# Changes between Version 2 and Version 3 of SingleTopNLO

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Timestamp:
04/12/12 14:53:59 (7 years ago)
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• ## SingleTopNLO

 v2 === Talks === [:SingleTopTalks:Single top talks] [wiki:SingleTopTalks Single top talks] === Results ===

[[br]] [[br]] [[br]] [[br]] [[br]] [[br]] [[br]] Old results without the interference terms:
[[br]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale--TeV.png, 300px)]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale--LHCtop.png, 300px)]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale--LHCantitop.png, 300px)]] The above plots show the cross section as a function of the scales. The renormalization and factorization scales are set equal to eachother and varied simultaneously. For the 2->2 processes (in particular at NLO) the scale dependence is extremely small over a very large range of scale choices. The dependence for the 2->3 is slightly larger, but is still small and very reasonable. At LO the cross sections for the 2->2 and 2->3 process become equal for small scale choices. For the NLO this is no longer the case. The difference between the 2->2 and 2->3 at NLO is large over the whole range of scales. Normalized:
[[br]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale-norm2--TeV.png, 300px)]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale-norm2--LHCtop.png, 300px)]] scale dependence at the LHC for independent scale variations for light and heavy fermion lines: [[br]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scaleLH--LHCtop.png, 300px)]] The above plot shows the scale dependence for the 2->3 process at NLO. In this plot the renormalization scale is set equal to the factorization scale $\mu_R=\mu_F$, but the scale for the heavy fermion line is varied independently from the scale of the light fermion line. The ''black'' curves show the scale variation of the heavy fermion line, i.e. the scales for the light line are fixed, and vice versa for the ''red'' line. The value to which the scales are fixed for a particular curve can be read of from the point where this black (or red) line crosses a red (or black) line in a point. ==== b-mass dependence ====
[[br]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/bmass--TeV.png, 300px)]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/bmass--LHCtop.png, 300px)]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/bmass--LHCantitop.png, 300px)]] In the above plots the cross section is plotted as a function of the mass of the (anti-)b quark (for the 2->3 process). From these plots it is clear the cross section is quite sensitive to the mass of the b-quark. In particular, using the running mass at the scale of the top quark or at the scale of the bottom quark could enhance the cross section by over 10-15%. We should figure out to which mass we should let the b-mass run. Note that the CTEQ6 PDF sets assume a bottom mass of 4.5 GeV. * The NLO plots lie perfectly on a straight line (within the statistical MC errors). This suggests that the 'large logarithms' at NLO (that would be the terms proportional to $\alpha_s^2\log^2(m_b/m_t)$) do not play an important role and that using the resummed calculation with the b-quark PDF is not the best estimation for this process. ===== scale dependence for $m_b=m_c$  =====
[[br]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale-mb=mc--TeV.png, 300px)]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale-mb=mc--LHCtop.png, 300px)]] [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/scale-mb=mc--LHCantitop.png, 300px)]] In the above plots the cross section as a function of the scales is plotted. The mass of the bottom quark is set equal to the mass of the charm. The scale dependence for the NLO calculation is still very small, but the k-factors are much larger as compared to the $m_b=4.7\textrm{ GeV}$. We need to be able to check all possible factorization and renormalization scales. The main point is that we can treat the light quark line and the heavy quark line independently, since as  in the 2->2 there is no talking between the lines. The aim is to have four scales: muf_light, mur_light, muf_heavy, mur_heavy. So first thing is to assess the real scale dependence of the results by varying these scale independently. Scott suggested that we used a dynamical scale for the heavy line. After some thought I think that min(mT(b),mT(t)) =~ mT(b) should be used. By doing so we will slightly overestimate the diagrams where the initial gluon splits into a ttbar pair. However this contribution is anyway very small and should have no impact on the final result. This is also similar to the choice made by PS MC. [[Image(https://server06.fynu.ucl.ac.be/projects/madgraph/raw-attachment/wiki/SingleTopNLO/63.png, 300px)]]