MadGraph5_aMC@NLO

ZZ to HH cross section not tending to 0

Asked by Shameran Mahmud

For some reason, generating Madgraph events of a tree-level process with two Z bosons producing two Higgses at very high energy (around 30-100 TeV) does not seem to tend towards 0. It seems to be going towards a finite value of ~7.7 picobarns. I tried generating events in both Feynman gauge and Unitarity gauge, yet the cross section seems to only change by about 0.1 picobarns, so both gauges give a cross section tending towards ~7.7 picobarns. Is there some issue with what I did, and a way to fix this? I am using version 3.1.1, and not using Pythia or Delphes.

Thank you in advance.

Here is an example of the event tag output after generating this event in the Feynman gauge: at 30 TeV:

<LesHouchesEvents version="3.0">
<header>
<!--
#*********************************************************************
# *
# MadGraph5_aMC@NLO *
# *
# Going Beyond *
# *
# http://madgraph.hep.uiuc.edu *
# http://madgraph.phys.ucl.ac.be *
# http://amcatnlo.cern.ch *
# *
# The MadGraph5_aMC@NLO team *
# *
#....................................................................*
# *
# This file contains all the information necessary to reproduce *
# the events generated: *
# *
# 1. software version *
# 2. proc_card : code generation info including model *
# 3. param_card : model primary parameters in the LH format *
# 4. run_card : running parameters (collider and cuts) *
# 5. pythia_card : present only if pythia has been run *
# 6. pgs_card : present only if pgs has been run *
# 7. delphes_cards : present only if delphes has been run *
# *
# *
#*********************************************************************
-->
<MGVersion>
3.1.1
</MGVersion>
<MG5ProcCard>
<![CDATA[
#************************************************************
#* MadGraph5_aMC@NLO *
#* *
#* * * *
#* * * * * *
#* * * * * 5 * * * * *
#* * * * * *
#* * * *
#* *
#* *
#* VERSION 3.1.1 2021-05-28 *
#* *
#* 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 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
set gauge Feynman
import model sm
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~
generate Z Z > H H
output
]]>
</MG5ProcCard>
<MGProcCard>
#*********************************************************************
# MadGraph/MadEvent *
# http://madgraph.hep.uiuc.edu *
# *
# proc_card.dat *
#*********************************************************************
# *
# This Files is generated by MADGRAPH 5 *
# *
# WARNING: This Files is generated for MADEVENT (compatibility issue)*
# This files is NOT a valid MG4 proc_card.dat *
# Running this in MG4 will NEVER reproduce the result of MG5*
# *
#*********************************************************************
#*********************************************************************
# Process(es) requested : mg2 input *
#*********************************************************************
# Begin PROCESS # This is TAG. Do not modify this line
Z Z > H H #Process
# Be carefull the coupling are here in MG5 convention

end_coup # End the couplings input

done # this tells MG there are no more procs
# End PROCESS # This is TAG. Do not modify this line
#*********************************************************************
# Model information *
#*********************************************************************
# Begin MODEL # This is TAG. Do not modify this line
sm
# End MODEL # This is TAG. Do not modify this line
#*********************************************************************
# Start multiparticle definitions *
#*********************************************************************
# Begin MULTIPARTICLES # This is TAG. Do not modify this line

# End MULTIPARTICLES # This is TAG. Do not modify this line
</MGProcCard>
<MGRunCard>
<![CDATA[
#*********************************************************************
# MadGraph5_aMC@NLO *
# *
# run_card.dat MadEvent *
# *
# This file is used to set the parameters of the run. *
# *
# Some notation/conventions: *
# *
# Lines starting with a '# ' are info or comments *
# *
# mind the format: value = variable ! comment *
# *
# To display more options, you can type the command: *
# update full_run_card *
#*********************************************************************
#
#*********************************************************************
# Tag name for the run (one word) *
#*********************************************************************
  tag_1 = run_tag ! name of the run
#*********************************************************************
# Number of events and rnd seed *
# Warning: Do not generate more than 1M events in a single run *
#*********************************************************************
  10 = nevents ! Number of unweighted events requested
 21 = iseed ! rnd seed (0=assigned automatically=default))
#*********************************************************************
# Collider type and energy *
# lpp: 0=No PDF, 1=proton, -1=antiproton, 2=photon from proton, *
# 3=photon from electron, 4=photon from muon *
#*********************************************************************
  0 = lpp1 ! beam 1 type
  0 = lpp2 ! beam 2 type
  15000.0 = ebeam1 ! beam 1 total energy in GeV
  15000.0 = ebeam2 ! beam 2 total energy in GeV
#*********************************************************************
# Beam polarization from -100 (left-handed) to 100 (right-handed) *
#*********************************************************************
  0.0 = polbeam1 ! beam polarization for beam 1
  0.0 = polbeam2 ! beam polarization for beam 2

