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

6.5. LHC results 161p Hp 1 p 2p 1j 2p 2p Hj 1j 2j 1Figure 6.5: Possible momentum configurations in a Higgs plus two jet events. On theleft hand diagram two jets are produced with large p T and the Higgs is a relativelysoft in comparison. On the right hand side the Higgs has a high p T . Whilst µ = m Hmight adequately describe the physics of the second diagram one might not expectit to be a good choice on the left hand side.ensure that ∆ NLO (µ 1 , µ 2 ) ∈ ∆ LO (µ 1 , µ 2 ), whereas to ensure this condition for H Tone finds, µ 1 ∼ (0.3 − 0.4)H T . The results are summarised in Fig. 6.9 and we notethat the total variation over the range µ 0 /4 ≤ µ ≤ 4µ 0 is roughly equal for bothscale choices. What should be noted is that when attempting to estimate the totalscale uncertainty for dynamic scales one should use a lower limit of around H T /4rather than H T /2 (which is often the choice used for fixed scales).6.5.3 Considerations from the effective theoryWe observed in the previous section that the dynamic scale H T preserved the shapesof the LO distributions for p T and H T , whereas the fixed scale m H failed to do so.We note, however, that typical values of H T are ∼ 350 GeV ≈ 2m t . This is preciselythe scale at which our effective theory breaks down, therefore one could argue thatthis scale choice is inappropriate for our calculation. In addition we note that topquark mass effects become important when p T > m t .To clarify the situation we investigated the effects of the top mass on the p Tdistribution for Higgs plus jet events at the LHC, (for which the full theory result