Difference between LO cross section and NLO cross section

Asked by Muhammad Irfan

I tried to generate process (p p > o w , W+ > mu+ vm , W- > mu- vm~ where o = c c~and w = W+ W-)to calculate the LO cross section.
which agreement with the cross section given in the paper i.e 1039-+3.206pb
But when i tried to calculate NLO cross section for the same process there is a huge difference in there cross section. (for NLO the cross section =3.06e+04 ± 5.4e+02 ) .I do not know why there such a huge difference.
The relevant paper is https://arxiv.org/pdf/1811.10021.pdf
I have NNPDF30lo(262000) for LO and NNPDF30 nlo(260000) for NLO
The events.lhe file for NLO is
<LesHouchesEvents version="3.0">
  <header>
  <MG5ProcCard>
#************************************************************
#* MadGraph5_aMC@NLO *
#* *
#* * * *
#* * * * * *
#* * * * * 5 * * * * *
#* * * * * *
#* * * *
#* *
#* *
#* VERSION 3.2.0 2021-08-22 *
#* *
#* The MadGraph5_aMC@NLO Development Team - Find us at *
#* https://server06.fynu.ucl.ac.be/projects/madgraph *
#* *
#************************************************************
#* *
#* Command File for MadGraph5_aMC@NLO *
#* *
#* run as ./bin/mg5_aMC filename *
#* *
#************************************************************
set group_subprocesses Auto
set ignore_six_quark_processes False
set low_mem_multicore_nlo_generation False
set complex_mass_scheme False
set include_lepton_initiated_processes False
set gauge unitary
set loop_optimized_output True
set loop_color_flows False
set max_npoint_for_channel 0
set default_unset_couplings 99
set max_t_for_channel 99
set zerowidth_tchannel True
set nlo_mixed_expansion True
define o = c c~
define p = g u c d s u~ c~ d~ s~
define j = g u c d s u~ c~ d~ s~
define l+ = e+ mu+
define l- = e- mu-
define vl = ve vm vt
define vl~ = ve~ vm~ vt~
define o = c c~
define w = W+ W-
import model loop_sm
generate p p > o w [QCD]
output lhapdf4
  </MG5ProcCard>
  <slha>
######################################################################
## PARAM_CARD AUTOMATICALY GENERATED BY MG5 FOLLOWING UFO MODEL ####
######################################################################
## ##
## Width set on Auto will be computed following the information ##
## present in the decay.py files of the model. ##
## See arXiv:1402.1178 for more details. ##
## ##
######################################################################

###################################
## INFORMATION FOR MASS
###################################
Block mass
    5 4.700000e+00 # MB
    6 1.730000e+02 # MT
   15 1.777000e+00 # MTA
   23 9.118800e+01 # MZ
   25 1.250000e+02 # MH
## Dependent parameters, given by model restrictions.
## Those values should be edited following the
## analytical expression. MG5 ignores those values
## but they are important for interfacing the output of MG5
## to external program such as Pythia.
  1 0.000000e+00 # d : 0.0
  2 0.000000e+00 # u : 0.0
  3 0.000000e+00 # s : 0.0
  4 0.000000e+00 # c : 0.0
  11 0.000000e+00 # e- : 0.0
  12 0.000000e+00 # ve : 0.0
  13 0.000000e+00 # mu- : 0.0
  14 0.000000e+00 # vm : 0.0
  16 0.000000e+00 # vt : 0.0
  21 0.000000e+00 # g : 0.0
  22 0.000000e+00 # a : 0.0
  24 8.041900e+01 # w+ : cmath.sqrt(MZ__exp__2/2. + cmath.sqrt(MZ__exp__4/4. - (aEW*cmath.pi*MZ__exp__2)/(Gf*sqrt__2)))

###################################
## INFORMATION FOR SMINPUTS
###################################
Block sminputs
    1 1.325070e+02 # aEWM1
    2 1.166390e-05 # Gf
    3 1.180000e-01 # aS (Note that Parameter not used if you use a PDF set)

###################################
## INFORMATION FOR YUKAWA
###################################
Block yukawa
    5 4.700000e+00 # ymb
    6 1.730000e+02 # ymt
   15 1.777000e+00 # ymtau