#*********************************************************************
# PDF CHOICE: this automatically fixes also alpha_s and its evol. *
#*********************************************************************
  nn23lo1 = pdlabel ! PDF set
  230000 = lhaid ! if pdlabel=lhapdf, this is the lhapdf number
# To see heavy ion options: type "update ion_pdf"
#*********************************************************************
# Renormalization and factorization scales *
#*********************************************************************
  False = fixed_ren_scale ! if .true. use fixed ren scale
  False = fixed_fac_scale ! if .true. use fixed fac scale
  91.188 = scale ! fixed ren scale
  91.188 = dsqrt_q2fact1 ! fixed fact scale for pdf1
  91.188 = dsqrt_q2fact2 ! fixed fact scale for pdf2
  -1 = dynamical_scale_choice ! Choose one of the preselected dynamical choices
  1.0 = scalefact ! scale factor for event-by-event scales
#*********************************************************************
# Type and output format
#*********************************************************************
  False = gridpack !True = setting up the grid pack
  -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. Normalization of the weight in the LHEF
# To see MLM/CKKW merging options: type "update MLM" or "update CKKW"

#*********************************************************************
#
#*********************************************************************
# Phase-Space Optimization strategy (basic options)
#*********************************************************************
  0 = nhel ! using helicities importance sampling or not.
                             ! 0: sum over helicity, 1: importance sampling
  2 = sde_strategy ! default integration strategy (hep-ph/2021.xxxxx)
                             ! 1 is old strategy (using amp square)
        ! 2 is new strategy (using only the denominator)
# To see advanced option for Phase-Space optimization: type "update psoptim"
#*********************************************************************
# Generation bias, check the wiki page below for more information: *
# 'cp3.irmp.ucl.ac.be/projects/madgraph/wiki/LOEventGenerationBias' *
#*********************************************************************
  None = bias_module ! Bias type of bias, [None, ptj_bias, -custom_folder-]
  {} = bias_parameters ! Specifies the parameters of the module.
#
#*******************************
# Parton level cuts definition *
#*******************************
#
#
#*********************************************************************
# BW cutoff (M+/-bwcutoff*Gamma) ! Define on/off-shell for "$" and decay
#*********************************************************************
  15.0 = bwcutoff ! (M+/-bwcutoff*Gamma)
#*********************************************************************
# Standard Cuts *
#*********************************************************************
# Minimum and maximum pt's (for max, -1 means no cut) *
#*********************************************************************
  {} = pt_min_pdg ! pt cut for other particles (use pdg code). Applied on particle and anti-particle
  {} = pt_max_pdg ! pt cut for other particles (syntax e.g. {6: 100, 25: 50})
#*********************************************************************
# Minimum and maximum E's (in the center of mass frame) *
#*********************************************************************
  0.0 = ej ! minimum E for the jets
  0.0 = eb ! minimum E for the b
  0.0 = ea ! minimum E for the photons
  0.0 = el ! minimum E for the charged leptons
  -1.0 = ejmax ! maximum E for the jets
  -1.0 = ebmax ! maximum E for the b
  -1.0 = eamax ! maximum E for the photons
  -1.0 = elmax ! maximum E for the charged leptons
  {} = e_min_pdg ! E cut for other particles (use pdg code). Applied on particle and anti-particle
  {} = e_max_pdg ! E cut for other particles (syntax e.g. {6: 100, 25: 50})

