Preliminary fixed-order parton-level study (done with Sherpa+OpenLoops) to compare scale1 and scale2 (see definition in ProposalTtbb)

The following results are at 8TeV with MSWT2008 4F PDFs! The notation is as follows:

  • ttbb = cross section for ttbar+>=1 b-jets (pT>25 geV and eta<2.5)
  • ttbb= idem for ttbar+>=2 b-jets
  • ttbb100= same as ttbb with extra cut m_bb>100GeV
LO predictions are computed with LO PDFS and, alternatively with NLO ones. The corresponding K factors are defined as K_(n)lopdfs=NLO/LO_(n)lopdfs. "scale2/scale1" denotes the ratio of predictions obtained with scale2 and scale 1.

scale subsample LO_lopdfs LO_nlopdfs NLO K_lopdfs K_nlopdfs
scale1 (CKKW inspired) ttb 2.64 1.68 3.30 1.25 1.96
  ttbb 0.463 0.300 0.560 1.21 1.87
  ttbb100 0.123 0.0807 0.142 1.15 1.76
scale2 (HT/2) ttb 1.201 0.818 1.835 1.53 2.24
  ttbb 0.242 0.165 0.349 1.45 2.11
  ttbb100 0.0671 0.0461 0.0933 1.39 2.03
scale2/scale1-1 ttb -55% -51.3% -44% +22% +14%
  ttbb -48% -45% -38% +20% +13%
  ttbb100 -46% -43% -34% +21% +15%
scale2 (HT/2) 5F ttbb 0.270 0.190      
  ttbb100 0.0718 0.0508      
Preliminary considerations (by SP) against "scale2":
  1. Both scale choices lead to a positive K-factor, i.e the LO cross section is always too low => this calls for a renormalisation scale that is even softer than scale1, while scale2 is harder and leads to LO cross sectoin that is half as large as with scale1 (here one should keep in mind that the scale dependence of the LO ttbb cross section is completely dominated by renormalisation scale variations).
  2. This is partly compensated by a 15-20% increase of the K-factor, which is however not sufficient to bring scale1 and scale2 predictions in decent agreement at NLO: the discrepancy remains around -40% (which corresponds to +67% if one considers the inverse ratio "scale1/scale2"!). This can be interpreted as a lack of perturbative convergence of scale2.
  3. Using LO PDFS for LO predictions leads to non-pathologic K-factors for both scale choices. However, using NLO PDFS for LO predictions leads to very large ttbb K-factors: 1.87 for scale1 and 2.11 for scale 2. This calls again for a softer scale (even softer than scale1!)
  4. Note also that using NLO PDFS with scale 2 yields a LO ttbb cross section that is 3.4 times lower than the NLO predictions with scale 1, while the latter is still ~30% below data in the framework of the ATLAS ttH(bb) analysis.
  5. The last two rows of the table illustrate that the scale HT/2 yields a similarly low LO cross section also in the 5F scheme (Mb=0 and 5F MSTW2008 LO or NLO PDFs). For instance, the 5F LO ttbb cross section obtained with NLO PDFs is 2.95 times lower wrt the 4F NLO PDF.

-- StefanoPozzorini - 2015-07-22

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Topic revision: r1 - 2015-07-22 - StefanoPozzorini
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