Cross-section for interference among SM and dim-6 operator doesn't match at LO and NLO

Dear MG5 experts,

I generated the interference among the O_W dim-6 operator (SMEFTatNLO) and the SM for the following process:

generate p p > l+ vl a QCD=0 QED=3 NP^2==2 @0
add process p p > l- vl~ a QCD=0 QED=3 NP^2==2 @1
add process p p > l+ vl a j QCD=1 QED=3 NP^2==2 @2
add process p p > l- vl~ a j QCD=1 QED=3 NP^2==2 @3

interfaced with Pythia8, and I got the following cross-section results, after the cuts:

SM LO: 47 fb
Interf LO 0jets: -1 fb
Interf LO 0+1jets with MLM: -7 fb
Interf LO 0+1jets without MLM: -5 fb

After this, I generated the same process at NLO, again with Pythia8:

generate p p > l+ vl a QCD=0 QED=3 NP^2==2 [QCD] @0
add process p p > l- vl~ a QCD=0 QED=3 NP^2==2 [QCD] @1
add process p p > l+ vl a j QCD=1 QED=3 NP^2==2 [QCD] @2
add process p p > l- vl~ a j QCD=1 QED=3 NP^2==2 [QCD] @3

getting the following results:

SM NLO: 59 fb
Interf NLO 0jets: 20 fb
Interf NLO 0+1jets with FxFx: 51 fb
Interf NLO 0+1jets without FxFx: 73 fb

It seems that the interference results are a bit far away from the previous ones, and indeed when I ran the last sample with order=LO, without any merging as FxFx is not available at LO, I got results that don't match with the LO sample ones:

Interf LO 0jets: 16 fb
Interf LO 0+1jets without merging: 41 fb

The cuts are the same for all the generations, both at partonic and python analysis level: pT cut at 80 GeV for the lepton and 150 GeV for the photon, MET above 40 GeV and minimum angular distance of 0.7 among photon and lepton.
The Qcut is the same as well. As the difference is already evident for the 0jet case, the issue doesn't seem to be related to merging; also, the dim-6 operator should only affect the EW part of the SM.

As a comparison, I generated the same process at fixed-order, and the results seem to agree with the first LO case:

SM LO: 47 fb
SM NLO: 51 fb
Interf LO 0jet: -1 fb
Interf LO 0+1jets: -7 fb
Interf NLO 0jets: -9 fb

Do you know what might cause this difference? I'll paste below the banner for the NLO run, let me know if you need to see the ones from the other generations as well, or if you need more info in general.

