3-body decay width doesn't match

Asked by Han Qin on 2020-08-17

Dear Madgraph authors,

I have a question about the width calculation by MG5.

I am working on a global B-L extension of SM. The model has a SU(2) triplet with hyper-charge +1 and B−L charge +2 (similar to Type-II see-saw), and has an additional complex scalar singlet with B−L charge +2. The new scalar fields in our model are: doubly charged Higgs: delta++(PID 900006), singly charged Higgs: h+(PID 900006), two CP even and two CP odd neutral Higgs: h2(PID 900001) h3(PID 900002) a2(PID 900003) a3 (PID 900004).

The scalar triplet doesn't have a vev due to B-L conservation, and delta++ > w+ w+ h3 decay is expected to be dominant in our phenomenologically preferred parameter space, and delta++ > l+ l+ is suppressed. I tried to calculate the decay width of this channel with MG5, so I used the command :

generate delta++ > w+ w+ h3

and run this process. In the mean time, I set the width of delta++ in param_card.dat as "Auto" so that MG5 can perform automatic width computation. However, the run result and the automatic computation result written in param_card don’t agree with each other. The run result shows the decay width for this channel is 2.3209E-3 GeV while the automatic computation result is 3.0189E-4 GeV.

Could you please help me figure out why these two results disagree and which method is more reliable regarding the N-body decay width calculation?

My MG5 version is 2.6.5 and I attach the banner of my run so that you can find details of run result and automatic computation. If you need more details about our model, I can send the UFO files separately.

**********************************************************************
<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) *
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2.6.5
</MGVersion>
<MG5ProcCard>
<![CDATA[
#************************************************************
#* MadGraph5_aMC@NLO *
#* *
#* * * *
#* * * * * *
#* * * * * 5 * * * * *
#* * * * * *
#* * * *
#* *
#* *
#* VERSION 2.6.5 2018-02-03 *
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#* 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 default_unset_couplings 99
set group_subprocesses Auto
set ignore_six_quark_processes False
set loop_optimized_output True
set loop_color_flows False
set gauge unitary
set complex_mass_scheme False
set max_npoint_for_channel 0
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~
import model /Users/qinhan/Downloads/MCTools/MG5_aMC_v2_6_5/models/lig\
ht_scalar_V3
generate delta++ > w+ w+ h3
output hpp_wwh3
]]>
</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*
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#*********************************************************************
#*********************************************************************
# Process(es) requested : mg2 input *
#*********************************************************************
# Begin PROCESS # This is TAG. Do not modify this line
delta++ > w+ w+ h3 #Process
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end_coup # End the couplings input

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# Begin MODEL # This is TAG. Do not modify this line
light_scalar_V3
# End MODEL # This is TAG. Do not modify this line
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# Start multiparticle definitions *
#*********************************************************************
# Begin MULTIPARTICLES # This is TAG. Do not modify this line

