MadGraph5_aMC@NLO

Virtual Corrections of top, bottom quarks in w w > h h

Asked by Samuel Homiller

(This is a refined version of question 704489)

Hi, I am attempting to compute the effects of heavy fermions arising in loops contributing to w+ w- > h h production, with the (top, bottom) pair as an example in the Standard Model. My understanding is that this is probably impossible to do beyond a fixed-order calculation, or interfacing with lepton PDFs, but I am happy with only the calculation of the matrix element for now, using the [virt=QED] syntax.

In that spirit, I have tried running
> import loop_qcd_qed_sm
> generate w+ w- > h h [virt=QED]
> output
> launch

This runs, but naturally includes a number of diagrams I am not interested in, and gives me a single pole, which I assume is an IR divergence due to the loops involving massless photons, since I don't include any corresponding real emissions.

I understand from Olivier's answer here (https://bugs.launchpad.net/mg5amcnlo/+bug/2003606) that I could try to isolate the top and bottom quark loops using the loop-filtering options. My worry in that case is that I will get a UV pole because the counterterms for the SM are computed assuming all the fermions running in the loop, while the virtual corrections are selecting out only the top and bottom quark (please let me know if I have misunderstood, and this is not the case).

As a workaround, I created a UFO model for the SM with all the fermions except the top and bottom quark removed, and added a new coupling (equal to 1) with order 'NP'=1 to all the t, b interactions, so that I can consistently ask for all the loop corrections involving the top and bottom in a gauge invariant way. I can then run,

> import model SM-TBonly
> generate w+ w- > h h QED<=4 NP<=4 [virt=NP]
> output
> launch

which, as far as I can tell, generates all the relevant virtual diagrams, and should have the correct UV countqerterms, since these were computed directly for this model (with only the t, b quarks), and should only include the relevant countqerterms (those involving the top, bottom, and not, e.g., loops of electroweak bosons) since I ask for virt=NP, and not virt=QED.

Unfortunately, this still leads to a single pole from the virtual corrections. (I've attached the output of running ./check in SubProcesses/P0_wpwm_hh below). I suppose it is possible there is a bug in my computation of the UV counterterms, but I wanted to ensure there are no other potential sources of this pole. There are no diagrams involving massless particles, so there should be no IR divergence. Have I understood what the [virt=NP] syntax does, as far as using the counterterms that have the correct NP coupling order, and not including all the virtual corrections to the propagators/vertices?

If there is in fact an error in my counterterm computations, it would be useful to try and compute loop amplitudes with a smaller number of external particles to check that there are no poles there. Is this possible with MadLoop? (e.g., can I compute w+ w- > h, with an unphysical set of four-momenta, and see if this vertex is renormalized properly?)

Apologies for the long, multi-part question, but thanks for any help you can provide.

Question information

Language:
English Edit question
Status:
Answered
For:
MadGraph5_aMC@NLO Edit question
Assignee:
Valentin Hirschi Edit question
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Last reply:
Revision history for this message
Samuel Homiller (shomiller) said : 		#1

Here is a link to a tarball for the SM-TBonly model file, including the counterterms:
https://www.dropbox.com/s/k7s8o9lb7ev3p76/SM-TBonly.tar.gz?dl=0

The output of ./check referenced above is copied below:

----

 AO2PI= 1.8843945262080407E-002
 *****************************************************
 * MadGraph/MadEvent *
 * -------------------------------- *
 * http://madgraph.hep.uiuc.edu *
 * http://madgraph.phys.ucl.ac.be *
 * http://madgraph.roma2.infn.it *
 * -------------------------------- *
 * *
 * PARAMETER AND COUPLING VALUES *
 * *
 *****************************************************

