# K-factor of ttb process

Asked by Ernesto Arganda on 2017-09-13

We have been trying to compute the cross-section of ttb process with the NLO-type generation. In order to do so we use the 5f scheme by importing the model 'sm-no_b_mass'. We copy below the run_cardNLOtype.dat file that we have used for running MadGraph5_aMC@NLO (version 2.6.0). We have obtained the following results:

--------------------------
NLO-type generation-ttb
--------------------------
xs_LO = 2.7 +- 0.01 pb
Scale uncertainty = +33% -24%
PDF uncertainty = +4% -5%

xs_NLO = 34.04 +- 1.8 pb
Scale uncertainty = +53% -32%
PDF uncertainty = +3% -4%

which give us a huge K-factor of 12.6. However, if we do the same computation for ttj, we obtain:

--------------------------
NLO-type generation-ttj
--------------------------
xs_LO = 315.5 +- 1.4 pb
Scale uncertainty = +45% -29%
PDF uncertainty = +2% -3%

xs_NLO = 415.4 +- 7.3 pb
Scale uncertainty = +9% -13%
PDF uncertainty = +2% -3%

so that we have a K-factor=1.32. This result is consistent with what you show in the table 5 of your paper arXiv:1405.0301 [hep-ph].

Taking into account the above results and the fact that the multiparticle 'j' already includes the b-quark, then we would like to understand if the K-factor obtained by including explicitly the b-quark in the final state is reliable. In other words, is it correct to generate the ttb@NLO in this way?

Thank you very much for your help.

Ernesto Arganda.