# End MULTIPARTICLES # This is TAG. Do not modify this line
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     nn23lo1 = pdlabel ! PDF set
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 0.0 = mmjj ! min invariant mass of a jet pair
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#*********************************************************************
# Minimum and maximum invariant mass for all letpons *
#*********************************************************************
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# (otherwise b cuts are applied) *
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#
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<slha>
######################################################################
## PARAM_CARD AUTOMATICALY GENERATED BY MG5 ####
######################################################################
###################################
## INFORMATION FOR BSM
###################################
BLOCK BSM #
      1 1.000000e-03 # ynuee
      2 1.000000e-03 # ynuemu
      3 1.000000e-03 # ynueta
      4 1.000000e-03 # ynumumu
      5 1.000000e-03 # ynumuta
      6 1.000000e-03 # ynutata
      7 1.000000e-01 # lamb1
      8 0.000000e+00 # lamb2
      9 0.000000e+00 # lamb3
      10 -1.000000e+00 # lamb4
      11 0.000000e+00 # lamb5
      12 0.000000e+00 # lamb7
      13 7.000000e-01 # lamb8
      14 3.500000e+02 # mdelta
      15 1.000000e+02 # mphi
###################################
## INFORMATION FOR MASS
###################################
BLOCK MASS #
      5 4.700000e+00 # mb
      6 1.720000e+02 # mt
      15 1.777000e+00 # mta
      23 9.118760e+01 # mz
      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
      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 7.982436e+01 # w+ : cmath.sqrt(mz__exp__2/2. + cmath.sqrt(mz__exp__4/4. - (aew*cmath.pi*mz__exp__2)/(gf*sqrt__2)))
      900001 3.165594e+02 # h2 : cmath.sqrt(2*mdelta__exp__2 + 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2 + cmath.sqrt(4*lamb8__exp__2*vev__exp__4 + (2*mdelta__exp__2 - 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2)**2))/2.
      900002 7.077495e+01 # h3 : cmath.sqrt(2*mdelta__exp__2 + 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2 - cmath.sqrt(4*lamb8__exp__2*vev__exp__4 + (2*mdelta__exp__2 - 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2)**2))/2.
      900003 3.165594e+02 # a2 : cmath.sqrt(2*mdelta__exp__2 + 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2 + cmath.sqrt(4*lamb8__exp__2*vev__exp__4 + (2*mdelta__exp__2 - 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2)**2))/2.
      900004 7.077495e+01 # a3 : cmath.sqrt(2*mdelta__exp__2 + 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2 - cmath.sqrt(4*lamb8__exp__2*vev__exp__4 + (2*mdelta__exp__2 - 2*mphi__exp__2 + (lamb1 + lamb4)*vev__exp__2)**2))/2.
      900005 3.322275e+02 # h+ : cmath.sqrt(mdelta__exp__2 + (lamb1*vev__exp__2)/2. + (lamb4*vev__exp__2)/4.)
      900006 3.543039e+02 # delta++ : cmath.sqrt(mdelta__exp__2 + (lamb1*vev__exp__2)/2.)
###################################
## INFORMATION FOR SMINPUTS
###################################
BLOCK SMINPUTS #
      1 1.279000e+02 # aewm1
      2 1.166370e-05 # gf
      3 1.184000e-01 # as
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BLOCK YUKAWA #
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###################################
BLOCK QNUMBERS 900001 # h2
      1 0 # 3 times electric charge
      2 1 # number of spin states (2s+1)
      3 1 # colour rep (1: singlet, 3: triplet, 8: octet)
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###################################
## INFORMATION FOR QNUMBERS 900002
###################################
BLOCK QNUMBERS 900002 # h3
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      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)
###################################
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###################################
BLOCK QNUMBERS 900003 # a2
      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)
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###################################
BLOCK QNUMBERS 900004 # a3
      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)
###################################
## INFORMATION FOR QNUMBERS 900005
###################################
BLOCK QNUMBERS 900005 # h+
      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 900006
###################################
BLOCK QNUMBERS 900006 # delta++
      1 6 # 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)
###################################
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###################################
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DECAY 2 0.000000e+00 #
DECAY 3 0.000000e+00 #
DECAY 4 0.000000e+00 #
DECAY 5 0.000000e+00 #
DECAY 6 1.508336e+00 #
DECAY 11 0.000000e+00 #
DECAY 12 0.000000e+00 #
DECAY 13 0.000000e+00 #
DECAY 14 0.000000e+00 #
DECAY 15 0.000000e+00 #
DECAY 16 0.000000e+00 #
DECAY 21 0.000000e+00 #
DECAY 22 0.000000e+00 #
DECAY 23 2.495200e+00 #
DECAY 24 2.085000e+00 #
DECAY 25 4.070000e-03 #
DECAY 900001 1.840833e+00 #
      7.083031e-01 2 23 900004 # 1.30386746059
      2.908105e-01 2 25 900002 # 0.535333412477
      7.486286e-04 3 -24 24 900002 # 0.00137810005599
      7.950207e-05 3 -24 24 900004 # 0.000146350004988
      6.483576e-06 2 14 16 # 1.19351782282e-05
      6.483576e-06 2 12 16 # 1.19351782282e-05
      6.483576e-06 2 12 14 # 1.19351782282e-05
      6.483576e-06 2 -14 -12 # 1.19351782282e-05
      6.483576e-06 2 -16 -12 # 1.19351782282e-05
      6.483576e-06 2 -16 -14 # 1.19351782282e-05
      3.241788e-06 2 16 16 # 5.96758911409e-06
      3.241788e-06 2 14 14 # 5.96758911409e-06
      3.241788e-06 2 12 12 # 5.96758911409e-06
      3.241788e-06 2 -12 -12 # 5.96758911409e-06
      3.241788e-06 2 -14 -14 # 5.96758911409e-06
      3.241788e-06 2 -16 -16 # 5.96758911409e-06