  External Params
  ---------------------------------

 MU_R = 91.188000000000002
 aEWM1 = 127.90000000000001
 mdl_Gf = 1.1663700000000000E-005
 aS = 0.11839999999999999
 mdl_ymb = 4.7000000000000002
 mdl_ymt = 172.00000000000000
 mdl_MZ = 91.187600000000003
 mdl_MT = 172.00000000000000
 mdl_MB = 4.7000000000000002
 mdl_MH = 125.00000000000000
 mdl_WZ = 2.4952000000000001
 mdl_WW = 2.0850000000000000
 mdl_WT = 1.5083359999999999
 mdl_WH = 4.0699999999999998E-003
  Internal Params
  ---------------------------------

 mdl_tbflag = 1.0000000000000000
 mdl_MZ__exp__2 = 8315.1783937600012
 mdl_MZ__exp__4 = 69142191.720053151
 mdl_sqrt__2 = 1.4142135623730951
 mdl_MH__exp__2 = 15625.000000000000
 mdl_complexi = (0.0000000000000000,1.0000000000000000)
 mdl_tbflag__exp__4 = 1.0000000000000000
 mdl_tbflag__exp__2 = 1.0000000000000000
 mdl_tbflag__exp__3 = 1.0000000000000000
 mdl_MB__exp__2 = 22.090000000000003
 mdl_MT__exp__2 = 29584.000000000000
 mdl_MB__exp__3 = 103.82300000000002
 mdl_MT__exp__3 = 5088448.0000000000
 mdl_aEW = 7.8186082877247844E-003
 mdl_MW = 79.824359746197842
 mdl_sqrt__aEW = 8.8422894590285753E-002
 mdl_ee = 0.31345100004952897
 mdl_MW__exp__2 = 6371.9284088904105
 mdl_sw2 = 0.23369913342182447
 mdl_cw = 0.87538612427783857
 mdl_sqrt__sw2 = 0.48342438232036300
 mdl_sw = 0.48342438232036300
 mdl_g1 = 0.35807170271074895
 mdl_gw = 0.64839716719502682
 mdl_vev = 246.22056907348590
 mdl_vev__exp__2 = 60624.568634871241
 mdl_lam = 0.12886689630821144
 mdl_yb = 2.6995322804122722E-002
 mdl_yt = 0.98791394091683138
 mdl_muH = 88.388347648318444
 mdl_ee__exp__2 = 9.8251529432049817E-002
 mdl_sw__exp__2 = 0.23369913342182450
 mdl_cw__exp__2 = 0.76630086657817542
 mdl_ee__exp__4 = 9.6533630357369515E-003
 mdl_cw__exp__3 = 0.67080914562461802
 mdl_sw__exp__3 = 0.11297585922324961
 mdl_cw__exp__4 = 0.58721701811846261
 mdl_sw__exp__4 = 5.4615284962111724E-002
 mdl_ee__exp__3 = 3.0797040156871746E-002
 mdl_yb__exp__2 = (7.28747453298788229E-004,0.0000000000000000)
 mdl_yt__exp__2 = (0.97597395465782455,0.0000000000000000)
 mdl_yb__exp__4 = (5.31072850689469538E-007,0.0000000000000000)
 mdl_yt__exp__4 = (0.95252516017043332,0.0000000000000000)
 mdl_yb__exp__3 = (1.96727727444831350E-005,0.0000000000000000)
 mdl_yt__exp__3 = (0.96417827577819637,0.0000000000000000)
 mdl_lam__exp__2 = 1.6606676964111319E-002
  Internal Params evaluated point by point
  ----------------------------------------

 mdl_sqrt__aS = 0.34409301068170506
 mdl_G__exp__2 = 1.4878582807401259
 mdl_G__exp__4 = 2.2137222635669636
 mdl_G__exp__3 = 1.8148567439626970
  Couplings of SM-TBonly_NLO_full_UFO
  ---------------------------------