The run_cardNLOtype.dat file is:
#***********************************************************************
# *
# run_card.dat aMC@NLO *
# *
# This file is used to set the parameters of the run. *
# *
# Some notation/conventions: *
# *
# Lines starting with a hash (#) are info or comments *
# *
# mind the format: value = variable ! comment *
# *
# Some of the values of variables can be list. These can either be *
# comma or space separated. *
#***********************************************************************
#
#*******************
# Running parameters
#*******************
#
#***********************************************************************
# Tag name for the run (one word) *
#***********************************************************************
tag_1 = run_tag ! name of the run
#***********************************************************************
# Number of LHE events (and their normalization) and the required *
# (relative) accuracy on the Xsec. *
# These values are ignored for fixed order runs *
#***********************************************************************
1000 = nevents ! Number of unweighted events requested
-1.0 = req_acc ! Required accuracy (-1=auto determined from nevents)
-1 = nevt_job! Max number of events per job in event generation.
! (-1= no split).
#***********************************************************************
# Normalize the weights of LHE events such that they sum or average to *
# the total cross section *
#***********************************************************************
average = event_norm ! valid settings: average, sum, bias
#***********************************************************************
# Number of points per itegration channel (ignored for aMC@NLO runs) *
#***********************************************************************
0.1 = req_acc_FO ! Required accuracy (-1=ignored, and use the
! number of points and iter. below)
# These numbers are ignored except if req_acc_FO is equal to -1
5000 = npoints_FO_grid ! number of points to setup grids
4 = niters_FO_grid ! number of iter. to setup grids
10000 = npoints_FO ! number of points to compute Xsec
6 = niters_FO ! number of iter. to compute Xsec
#***********************************************************************
# Random number seed *
#***********************************************************************
0 = iseed ! rnd seed (0=assigned automatically=default))
#***********************************************************************
# Collider type and energy *
#***********************************************************************
1 = lpp1 ! beam 1 type (0 = no PDF)
1 = lpp2 ! beam 2 type (0 = no PDF)
6500.0 = ebeam1 ! beam 1 energy in GeV
6500.0 = ebeam2 ! beam 2 energy in GeV
#***********************************************************************
# PDF choice: this automatically fixes also alpha_s(MZ) and its evol. *
#***********************************************************************
lhapdf = pdlabel ! PDF set
21100 = lhaid ! If pdlabel=lhapdf, this is the lhapdf number. Only
! numbers for central PDF sets are allowed. Can be a list;
! PDF sets beyond the first are included via reweighting.
#***********************************************************************
# Include the NLO Monte Carlo subtr. terms for the following parton *
# shower (HERWIG6 | HERWIGPP | PYTHIA6Q | PYTHIA6PT | PYTHIA8) *
# WARNING: PYTHIA6PT works only for processes without FSR!!!! *
#***********************************************************************
HERWIG6 = parton_shower
1.0 = shower_scale_factor ! multiply default shower starting
! scale by this factor
#***********************************************************************
# Renormalization and factorization scales *
# (Default functional form for the non-fixed scales is the sum of *
# the transverse masses divided by two of all final state particles *
# and partons. This can be changed in SubProcesses/set_scales.f or via *
# dynamical_scale_choice option) *
#***********************************************************************
False = fixed_ren_scale ! if .true. use fixed ren scale
False = fixed_fac_scale ! if .true. use fixed fac scale
91.118 = muR_ref_fixed ! fixed ren reference scale
91.118 = muF_ref_fixed ! fixed fact reference scale
3 = dynamical_scale_choice ! Choose one (or more) of the predefined
! dynamical choices. Can be a list; scale choices beyond the
