifies which particles reflect the
underlying hard structure of an event. We call those particles “Born” and their number, nB, for
a given process is just the number of outgoing particles at leading order (e.g. for Z+j, nB = 2).
The particles marked as Born will be those that participate in the nB hardest branchings, where
hardness is measured using the kt algorithm distance. Finally, a set of loop diagrams is produced
from the original event by “virtualizing” in all possible ways the non-Born final state particles.
The “virtualization” means a given particle disappears from the list of final state particles and
a special procedure 1 is used to redistribute its 4-momentum among remaining particles. Each
l-loop event from LoopSim has the weight wn−l = (−1) l wn, where wn is the weight of the original
event with n particles in the final state.
The input events can have exact loop contributions. To properly merge tree and loop events
the procedure is designed such that it avoids double counting. For instance, to obtain ¯nNLO
prediction, LoopSim first generates all diagrams from tree level event with n final state particles
q