DECAY 900002 1.328683e-06 #
      1.111111e-01 2 14 16 # 1.47631402772e-07
      1.111111e-01 2 12 16 # 1.47631402772e-07
      1.111111e-01 2 12 14 # 1.47631402772e-07
      1.111111e-01 2 -14 -12 # 1.47631402772e-07
      1.111111e-01 2 -16 -12 # 1.47631402772e-07
      1.111111e-01 2 -16 -14 # 1.47631402772e-07
      5.555556e-02 2 16 16 # 7.3815701386e-08
      5.555556e-02 2 14 14 # 7.3815701386e-08
      5.555556e-02 2 12 12 # 7.3815701386e-08
      5.555556e-02 2 -12 -12 # 7.3815701386e-08
      5.555556e-02 2 -14 -14 # 7.3815701386e-08
      5.555556e-02 2 -16 -16 # 7.3815701386e-08

DECAY 900003 1.840834e+00 #
      7.083027e-01 2 23 900002 # 1.30386746059
      2.908103e-01 2 25 900004 # 0.535333412477
      7.487368e-04 3 -24 24 900004 # 0.0013782999285
      7.996376e-05 3 -24 24 900002 # 0.000147199995225
      6.483572e-06 2 14 16 # 1.19351782282e-05
      6.483572e-06 2 12 16 # 1.19351782282e-05
      6.483572e-06 2 12 14 # 1.19351782282e-05
      6.483572e-06 2 -14 -12 # 1.19351782282e-05
      6.483572e-06 2 -16 -12 # 1.19351782282e-05
      6.483572e-06 2 -16 -14 # 1.19351782282e-05
      3.241786e-06 2 16 16 # 5.96758911409e-06
      3.241786e-06 2 14 14 # 5.96758911409e-06
      3.241786e-06 2 12 12 # 5.96758911409e-06
      3.241786e-06 2 -12 -12 # 5.96758911409e-06
      3.241786e-06 2 -14 -14 # 5.96758911409e-06
      3.241786e-06 2 -16 -16 # 5.96758911409e-06

DECAY 900004 1.328683e-06 #
      1.111111e-01 2 14 16 # 1.47631402772e-07
      1.111111e-01 2 12 16 # 1.47631402772e-07
      1.111111e-01 2 12 14 # 1.47631402772e-07
      1.111111e-01 2 -14 -12 # 1.47631402772e-07
      1.111111e-01 2 -16 -12 # 1.47631402772e-07
      1.111111e-01 2 -16 -14 # 1.47631402772e-07
      5.555556e-02 2 16 16 # 7.3815701386e-08
      5.555556e-02 2 14 14 # 7.3815701386e-08
      5.555556e-02 2 12 12 # 7.3815701386e-08
      5.555556e-02 2 -12 -12 # 7.3815701386e-08
      5.555556e-02 2 -14 -14 # 7.3815701386e-08
      5.555556e-02 2 -16 -16 # 7.3815701386e-08