#*********************************************************************
# Maximum and minimum absolute rapidity (for max, -1 means no cut) *
#*********************************************************************
  {} = eta_min_pdg ! rap cut for other particles (use pdg code). Applied on particle and anti-particle
  {} = eta_max_pdg ! rap cut for other particles (syntax e.g. {6: 2.5, 23: 5})
#*********************************************************************
# Minimum and maximum DeltaR distance *
#*********************************************************************
#*********************************************************************
# Minimum and maximum invariant mass for pairs *
#*********************************************************************
  {} = mxx_min_pdg ! min invariant mass of a pair of particles X/X~ (e.g. {6:250})
  {'default': False} = mxx_only_part_antipart ! if True the invariant mass is applied only
                       ! to pairs of particle/antiparticle and not to pairs of the same pdg codes.
#*********************************************************************
# Inclusive cuts *
#*********************************************************************
  0.0 = ptheavy ! minimum pt for at least one heavy final state
#*********************************************************************
# maximal pdg code for quark to be considered as a light jet *
# (otherwise b cuts are applied) *
#*********************************************************************
  4 = maxjetflavor ! Maximum jet pdg code
#*********************************************************************
#
#*********************************************************************
# Store info for systematics studies *
# WARNING: Do not use for interference type of computation *
#*********************************************************************
  False = use_syst ! Enable systematics studies
#
  systematics = systematics_program ! none, systematics [python], SysCalc [depreceted, C++]
  ['--mur=0.5,1,2', '--muf=0.5,1,2', '--pdf=errorset'] = systematics_arguments ! see: https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/Systematics#Systematicspythonmodule
# Syscalc is deprecated but to see the associate options type'update syscalc'
]]>
</MGRunCard>
<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)))
  250 9.118800e+01 # g0 : MZ
  251 8.041900e+01 # g+ : MW

###################################
## 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
DECAY 250 2.441404e+00 # g0 : WZ
DECAY 251 2.047600e+00 # g+ : WW
#===========================================================
# QUANTUM NUMBERS OF NEW STATE(S) (NON SM PDG CODE)
#===========================================================

Block QNUMBERS 250 # g0
        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 0 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 251 # g+
        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)
</slha>
<MGGenerationInfo>
# Number of Events : 10
# Integrated weight (pb) : 7.7200013083
</MGGenerationInfo>
</header>
</LesHouchesEvents>

And here is my event tag for the process at unitarity gauge at 30 TeV:
<LesHouchesEvents version="3.0">
<header>
<!--
#*********************************************************************
# *
# MadGraph5_aMC@NLO *
# *
# Going Beyond *
# *
# http://madgraph.hep.uiuc.edu *
# http://madgraph.phys.ucl.ac.be *
# http://amcatnlo.cern.ch *
# *
# The MadGraph5_aMC@NLO team *
# *
#....................................................................*
# *
# This file contains all the information necessary to reproduce *
# the events generated: *
# *
# 1. software version *
# 2. proc_card : code generation info including model *
# 3. param_card : model primary parameters in the LH format *
# 4. run_card : running parameters (collider and cuts) *
# 5. pythia_card : present only if pythia has been run *
# 6. pgs_card : present only if pgs has been run *
# 7. delphes_cards : present only if delphes has been run *
# *
# *
#*********************************************************************
-->
<MGVersion>
3.1.1
</MGVersion>
<MG5ProcCard>
<![CDATA[
#************************************************************
#* MadGraph5_aMC@NLO *
#* *
#* * * *
#* * * * * *
#* * * * * 5 * * * * *
#* * * * * *
#* * * *
#* *
#* *
#* VERSION 3.1.1 2021-05-28 *
#* *
#* 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
import model sm
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~
generate Z Z > H H
output
]]>
</MG5ProcCard>
<MGProcCard>
#*********************************************************************
# MadGraph/MadEvent *
# http://madgraph.hep.uiuc.edu *
# *
# proc_card.dat *
#*********************************************************************
# *
# This Files is generated by MADGRAPH 5 *
# *
# WARNING: This Files is generated for MADEVENT (compatibility issue)*
# This files is NOT a valid MG4 proc_card.dat *
# Running this in MG4 will NEVER reproduce the result of MG5*
# *
#*********************************************************************
#*********************************************************************
# Process(es) requested : mg2 input *
#*********************************************************************
# Begin PROCESS # This is TAG. Do not modify this line
Z Z > H H #Process
# Be carefull the coupling are here in MG5 convention

end_coup # End the couplings input

done # this tells MG there are no more procs
# End PROCESS # This is TAG. Do not modify this line
#*********************************************************************
# Model information *
#*********************************************************************
# Begin MODEL # This is TAG. Do not modify this line
sm
# End MODEL # This is TAG. Do not modify this line
#*********************************************************************
# Start multiparticle definitions *
#*********************************************************************
# Begin MULTIPARTICLES # This is TAG. Do not modify this line