         GC_1 = -0.00000E+00 -0.31345E+00
        GC_14 = 0.00000E+00 0.21021E+00
        GC_19 = -0.32420E+00 0.00000E+00
         GC_2 = 0.00000E+00 0.31345E+00
        GC_22 = 0.32420E+00 0.00000E+00
        GC_23 = -0.00000E+00 -0.56760E+00
        GC_24 = 0.00000E+00 0.56760E+00
        GC_37 = -0.00000E+00 -0.10448E+00
        GC_38 = 0.00000E+00 0.20897E+00
        GC_40 = 0.00000E+00 0.45849E+00
        GC_41 = 0.00000E+00 0.57700E-01
        GC_42 = -0.00000E+00 -0.11540E+00
        GC_43 = -0.00000E+00 -0.31265E+00
        GC_44 = 0.00000E+00 0.25495E+00
        GC_48 = -0.00000E+00 -0.19038E+03
        GC_51 = 0.00000E+00 0.51758E+02
        GC_61 = -0.26995E-01 0.00000E+00
        GC_62 = 0.26995E-01 0.00000E+00
        GC_63 = -0.00000E+00 -0.19089E-01
        GC_65 = -0.98791E+00 0.00000E+00
        GC_66 = 0.98791E+00 0.00000E+00
        GC_68 = -0.00000E+00 -0.69856E+00
  R2GC_144_71 = 0.00000E+00 0.13312E-02
 R2GC_162_117 = -0.00000E+00 -0.46148E-05
 R2GC_162_118 = -0.00000E+00 -0.61804E-02
 R2GC_164_121 = 0.00000E+00 0.61165E-03
 R2GC_164_122 = 0.00000E+00 0.10971E+04
 R2GC_166_133 = 0.00000E+00 0.74525E-05
 R2GC_166_134 = 0.00000E+00 0.13367E+02
 R2GC_167_140 = -0.00000E+00 -0.61850E-02
 R2GC_191_177 = -0.00000E+00 -0.11823E+03
 R2GC_192_182 = 0.00000E+00 0.54934E+03
 R2GC_230_332 = -0.00000E+00 -0.52006E-02
 R2GC_231_341 = 0.40104E-02 0.00000E+00
 R2GC_232_348 = -0.40104E-02 -0.00000E+00
 R2GC_235_372 = -0.00000E+00 -0.96037E+00
 UVGC_162_157_1e 0.13845E-04 0.00000E+00
 UVGC_162_158_1e 0.18541E-01 0.00000E+00
 UVGC_164_163_1e -0.18350E-02 0.00000E+00
 UVGC_164_169_1e -0.32912E+04 0.00000E+00
 UVGC_166_183_1e -0.14905E-04 0.00000E+00
 UVGC_166_187_1e -0.26733E+02 0.00000E+00
 UVGC_167_193_1e 0.18555E-01 0.00000E+00
 UVGC_179_233_1e -0.26623E-02 0.00000E+00
 UVGC_191_283_1e 0.11823E+03 0.00000E+00
 UVGC_192_296_1e -0.10971E+04 0.00000E+00
 UVGC_230_549_1e 0.39005E-02 0.00000E+00
 UVGC_231_564_1e 0.00000E+00 0.60155E-02
 UVGC_232_573_1e -0.00000E+00 -0.60155E-02
 UVGC_235_604_1e 0.96037E+00 0.00000E+00
  ==========================================================================================
 { }
 {   }
 {  ,,  }
 { `7MMM. ,MMF' `7MM `7MMF'  }
 {  MMMb dPMM MM MM  }
 {  M YM ,M MM ,6"Yb. ,M""bMM MM ,pW"Wq. ,pW"Wq.`7MMpdMAo.  }
 {  M Mb M' MM 8) MM ,AP MM MM 6W' `Wb 6W' `Wb MM `Wb  }
 {  M YM.P' MM ,pm9MM 8MI MM MM , 8M M8 8M M8 MM M8  }
 {  M `YM' MM 8M MM `Mb MM MM ,M YA. ,A9 YA. ,A9 MM ,AP  }
 { .JML. `' .JMML.`Moo9^Yo.`Wbmd"MML..JMMmmmmMMM `Ybmd9' `Ybmd9' MMbmmd'  }
 {  MM  }
 {  .JMML.  }
 { v3.4.2 (2023-01-20), Ref: arXiv:1103.0621v2, arXiv:1405.0301  }
 {   }
 { }
  ==========================================================================================
 ===============================================================
 INFO: MadLoop read these parameters from ./MadLoop5_resources/MadLoopParams.dat