! first are included via reweighting
1.0 = muR_over_ref ! ratio of current muR over reference muR
1.0 = muF_over_ref ! ratio of current muF over reference muF
#***********************************************************************
# Reweight variables for scale dependence and PDF uncertainty *
#***********************************************************************
1.0, 2.0, 0.5 = rw_rscale ! muR factors to be included by reweighting
1.0, 2.0, 0.5 = rw_fscale ! muF factors to be included by reweighting
True = reweight_scale ! Reweight to get scale variation using the
! rw_rscale and rw_fscale factors. Should be a list of
! booleans of equal length to dynamical_scale_choice to
! specify for which choice to include scale dependence.
True = reweight_PDF ! Reweight to get PDF uncertainty. Should be a
! list booleans of equal length to lhaid to specify for
! which PDF set to include the uncertainties.
#***********************************************************************
# Store reweight information in the LHE file for off-line model- *
# parameter reweighting at NLO+PS accuracy *
#***********************************************************************
False = store_rwgt_info ! Store info for reweighting in LHE file
#***********************************************************************
# ickkw parameter: *
# 0: No merging *
# 3: FxFx Merging - WARNING! Applies merging only at the hard-event *
# level. After showering an MLM-type merging should be applied as *
# well. See http://amcatnlo.cern.ch/FxFx_merging.htm for details. *
# 4: UNLOPS merging (with pythia8 only). No interface from within *
# MG5_aMC available, but available in Pythia8. *
# -1: NNLL+NLO jet-veto computation. See arxiv:1412.8408 [hep-ph]. *
#***********************************************************************
0 = ickkw
#***********************************************************************
#
#***********************************************************************
# BW cutoff (M+/-bwcutoff*Gamma). Determines which resonances are *
# written in the LHE event file *
#***********************************************************************
15.0 = bwcutoff
#***********************************************************************
# Cuts on the jets. Jet clustering is performed by FastJet. *
# - When matching to a parton shower, these generation cuts should be *
# considerably softer than the analysis cuts. *
# - More specific cuts can be specified in SubProcesses/cuts.f *
#***********************************************************************
-1.0 = jetalgo ! FastJet jet algorithm (1=kT, 0=C/A, -1=anti-kT)
30.0 = ptj ! Min jet transverse momentum
4.0 = etaj ! Max jet abs(pseudo-rap) (a value .lt.0 means no cut)
#***********************************************************************
# Cuts on the charged leptons (e+, e-, mu+, mu-, tau+ and tau-) *
# More specific cuts can be specified in SubProcesses/cuts.f *
#***********************************************************************
0.0 = ptl ! Min lepton transverse momentum
-1.0 = etal ! Max lepton abs(pseudo-rap) (a value .lt.0 means no cut)
0.0 = drll ! Min distance between opposite sign lepton pairs
0.0 = drll_sf ! Min distance between opp. sign same-flavor lepton pairs
0.0 = mll ! Min inv. mass of all opposite sign lepton pairs
30.0 = mll_sf ! Min inv. mass of all opp. sign same-flavor lepton pairs
#***********************************************************************
# Photon-isolation cuts, according to hep-ph/9801442. When ptgmin=0, *
# all the other parameters are ignored. *
# More specific cuts can be specified in SubProcesses/cuts.f *
#***********************************************************************
20.0 = ptgmin ! Min photon transverse momentum
2.0 = etagamma ! Max photon abs(pseudo-rap)
0.7 = R0gamma ! Radius of isolation code
1.0 = xn ! n parameter of eq.(3.4) in hep-ph/9801442
1.0 = epsgamma ! epsilon_gamma parameter of eq.(3.4) in hep-ph/9801442
True = isoEM ! isolate photons from EM energy (photons and leptons)
#***********************************************************************
# For aMCfast+APPLGRID use in PDF fitting (http://amcfast.hepforge.org)*
#***********************************************************************
0 = iappl ! aMCfast switch (0=OFF, 1=prepare grids, 2=fill grids)
#***********************************************************************

