Hadronic production of a Higgs boson in association with two jets at ...

6.5. LHC results 160of describing Tevatron data. As a result, the dynamic scale H T was suggested as asafer choice. H T , or the hotness, is defined as the sum over the transverse energy ofthe final state particles,H T = ∑ jE j T + EH T . (6.16)The motivation for this being a superior scale choice is shown schematically inFig 6.5. A fixed scale such as m H may do a good job of describing the physics whenthe Higgs boson is radiated with a large p T and the jets are softer in comparisonto the Higgs. However when one produces two hard jets and a relatively soft Higgsm H may not do such a good job of explaining the physics. Dynamic scales, whichadjust on an event by event basis, on the other hand, should be able to cope withboth sorts of kinematics in a reasonable manner. At the LHC high-p T jets will becommon, and hence the choice of scale could become an even more theoreticallyimportant issue than it is today.To investigate the role of dynamic scales we calculated distributions for p T andη for the two hardest jets, H T , at the LHC ( √ s = 7 TeV) using the basic jet cutsof eq. (6.14). The results are shown in Figs. 6.6, 6.7 and 6.8. For the p T andH T distributions the dynamic scale choice µ = H T preserves the shape of the LOcalculation much better than µ = m H . As expected the deviations in shape (for thep T distribution) are largest for the high-p T region. As is also expected, the shape ofthe pseudorapidity distribution is stable under both scale choices.We consider bands of scale uncertainty, which can be obtained by calculatingcross sections at two different scale choices ∆(µ 1 , µ 2 ) = [σ(µ 1 ), σ(µ 2 )] 1 . As is expected,performing a NLO calculation reduces ∆ for both scale choices relative tothe LO case. It is interesting to note that, when using a dynamic scale, one hasto choose lower values µ 1 to obtain ∆ NLO (µ 1 , µ 2 ) ∈ ∆ LO (µ 1 , µ 2 ). It is desirablefor ∆ NLO (µ 1 , µ 2 ) ∈ ∆ LO (µ 1 , µ 2 ) since this indicates that the perturbation series isconverging, and further that the scale variation is indicative of the theoretical uncertainty.Typically when using fixed scales a choice of µ 1 ∼ (0.75 − 0.5)m i will1 Here we define [x 1 , x 2 ] to be the continuous region between x 1 and x 2 including endpoints.