Best,

Matteo

#*******************
# 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 *
#***********************************************************************
  100000 = 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).
#***********************************************************************
# 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 *
#***********************************************************************
  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
  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!!!! *
#***********************************************************************
  PYTHIA8 = 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]. *
#***********************************************************************
  3 = 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 with jets. *
# Otherwise, they will be treated as tagged particles and photon *
# isolation will be applied. Note that photons in the real emission *
# will always be clustered with QCD partons. *
# - 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)
  1.0 = jetradius ! The radius parameter for the jet algorithm
  30.0 = ptj ! Min jet transverse momentum
  2.5 = etaj ! Max jet abs(pseudo-rap) (a value .lt.0 means no cut)
  False = 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 *
#***********************************************************************
  80.0 = ptl ! Min lepton transverse momentum
  2.5 = 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)
  False = lepphreco ! Recombine photons and leptons together
  False = 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 *
#***********************************************************************
  150.0 = ptgmin ! Min photon transverse momentum
  2.5 = 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
#***********************************************************************
]]>
</MGRunCard>
<slha>
######################################################################
## PARAM_CARD AUTOMATICALY GENERATED BY MG5 ####
######################################################################
###################################
## INFORMATION FOR DIM6
###################################
BLOCK DIM6 #
      1 1.100000e+03 # lambda
      6 1.100000e+00 # cwww
###################################
## INFORMATION FOR MASS
###################################
BLOCK MASS #
      6 1.720000e+02 # mt
      23 9.118760e+01 # mz
      24 7.982440e+01 # mw
      25 1.250000e+02 # mh
      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
      5 0.000000e+00 # b : 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
      15 0.000000e+00 # ta- : 0.0
      16 0.000000e+00 # vt : 0.0
      21 0.000000e+00 # g : 0.0
      22 0.000000e+00 # a : 0.0
      9000002 9.118760e+01 # ghz : mz
      9000003 7.982440e+01 # ghwp : mw
      9000004 7.982440e+01 # ghwm : mw
###################################
## INFORMATION FOR RENOR
###################################
BLOCK RENOR #
      1 9.118800e+01 # mueft
###################################
## INFORMATION FOR SMINPUTS
###################################
BLOCK SMINPUTS #
      2 1.166370e-05 # gf
      3 1.180023e-01 # as (note that parameter not used if you use a pdf set)
###################################
## INFORMATION FOR YUKAWA
###################################
BLOCK YUKAWA #
      6 1.720000e+02 # ymt
###################################
## INFORMATION FOR DECAY
###################################
DECAY 6 1.470800e+00 # wt
DECAY 23 2.416023e+00 # wz
DECAY 24 2.002950e+00 # ww
DECAY 25 4.088000e-03 # wh
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
DECAY 9000002 2.416023e+00 # ghz : wz
DECAY 9000003 2.002950e+00 # ghwp : ww
DECAY 9000004 2.002950e+00 # ghwm : ww
###################################
## INFORMATION FOR QNUMBERS 9000001
###################################
BLOCK QNUMBERS 9000001 # gha
      1 0 # 3 times electric charge
      2 1 # number of spin states (2s+1)
      3 1 # colour rep (1: singlet, 3: triplet, 8: octet)
      4 1 # particle/antiparticle distinction (0=own anti)
###################################
## INFORMATION FOR QNUMBERS 9000002
###################################
BLOCK QNUMBERS 9000002 # ghz
      1 0 # 3 times electric charge
      2 1 # number of spin states (2s+1)
      3 1 # colour rep (1: singlet, 3: triplet, 8: octet)
      4 1 # particle/antiparticle distinction (0=own anti)
###################################
## INFORMATION FOR QNUMBERS 9000003
###################################
BLOCK QNUMBERS 9000003 # ghwp
      1 3 # 3 times electric charge
      2 1 # number of spin states (2s+1)
      3 1 # colour rep (1: singlet, 3: triplet, 8: octet)
      4 1 # particle/antiparticle distinction (0=own anti)
###################################
## INFORMATION FOR QNUMBERS 9000004
###################################
BLOCK QNUMBERS 9000004 # ghwm
      1 -3 # 3 times electric charge
      2 1 # number of spin states (2s+1)
      3 1 # colour rep (1: singlet, 3: triplet, 8: octet)
      4 1 # particle/antiparticle distinction (0=own anti)
###################################
## INFORMATION FOR QNUMBERS 9000005
###################################
BLOCK QNUMBERS 9000005 # ghg
      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>
<MGShowerCard>
<![CDATA[
#***********************************************************************
# MadGraph5_aMC@NLO *
# *
# shower_card.dat aMC@NLO *
# *
# This file is used to set the parameters for the shower. *
# *
# Some notation/conventions: *
# *
# Lines starting with a hash (#) are info or comments *
# *
# mind the format: variable = value # comment *
#***********************************************************************
#
#***********************************************************************
# Shower settings *
#***********************************************************************