DECAY 900005 1.785203e+00 #
      4.999667e-01 2 24 900004 # 0.892542231505
      4.999667e-01 2 24 900002 # 0.892542231505
      7.404708e-06 2 -12 -11 # 1.3218910688e-05
      7.404708e-06 2 -14 -11 # 1.3218910688e-05
      7.404708e-06 2 -16 -11 # 1.3218910688e-05
      7.404708e-06 2 -13 -12 # 1.3218910688e-05
      7.404708e-06 2 -14 -13 # 1.3218910688e-05
      7.404708e-06 2 -16 -13 # 1.3218910688e-05
      7.404285e-06 2 -15 -12 # 1.32181543373e-05
      7.404285e-06 2 -15 -14 # 1.32181543373e-05
      7.404285e-06 2 -16 -15 # 1.32181543373e-05

DECAY 900006 7.579056e-04 #
      3.999707e-01 3 24 24 900004 # 0.000303140010266
      3.983214e-01 3 24 24 900002 # 0.000301889994817
      3.720068e-02 2 -13 -11 # 2.81946056995e-05
      3.719881e-02 2 -15 -11 # 2.81931872508e-05
      3.719881e-02 2 -15 -13 # 2.81931872508e-05
      1.860034e-02 2 -11 -11 # 1.40973028497e-05
      1.860034e-02 2 -13 -13 # 1.40973028497e-05
      1.859847e-02 2 -15 -15 # 1.4095884401e-05
      1.143546e-02 3 -1 2 900005 # 8.66700094986e-06
      1.143546e-02 3 -3 4 900005 # 8.66700094986e-06
      3.870007e-03 3 -11 12 900005 # 2.9331001347e-06
      3.836757e-03 3 -13 14 900005 # 2.90789978792e-06
      3.732787e-03 3 -15 16 900005 # 2.82910003571e-06
</slha>
<MGGenerationInfo>
# Number of Events : 10000
# Integrated weight (pb) : 0.0023209
</MGGenerationInfo>
</header>
</LesHouchesEvents>

Question information

Language:
English Edit question
Status:
Answered
For:
MadGraph5_aMC@NLO Edit question
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Last query:
2020-08-26
Last reply:
2020-09-03

Hi,

You will have all the details of the description of the Auto algorithm in the associate paper obviously:
1402.1178

You will notice that for three body decay you have the same phase-space integrator as of the standard madevent but that you have a different Feynman Diagram generator. Indeed in general using "generate A > X Y Z " is not the correct syntax in order to get the correct partial-width.

So I would suggest to compare the Feynman diagram generated by
generate delta++ > w+ w+ h3
from the one generated for the auto command
"decay_diagram delta++"
After each of those command you can do "display diagrams" and/or "output;launch" to create the fortran code and launch the phase-space integration

Cheers,

Olivier

Han Qin (qh7053) said : #2

Hi Olivier,

Thank you very much for your reply!

I tried the command "decay_diagram delta++", it only gave me 2-body decay diagrams so it didn't help too much.

You said "in general using 'generate A > X Y Z ' is not the correct syntax in order to get the correct partial-width". If I understand it correctly, it's because cascade-decay diagrams might be included, am I right?

In our case, however, delta++ > w+ w+ h3 contains 3 diagrams ( it's also what I got by using "generate" command), one is a contact diagram, the other two are similar to the right-most diagram in Figure 1 of 1402.1178: an off-shell h+ propagates from delta++ to w+ and h3. According to 1402.1178, all three diagrams are not considered as cascade decays. Therefore I expect that the Auto computation and the command "generate delta++ > w+ w+ h3" would produce same result. But it turns out these two methods differed by an order of magnitude.

could you please help me figure out why this happens? If I want to get the correct partial width of "delta++ > w+ w+ h3", what method shall I use?

Thank you very much for your help!

Is your model public? If it is I could look at the model directly.

> I tried the command "decay_diagram delta++", it only gave me 2-body decay diagrams so it didn't help too much.

Well it means that they are filter out because they are consider as irrelevant.
you can try to do
decay_diagram delta++ --body_decay=3
To force to include all three-body decay even if the first/second estimator consider them as irrelevant.

Cheers,

Olivier

Thanks for the model,

So indeed the diagram was wrongly discarded.
You will find the patch/link to a full tarball/... here:
https://bazaar.launchpad.net/~mg5core1/mg5amcnlo/2.8.1/revision/292

Cheers,

Olivier

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