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

Reaching beyond NLO in processes with giant K-factors
S. SAPETA
LPTHE, UPMC Univ. Paris 6 and CNRS UMR 7589
Paris, France
We present a method, called LoopSim, which allows one to obtain approximate higher order
perturbative predictions for observables which exhibit large, kinematically induced NLO corrections.
The approach makes use of combining NLO results for different multiplicities. We
validate the method against known NNLO results for Drell-Yan lepton pt spectra and then
we use it to compute approximate NNLO results for Z+jet observables. We also study dijet
events and show that LoopSim can provide useful information even in cases without giant
K-factors.
1 Introduction
Next-to-leading order accuracy of QCD predictions has become a standard for processes calculated
for the LHC. Most results show good convergence at NLO with corrections of the order of
10-20%. There are however cases of distributions which show very large K-factors from LO to
NLO.
One such example is inclusive Z+j production. At LO, the distributions of the transverse
momentum of the Z-boson, pt,Z, the transverse momentum of the hardest jet, pt,j1, and the
scalar sum of transverse momenta of all jets HT,jets are identical. This is because, as shown in
the left diagram of Fig. 1, there are only two particles in the final state: the Z-boson and the
parton and therefore their transverse momenta balance each other. At NLO, however, each of
these distributions looks very different. While pt,Z spectrum is only slightly higher than at LO,
the hadronic observables, pt,j1 and HT,jets, receive very large corrections that grow with pt and
correspond to K-factors of 4 − 6 and 50 − 100, respectively. The reason is that most of the
correction to pt,Z spectra at high values of transverse momenta comes from the NLO diagram
which preserves LO topology, i.e. the Z-boson the leading jet are back-to-back as depicted in
the middle diagram of Fig. 1. For hadronic observables, however, it is not important whether
the Z-boson is hard or soft and the dominant topology turns out to be that of dijet type (right
diagram of Fig. 1). Integration over soft and collinear emissions of the Z-boson leads to double
logarithmic enhancement, which produces the large K-factors for pt,j1 and HT,jets distributions.
For the HT,jets observable the enhancement is even bigger because the dijet topology leads to
HT,jets ∼ 2pt,j1 instead of HT,jets = pt,j1 at LO.
Hence, even though the pt,j1 and HT,jets distributions for Z+j are formally NLO they are,
in some sense, leading contributions. This may raise some doubts about the accuracy of those
predictions. Ideally, one would like to calculate the full NNLO corrections for Z+j to see if the
convergence is restored. This result is however not yet available, the main difficulty being a
proper combination of the tree and the 1-loop diagrams (i.e. Z+2j at NLO) with the 2-loop