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2017-09-13
2017-09-13
 Olivier Mattelaer (olivier-mattelaer) said on 2017-09-13: #1

Hi,

If you did the following:
Import model sm-no_b_mass
Generate p p > t t~ b [QCD]
You should have seen the following warning:
WARNING: Process: g/u/c/d/s/u~/c~/d~/s~/b/b~ g/u/c/d/s/u~/c~/d~/s~/b/b~ > t t~ b WEIGHTED=3 [ all = QCD ] can have real emission processes which are not finite.
To avoid this, please use multiparticles when generating the process and be sure to include all the following particles in the multiparticle definition:
g, b, c, s, u, d, d~, u~, s~, c~, b~

If the b is massless, you can not distinguish it from the other quark/gluon without breaking the NLO accuracy.
So for such type of process, you need to do the computation in 4FS, and therefore p p > t t~ b b~ [QCD]

Cheers,

Olivier

> On 13 Sep 2017, at 19:53, Ernesto Arganda <email address hidden> wrote:
>
> New question #657974 on MadGraph5_aMC@NLO:
>
>
> We have been trying to compute the cross-section of ttb process with the NLO-type generation. In order to do so we use the 5f scheme by importing the model 'sm-no_b_mass'. We copy below the run_cardNLOtype.dat file that we have used for running MadGraph5_aMC@NLO (version 2.6.0). We have obtained the following results:
>
> --------------------------
> NLO-type generation-ttb
> --------------------------
> xs_LO = 2.7 +- 0.01 pb
> Scale uncertainty = +33% -24%
> PDF uncertainty = +4% -5%
>
> xs_NLO = 34.04 +- 1.8 pb
> Scale uncertainty = +53% -32%
> PDF uncertainty = +3% -4%
>
> which give us a huge K-factor of 12.6. However, if we do the same computation for ttj, we obtain:
>
> --------------------------
> NLO-type generation-ttj
> --------------------------
> xs_LO = 315.5 +- 1.4 pb
> Scale uncertainty = +45% -29%
> PDF uncertainty = +2% -3%
>
> xs_NLO = 415.4 +- 7.3 pb
> Scale uncertainty = +9% -13%
> PDF uncertainty = +2% -3%
>
> so that we have a K-factor=1.32. This result is consistent with what you show in the table 5 of your paper arXiv:1405.0301 [hep-ph].
>
> Taking into account the above results and the fact that the multiparticle 'j' already includes the b-quark, then we would like to understand if the K-factor obtained by including explicitly the b-quark in the final state is reliable. In other words, is it correct to generate the ttb@NLO in this way?
>
>
> Thank you very much for your help.
>
> Ernesto Arganda.
>
>
> The run_cardNLOtype.dat file is:
> #***********************************************************************
> # *
> # run_card.dat aMC@NLO *
> # *
> # This file is used to set the parameters of the run. *
> # *
> # Some notation/conventions: *
> # *
> # Lines starting with a hash (#) are info or comments *
> # *
> # mind the format: value = variable ! comment *
> # *
> # Some of the values of variables can be list. These can either be *
> # comma or space separated. *
> #***********************************************************************
> #
> #*******************
> # Running parameters
> #*******************
> #
> #***********************************************************************
> # Tag name for the run (one word) *
> #***********************************************************************
> tag_1 = run_tag ! name of the run
> #***********************************************************************
> # Number of LHE events (and their normalization) and the required *
> # (relative) accuracy on the Xsec. *
> # These values are ignored for fixed order runs *
> #***********************************************************************
> 1000 = nevents ! Number of unweighted events requested
> -1.0 = req_acc ! Required accuracy (-1=auto determined from nevents)
> -1 = nevt_job! Max number of events per job in event generation.
> ! (-1= no split).
> #***********************************************************************
> # Normalize the weights of LHE events such that they sum or average to *
> # the total cross section *
> #***********************************************************************
> average = event_norm ! valid settings: average, sum, bias
> #***********************************************************************
> # Number of points per itegration channel (ignored for aMC@NLO runs) *
> #***********************************************************************
> 0.1 = req_acc_FO ! Required accuracy (-1=ignored, and use the
> ! number of points and iter. below)
> # These numbers are ignored except if req_acc_FO is equal to -1
> 5000 = npoints_FO_grid ! number of points to setup grids
> 4 = niters_FO_grid ! number of iter. to setup grids
> 10000 = npoints_FO ! number of points to compute Xsec
> 6 = niters_FO ! number of iter. to compute Xsec
> #***********************************************************************
> # Random number seed *
> #***********************************************************************
> 0 = iseed ! rnd seed (0=assigned automatically=default))
> #***********************************************************************
> # Collider type and energy *
> #***********************************************************************
> 1 = lpp1 ! beam 1 type (0 = no PDF)
> 1 = lpp2 ! beam 2 type (0 = no PDF)
> 6500.0 = ebeam1 ! beam 1 energy in GeV
> 6500.0 = ebeam2 ! beam 2 energy in GeV
> #***********************************************************************
> # PDF choice: this automatically fixes also alpha_s(MZ) and its evol. *
> #***********************************************************************
> lhapdf = pdlabel ! PDF set
> 21100 = lhaid ! If pdlabel=lhapdf, this is the lhapdf number. Only
> ! numbers for central PDF sets are allowed. Can be a list;
> ! PDF sets beyond the first are included via reweighting.
> #***********************************************************************