# End MULTIPARTICLES # This is TAG. Do not modify this line
</MGProcCard>
<MGRunCard>
<![CDATA[
#*********************************************************************
# MadGraph5_aMC@NLO *
# *
# run_card.dat MadEvent *
# *
# This file is used to set the parameters of the run. *
# *
# Some notation/conventions: *
# *
# Lines starting with a '# ' are info or comments *
# *
# mind the format: value = variable ! comment *
# *
# To display more options, you can type the command: *
# update full_run_card *
#*********************************************************************
#
#*********************************************************************
# Tag name for the run (one word) *
#*********************************************************************
  tag_1 = run_tag ! name of the run
#*********************************************************************
# Number of events and rnd seed *
# Warning: Do not generate more than 1M events in a single run *
#*********************************************************************
  10000 = nevents ! Number of unweighted events requested
 21 = iseed ! rnd seed (0=assigned automatically=default))
#*********************************************************************
# Collider type and energy *
# lpp: 0=No PDF, 1=proton, -1=antiproton, 2=photon from proton, *
# 3=photon from electron, 4=photon from muon *
#*********************************************************************
  0 = lpp1 ! beam 1 type
  0 = lpp2 ! beam 2 type
  15000.0 = ebeam1 ! beam 1 total energy in GeV
  15000.0 = ebeam2 ! beam 2 total energy in GeV
#*********************************************************************
# Beam polarization from -100 (left-handed) to 100 (right-handed) *
#*********************************************************************
  0.0 = polbeam1 ! beam polarization for beam 1
  0.0 = polbeam2 ! beam polarization for beam 2

#*********************************************************************
# PDF CHOICE: this automatically fixes also alpha_s and its evol. *
#*********************************************************************
  nn23lo1 = pdlabel ! PDF set
  230000 = lhaid ! if pdlabel=lhapdf, this is the lhapdf number
# To see heavy ion options: type "update ion_pdf"
#*********************************************************************
# Renormalization and factorization scales *
#*********************************************************************
  False = fixed_ren_scale ! if .true. use fixed ren scale
  False = fixed_fac_scale ! if .true. use fixed fac scale
  91.188 = scale ! fixed ren scale
  91.188 = dsqrt_q2fact1 ! fixed fact scale for pdf1
  91.188 = dsqrt_q2fact2 ! fixed fact scale for pdf2
  -1 = dynamical_scale_choice ! Choose one of the preselected dynamical choices
  1.0 = scalefact ! scale factor for event-by-event scales
#*********************************************************************
# Type and output format
#*********************************************************************
  False = gridpack !True = setting up the grid pack
  -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. Normalization of the weight in the LHEF
# To see MLM/CKKW merging options: type "update MLM" or "update CKKW"

#*********************************************************************
#
#*********************************************************************
# Phase-Space Optimization strategy (basic options)
#*********************************************************************
  0 = nhel ! using helicities importance sampling or not.
                             ! 0: sum over helicity, 1: importance sampling
  2 = sde_strategy ! default integration strategy (hep-ph/2021.xxxxx)
                             ! 1 is old strategy (using amp square)
        ! 2 is new strategy (using only the denominator)
# To see advanced option for Phase-Space optimization: type "update psoptim"
#*********************************************************************
# Generation bias, check the wiki page below for more information: *
# 'cp3.irmp.ucl.ac.be/projects/madgraph/wiki/LOEventGenerationBias' *
#*********************************************************************
  None = bias_module ! Bias type of bias, [None, ptj_bias, -custom_folder-]
  {} = bias_parameters ! Specifies the parameters of the module.
#
#*******************************
# Parton level cuts definition *
#*******************************
#
#
#*********************************************************************
# BW cutoff (M+/-bwcutoff*Gamma) ! Define on/off-shell for "$" and decay
#*********************************************************************
  15.0 = bwcutoff ! (M+/-bwcutoff*Gamma)
#*********************************************************************
# Standard Cuts *
#*********************************************************************
# Minimum and maximum pt's (for max, -1 means no cut) *
#*********************************************************************
  {} = pt_min_pdg ! pt cut for other particles (use pdg code). Applied on particle and anti-particle
  {} = pt_max_pdg ! pt cut for other particles (syntax e.g. {6: 100, 25: 50})
#*********************************************************************
# Minimum and maximum E's (in the center of mass frame) *
#*********************************************************************
  0.0 = ej ! minimum E for the jets
  0.0 = eb ! minimum E for the b
  0.0 = ea ! minimum E for the photons
  0.0 = el ! minimum E for the charged leptons
  -1.0 = ejmax ! maximum E for the jets
  -1.0 = ebmax ! maximum E for the b
  -1.0 = eamax ! maximum E for the photons
  -1.0 = elmax ! maximum E for the charged leptons
  {} = e_min_pdg ! E cut for other particles (use pdg code). Applied on particle and anti-particle
  {} = e_max_pdg ! E cut for other particles (syntax e.g. {6: 100, 25: 50})