###################################
## INFORMATION FOR DECAY
###################################
DECAY 6 1.491500e+00 # WT
DECAY 23 2.441404e+00 # WZ
DECAY 24 2.047600e+00 # WW
DECAY 25 6.382339e-03 # WH
## Dependent parameters, given by model restrictions.
## Those values should be edited following the
## analytical expression. MG5 ignores those values
## but they are important for interfacing the output of MG5
## to external program such as Pythia.
DECAY 1 0.000000e+00 # d : 0.0
DECAY 2 0.000000e+00 # u : 0.0
DECAY 3 0.000000e+00 # s : 0.0
DECAY 4 0.000000e+00 # c : 0.0
DECAY 5 0.000000e+00 # b : 0.0
DECAY 11 0.000000e+00 # e- : 0.0
DECAY 12 0.000000e+00 # ve : 0.0
DECAY 13 0.000000e+00 # mu- : 0.0
DECAY 14 0.000000e+00 # vm : 0.0
DECAY 15 0.000000e+00 # ta- : 0.0
DECAY 16 0.000000e+00 # vt : 0.0
DECAY 21 0.000000e+00 # g : 0.0
DECAY 22 0.000000e+00 # a : 0.0
#===========================================================
# QUANTUM NUMBERS OF NEW STATE(S) (NON SM PDG CODE)
#===========================================================

Block QNUMBERS 82 # gh
        1 0 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 8 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
  </slha>
  <MGRunCard>
#***********************************************************************
# MadGraph5_aMC@NLO *
# *
# 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. *
# *
# To display additional parameter, you can use the command: *
# update to_full *
#***********************************************************************
#
#*******************
# 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 *
#***********************************************************************
      10000 = nevents
  -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).
#***********************************************************************
# Output format
#***********************************************************************
  -1.0 = time_of_flight ! threshold (in mm) below which the invariant livetime is not written (-1 means not written)
  average = event_norm ! average/sum/bias. Normalization of the weight in the LHEF
#***********************************************************************
# Number of points per itegration channel (ignored for aMC@NLO runs) *
#***********************************************************************
  0.01 = 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 *
#***********************************************************************
         33 = iseed
#***********************************************************************
# 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
  260000 = 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!!!! *
#***********************************************************************
  PYTHIA6Q = 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
  -1 = 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.
  False = 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. *
# - If gamma_is_j, photons are also clustered *
# - 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)
  0.7 = jetradius ! The radius parameter for the jet algorithm
  5.0 = ptj ! Min jet transverse momentum
  -1.0 = etaj ! Max jet abs(pseudo-rap) (a value .lt.0 means no cut)
  True = gamma_is_j ! Wether to cluster photons as jets or not
#***********************************************************************
# Cuts on the charged leptons (e+, e-, mu+, mu-, tau+ and tau-) *
# More specific cuts can be specified in SubProcesses/cuts.f *
#***********************************************************************
  26.0 = ptl ! Min lepton transverse momentum
  2.4 = 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
#***********************************************************************
# Fermion-photon recombination parameters *
# If Rphreco=0, no recombination is performed *
#***********************************************************************
  0.1 = rphreco ! Minimum fermion-photon distance for recombination
  -1.0 = etaphreco ! Maximum abs(pseudo-rap) for photons to be recombined (a value .lt.0 means no cut)
  True = lepphreco ! Recombine photons and leptons together
  True = quarkphreco ! Recombine photons and quarks together
#***********************************************************************
# Photon-isolation cuts, according to hep-ph/9801442 *
# Not applied if gamma_is_j *
# 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
  -1.0 = etagamma ! Max photon abs(pseudo-rap)
  0.4 = 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)
#***********************************************************************
# Cuts associated to MASSIVE particles identified by their PDG codes. *
# All cuts are applied to both particles and anti-particles, so use *
# POSITIVE PDG CODES only. Example of the syntax is {6 : 100} or *
# {6:100, 25:200} for multiple particles *
#***********************************************************************
  {} = pt_min_pdg ! Min pT for a massive particle
  {} = pt_max_pdg ! Max pT for a massive particle
  {} = mxx_min_pdg ! inv. mass for any pair of (anti)particles
#***********************************************************************
# Use PineAPPL to generate PDF-independent fast-interpolation grid *
# (https://zenodo.org/record/3992765#.X2EWy5MzbVo) *
#***********************************************************************
  False = pineappl ! PineAPPL switch

  regard

Muhammad Irfan

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Olivier Mattelaer (olivier-mattelaer) said :
#1

You can not ask for massless quark in the final state at NLO.
So this process is not consistent (NLO accurate).
You should have seen warning about that.

You need to use loop_sm-c_mass model for such computation.
Also your PDF need to be a 3 flavour PDF to be fully consistent (since you can not have massive c in the initial state, your gluon pdf need to compensate).

Cheers,

Olivier

Revision history for this message
Muhammad Irfan (iwan1234) said (last edit ):
#3

I have changed the model to loop_sm-c_mass and lhapdf to NNPDF30_nlo_as_0118_nf_3 (260200) but still there is a huge difference in LO cross section and NLO.

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Launchpad Janitor (janitor) said :
#4

This question was expired because it remained in the 'Open' state without activity for the last 15 days.