> # Include the NLO Monte Carlo subtr. terms for the following parton *
> # shower (HERWIG6 | HERWIGPP | PYTHIA6Q | PYTHIA6PT | PYTHIA8) *
> # WARNING: PYTHIA6PT works only for processes without FSR!!!! *
> #***********************************************************************
> HERWIG6 = parton_shower
> 1.0 = shower_scale_factor ! multiply default shower starting
> ! scale by this factor
> #***********************************************************************
> # Renormalization and factorization scales *
> # (Default functional form for the non-fixed scales is the sum of *
> # the transverse masses divided by two of all final state particles *
> # and partons. This can be changed in SubProcesses/set_scales.f or via *
> # dynamical_scale_choice option) *
> #***********************************************************************
> False = fixed_ren_scale ! if .true. use fixed ren scale
> False = fixed_fac_scale ! if .true. use fixed fac scale
> 91.118 = muR_ref_fixed ! fixed ren reference scale
> 91.118 = muF_ref_fixed ! fixed fact reference scale
> 3 = dynamical_scale_choice ! Choose one (or more) of the predefined
> ! dynamical choices. Can be a list; scale choices beyond the
> ! first are included via reweighting
> 1.0 = muR_over_ref ! ratio of current muR over reference muR
> 1.0 = muF_over_ref ! ratio of current muF over reference muF
> #***********************************************************************
> # Reweight variables for scale dependence and PDF uncertainty *
> #***********************************************************************
> 1.0, 2.0, 0.5 = rw_rscale ! muR factors to be included by reweighting
> 1.0, 2.0, 0.5 = rw_fscale ! muF factors to be included by reweighting
> True = reweight_scale ! Reweight to get scale variation using the
> ! rw_rscale and rw_fscale factors. Should be a list of
> ! booleans of equal length to dynamical_scale_choice to
> ! specify for which choice to include scale dependence.
> True = reweight_PDF ! Reweight to get PDF uncertainty. Should be a
> ! list booleans of equal length to lhaid to specify for
> ! which PDF set to include the uncertainties.
> #***********************************************************************
> # Store reweight information in the LHE file for off-line model- *
> # parameter reweighting at NLO+PS accuracy *
> #***********************************************************************
> False = store_rwgt_info ! Store info for reweighting in LHE file
> #***********************************************************************
> # ickkw parameter: *
> # 0: No merging *
> # 3: FxFx Merging - WARNING! Applies merging only at the hard-event *
> # level. After showering an MLM-type merging should be applied as *
> # well. See http://amcatnlo.cern.ch/FxFx_merging.htm for details. *
> # 4: UNLOPS merging (with pythia8 only). No interface from within *
> # MG5_aMC available, but available in Pythia8. *
> # -1: NNLL+NLO jet-veto computation. See arxiv:1412.8408 [hep-ph]. *
> #***********************************************************************
> 0 = ickkw
> #***********************************************************************
> #
> #***********************************************************************
> # BW cutoff (M+/-bwcutoff*Gamma). Determines which resonances are *
> # written in the LHE event file *
> #***********************************************************************
> 15.0 = bwcutoff
> #***********************************************************************
> # Cuts on the jets. Jet clustering is performed by FastJet. *
> # - When matching to a parton shower, these generation cuts should be *
> # considerably softer than the analysis cuts. *
> # - More specific cuts can be specified in SubProcesses/cuts.f *
> #***********************************************************************
> -1.0 = jetalgo ! FastJet jet algorithm (1=kT, 0=C/A, -1=anti-kT)
> 0.5 = jetradius ! The radius parameter for the jet algorithm
> 30.0 = ptj ! Min jet transverse momentum
> 4.0 = etaj ! Max jet abs(pseudo-rap) (a value .lt.0 means no cut)
> #***********************************************************************
> # Cuts on the charged leptons (e+, e-, mu+, mu-, tau+ and tau-) *
> # More specific cuts can be specified in SubProcesses/cuts.f *
> #***********************************************************************
> 0.0 = ptl ! Min lepton transverse momentum
> -1.0 = etal ! Max lepton abs(pseudo-rap) (a value .lt.0 means no cut)
> 0.0 = drll ! Min distance between opposite sign lepton pairs
> 0.0 = drll_sf ! Min distance between opp. sign same-flavor lepton pairs
> 0.0 = mll ! Min inv. mass of all opposite sign lepton pairs
> 30.0 = mll_sf ! Min inv. mass of all opp. sign same-flavor lepton pairs
> #***********************************************************************
> # Photon-isolation cuts, according to hep-ph/9801442. When ptgmin=0, *
> # all the other parameters are ignored. *
> # More specific cuts can be specified in SubProcesses/cuts.f *
> #***********************************************************************
> 20.0 = ptgmin ! Min photon transverse momentum
> 2.0 = etagamma ! Max photon abs(pseudo-rap)
> 0.7 = R0gamma ! Radius of isolation code
> 1.0 = xn ! n parameter of eq.(3.4) in hep-ph/9801442
> 1.0 = epsgamma ! epsilon_gamma parameter of eq.(3.4) in hep-ph/9801442
> True = isoEM ! isolate photons from EM energy (photons and leptons)
> #***********************************************************************
> # For aMCfast+APPLGRID use in PDF fitting (http://amcfast.hepforge.org)*
> #***********************************************************************
> 0 = iappl ! aMCfast switch (0=OFF, 1=prepare grids, 2=fill grids)
> #***********************************************************************
>
> --