#*********************************************************************
# Maximum and minimum absolute rapidity (for max, -1 means no cut) *
#*********************************************************************
  {} = eta_min_pdg ! rap cut for other particles (use pdg code). Applied on particle and anti-particle
  {} = eta_max_pdg ! rap cut for other particles (syntax e.g. {6: 2.5, 23: 5})
#*********************************************************************
# Minimum and maximum DeltaR distance *
#*********************************************************************
#*********************************************************************
# Minimum and maximum invariant mass for pairs *
#*********************************************************************
  {} = mxx_min_pdg ! min invariant mass of a pair of particles X/X~ (e.g. {6:250})
  {'default': False} = mxx_only_part_antipart ! if True the invariant mass is applied only
                       ! to pairs of particle/antiparticle and not to pairs of the same pdg codes.
#*********************************************************************
# Inclusive cuts *
#*********************************************************************
  0.0 = ptheavy ! minimum pt for at least one heavy final state
#*********************************************************************
# maximal pdg code for quark to be considered as a light jet *
# (otherwise b cuts are applied) *
#*********************************************************************
  4 = maxjetflavor ! Maximum jet pdg code
#*********************************************************************
#
#*********************************************************************
# Store info for systematics studies *
# WARNING: Do not use for interference type of computation *
#*********************************************************************
  False = use_syst ! Enable systematics studies
#
  systematics = systematics_program ! none, systematics [python], SysCalc [depreceted, C++]
  ['--mur=0.5,1,2', '--muf=0.5,1,2', '--pdf=errorset'] = systematics_arguments ! see: https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/Systematics#Systematicspythonmodule
# Syscalc is deprecated but to see the associate options type'update syscalc'
]]>
</MGRunCard>
<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
</slha>
<MGGenerationInfo>
# Number of Events : 10000
# Integrated weight (pb) : 7.7830025925
</MGGenerationInfo>
</header>
</LesHouchesEvents>

Let me know if I should share something else pertaining to this process that may help solve the issue.

Question information

Language:
English Edit question
Status:
Open
For:
MadGraph5_aMC@NLO Edit question
Assignee:
Richard Ruiz Edit question
Last query:
Last reply:
Revision history for this message
Richard Ruiz (rruiz) said : 		#1

Dear Shameran,

I suspect that this "constant" cross section is due to the absence of phase space cuts on the final-state Higgs pair.

In the massless limit, the matrix element for ZZ > HH has a pair of poles when the outgoing H are parallel / antiparallel to the incoming Zs, i.e., when the two t_ij (or t and u if you prefer) are zero.

Returning to the massive limit, one can expect numerical instabilities when

t_ij = (p_Z - p_H)^2 = mZ^2 + mH^2 -2pZ*pH \sim mZ^2

or equally when

2pZ*pH = 2EZ EH (1 - betaZ beta H Cos theta) \sim mH^2

or when

Cos theta \sim (1- mH^2 / 2EZ EH) / betaZ betaH

Since MadGraph uses adaptive sampling, the routines will learn / discover the value of theta that best solves this relationship. Unfortunately, this leads to divergent-like behavior since the matrix element is very nearly singular given your choice of collider energies.

I recommend placing maximum rapidity cuts on H to remove the collinear region of phase space. Something like,
set eta_max_pdg {25: 3}

With this cut, you should observe a cross section that falls with increasing collider energy.

cheers,
richard

Revision history for this message
Shameran Mahmud (shameranmahmud) said : 		#2

Hi Richard,

Thank you for the solution. While using this did solve the issue with the divergence I was having, I decided to try using some other value for the rapidity cuts at first, specifically, editing the line to "set eta_max_pdg {25: 2.5}" and "set eta_max_pdg {25: 3.5}".

 While the cross sections were still consistently decreasing with increasing collider energy, their values with the different eta cuts at the same collider energy were much beyond the ~0.9% uncertainty range. For example, with a rapidity cut of 3, the cross sections were ~0.03 pb at 30 TeV and ~0.002 pb at 100 TeV, while with a cut of 2.5, they were ~0.01 pb at 30 TeV and ~0.001 TeV at 100 TeV, and with a cut of 3.5, they were ~0.07 pb at 30 TeV and ~0.007 TeV at 100 TeV.

Due to these big fluctuations in the values, there does not seem to be a clear criteria for which rapidity cut to choose. Is there a way to know whether a given cut is giving an accurate value for the cross section, or could this be due to some other issue?

Thank you again,
Shameran

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