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In order to motivate these ideas, I shall give a brief introduction to spinor techniques. I denote the right-handed and left-handed spinors for a quark of momentum k as follows:|k+ = right-handed spinor for massless vector k |k− = left-handed spinor for massless vector k (2) In terms of these spinors we may write the gluon polarization vectors ε+ µ (k) = − q |γµ |k √ 2 qk − , ε− µ (k) = q |γµ |k √ 2[kq] + Fig. 1. Class of diagrams which can be calculated using MHV eﬀective theory i + 4 i +1 + + + 3− − n+ + (3) 2 where the choice of the auxiliary momentum q is equivalent to a gauge choice.

M. Patel, these proceedings. 6. T. , Comp. Phys. Commun. 135 (2001) 238. 7. ch/wwwasd/geant4. 8. A. van Lysebetten, these proceedings. 9. M. Schmelling, these proceedings. 10. Y. Xie, these proceedings. Section 2 QCD Physics at the Tevatron and LHC Theoretical Perspectives in QCD: Key issues, now and towards LHC R. Keith Ellis1 Fermilab PO Box 500 Batavia, IL 60510, USA Abstract. A review of the current status of perturbative QCD as applied to high energy collisions is presented. 1 Introduction 2 The role of tree graphs This article provides a review of processes which have been recently calculated in perturbative QCD.

First, the overall normalization is uncertain. For example, the process W +4 jets occurs at tree graph level in O(α4S ). Hence if the scale uncertainty changes αS by 10%, this leads to a 40% uncertainty in cross section. Second, if we wish to calculate the rates for hadron production, (rather than parton production) we must apply fragmentation. To use universal fragmentation, we must evolve to a ﬁxed scale. In this case tree graphs require a procedure to combine with parton showers. , the appearance in NLO of gluon induced processes at the LHC).