# Number of events, jobs, errors, and random seeds *
#***********************************************************************
nevents = -1 # N evts to shower (< 0 = all)
nsplit_jobs = 1 # N jobs to run in parallel (< 100!!)
combine_td = T # combine the topdrawer/HwU files if nsplit_jobs>1
maxprint = 2 # N evts to print in the log
maxerrs = 0.1 # max fraction of errors
rnd_seed = 0 # 1st random seed (0 = default)
rnd_seed2 = 0 # 2nd random seed (0 = default) !ONLY FOR HWERIG6!
#***********************************************************************
# PDFs and non-perturbative modelling *
#***********************************************************************
pdfcode = 1 # 0 = internal, 1 = same as NLO, other = lhaglue
ue_enabled = F # underlying event
hadronize = T # hadronisation on/off !IGNORED BY HERWIG6!
lambda_5 = -1 # Lambda_5 (< 0 = default) !IGNORED BY PYTHIA8!
#***********************************************************************
# Stable or unstable particles *
#***********************************************************************
b_stable = F # set B hadrons stable
pi_stable = T # set pi0's stable
wp_stable = F # set w+'s stable
wm_stable = F # set w-'s stable
z_stable = F # set z0's stable
h_stable = F # set Higgs' stable
tap_stable = F # set tau+'s stable
tam_stable = F # set tau-'s stable
mup_stable = F # set mu+'s stable
mum_stable = F # set mu-'s stable
#***********************************************************************
# Mass of the b quark *
#***********************************************************************
b_mass = -1 # if < 0 = read from SubProcesses/MCmasses_*.inc
#***********************************************************************
# Special settings *
#***********************************************************************
is_4lep = F # T if 4-lepton production !ONLY FOR PYTHIA6!
is_bbar = F # T if bb~ production !ONLY FOR HERWIG6!
#***********************************************************************
# FxFx merging parameters !ONLY FOR PYTHIA8!
#***********************************************************************
Qcut = 75 # Merging scale
njmax = 1 # Maximal multiplicity in the merging.
# # -1 means guessed from the process definition
#***********************************************************************
# Decay channels *
#***********************************************************************
# Syntax for HERWIG6 *
# DM_I = M > D1 D2 @ BR @ ME *
# corresponding to call to HWMODK(M,BR,ME,D1,D2) *
# I < 100, M is the decaying resonance, D1, D2, ... are the decay *
# products (up to five), BR is the branching ratio and ME is the type *
# of matrix element to be used in the decay. *
# BR's are correctly understood only if they add up to 1, and only if *
# no more than three modes are required for a given resonance. *
# WARNING: the order of decay products in > 2-body decays IS RELEVANT. *
# *
# Syntax for PYTHIA6 *
# DM_I = M > D1 D2 @ BR @ ME *
# WARNING: turning hadronisation off disables top decays *
# WARNING: 1 -> n decays (with n > 2) are handled through a sequence *
# of 1 -> 2 decays. *
# WARNING: entries BR and ME are ignored *
# *
# Syntax for HERWIG++ *
# DM_I = M > D1 D2 @ BR @ ME *
# WARNING: entries BR and ME are ignored *
# *
# Syntax for PYTHIA8 *
# DM_I = M:onIfAny = D1 D2 *
# or similar, according to the offical PYTHIA8 decay syntax, see *
# the online PYTHIA8 manual *
# WARNING: 1 -> n decays (with n > 2) are handled through a sequence *
# of 1 -> 2 decays. *
# *
# Examples *
# Z -> e+ e- or mu+ mu- with BR = 0.5 each, HERWIG6 *
# DM_1 = 23 > -11 11 @ 0.5d0 @ 100
# DM_2 = 23 > -13 13 @ 0.5d0 @ 100
# H -> ta+ ta- with BR = 1, HERWIG6 or HERWIG++ *
# DM_3 = 25 > -15 15 @ 1.0d0 @ 0
# t -> ve e+ b with BR = 1, HERWIG6 or HERWIG++ *
# DM_4 = 6 > 12 -11 5 @ 1d0 @ 100
# t -> ve e+ b with BR = 1, PYTHIA6 *
# DM_5 = 6 > 24 5 @ 1d0 @ 100
# DM_6 = 24 > 12 -11 @ 1d0 @ 100
# W+ -> ve e+, W- -> vm~ mu-, PYTHIA8 *
# DM_1 = 24:onMode = off
# DM_2 = 24:onPosIfAny = 11 12
# DM_3 = 24:onNegIfAny = 13 14
# W+ -> ve e+, W- -> ve~ e- and vm~ mu-, PYTHIA8 *
# DM_1 = 24:onMode = off
# DM_2 = 24:onIfAny = 11 12
# DM_3 = 24:onNegIfAny = 13 14
#***********************************************************************
# Extra libraries/analyses *
#***********************************************************************
# The following lines need to be changed if the user does not want to *
# create a StdHEP/HepMC file, but to directly run an own analysis (to *
# be placed in HWAnalyzer or analogous MCatNLO subfolders). *
# Please use files in those folders as examples. *
# Remember that if your analysis uses hbook or is in the HwU format, *
# you must also add to hbook.o or HwU.o to the ANALYSE list as well. *
#***********************************************************************
extralibs = pythia8 z dl stdc++ # Extra-libraries (not LHAPDF)
                                 # Default: "stdhep Fmcfio"
                                 # PYTHIA > 8.200 may require library dl
extrapaths = ../lib /home/users/m/m/mmaltoni/MG5_aMC_v3_4_2/HEPTools/pythia8//lib l,-rpath,/home/users/m/m/mmaltoni/MG5_aMC_v3_4_2/HEPTools/pythia8//lib /home/users/m/m/mmaltoni/MG5_aMC_v3_4_2/HEPTools/zlib/lib l,-rpath,/home/users/m/m/mmaltoni/MG5_aMC_v3_4_2/HEPTools/zlib/lib # Path to the extra-libraries
                                 # Default: "../lib"
INCLUDEPATHS = # Path to header files needed by c++
                                 # Dir names separated by white spaces
ANALYSE = # User's analysis and histogramming
                                 # routines (please use .o as extension
                                 # and use spaces to separate files).
                                 # If the HwU.o files has to be linked,
                                 # it should be put *first*.
]]>
</MGShowerCard>
<run_settings>
order = NLO
fixed_order = OFF
shower = PYTHIA8
madspin = OFF
reweight = OFF
madanalysis = OFF
runshower = True
</run_settings>
</header>
</LesHouchesEvents>