  +----------------------------------------------------------------+
  | |
  | Ninja - version 1.1.0 |
  | |
  | Author: Tiziano Peraro |
  | |
  | Based on: |
  | |
  | P. Mastrolia, E. Mirabella and T. Peraro, |
  | "Integrand reduction of one-loop scattering amplitudes |
  | through Laurent series expansion," |
  | JHEP 1206 (2012) 095 [arXiv:1203.0291 [hep-ph]]. |
  | |
  | T. Peraro, |
  | "Ninja: Automated Integrand Reduction via Laurent |
  | Expansion for One-Loop Amplitudes," |
  | Comput.Phys.Commun. 185 (2014) [arXiv:1403.1229 [hep-ph]] |
  | |
  +----------------------------------------------------------------+

 ===============================================================
  > MLReductionLib = 6|7|1
  > CTModeRun = -1
  > MLStabThres = 1.0000000000000000E-003
  > NRotations_DP = 0
  > NRotations_QP = 0
  > CTStabThres = 1.0000000000000000E-002
  > CTLoopLibrary = 2
  > CTModeInit = 1
  > CheckCycle = 3
  > MaxAttempts = 10
  > UseLoopFilter = F
  > HelicityFilterLevel = 2
  > ImprovePSPoint = 2
  > DoubleCheckHelicityFilter = T
  > LoopInitStartOver = F
  > HelInitStartOver = F
  > ZeroThres = 1.0000000000000001E-009
  > OSThres = 1.0000000000000000E-013
  > WriteOutFilters = T
  > UseQPIntegrandForNinja = T
  > UseQPIntegrandForCutTools = T
  > IREGIMODE = 2
  > IREGIRECY = T
  > COLLIERMode = 1
  > COLLIERRequiredAccuracy = 1.0000000000000000E-008
  > COLLIERCanOutput = F
  > COLLIERComputeUVpoles = T
  > COLLIERComputeIRpoles = T
  > COLLIERGlobalCache = -1
  > COLLIERUseCacheForPoles = F
  > COLLIERUseInternalStabilityTest = T
 ===============================================================
 INFO:: Attempting to rescue the precision improvement with an alternative method.

------------------------------------------------------------------------
| You are using CutTools - Version 1.9.3 |
| Authors: G. Ossola, C. Papadopoulos, R. Pittau |
| Published in JHEP 0803:042,2008 |
| http://www.ugr.es/~pittau/CutTools |
| |
| Compiler with 34 significant digits detetected |
  ----------------------------------------------------------------------

########################################################################
# #
# You are using OneLOop-3.6 #
# #
# for the evaluation of 1-loop scalar 1-, 2-, 3- and 4-point functions #
# #
# author: Andreas van Hameren <email address hidden> #
# date: 18-02-2015 #
# #
# Please cite #
# A. van Hameren, #
# Comput.Phys.Commun. 182 (2011) 2427-2438, arXiv:1007.4716 #
# A. van Hameren, C.G. Papadopoulos and R. Pittau, #
# JHEP 0909:106,2009, arXiv:0903.4665 #
# in publications with results obtained with the help of this program. #
# #
########################################################################
########################################################################
# #
# You are using OneLOop-3.6 #
# #
# for the evaluation of 1-loop scalar 1-, 2-, 3- and 4-point functions #
# #
# author: Andreas van Hameren <email address hidden> #
# date: 18-02-2015 #
# #
# Please cite #
# A. van Hameren, #
# Comput.Phys.Commun. 182 (2011) 2427-2438, arXiv:1007.4716 #
# A. van Hameren, C.G. Papadopoulos and R. Pittau, #
# JHEP 0909:106,2009, arXiv:0903.4665 #
# in publications with results obtained with the help of this program. #
# #
########################################################################

  Phase space point:

 ---------------------------------
 n E px py pz m
 1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.4935869E+03 0.7982436E+02
 2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.4935869E+03 0.7982436E+02
 3 0.5000000E+03 0.1074020E+03 0.4307056E+03 -0.1932163E+03 0.1250000E+03
 4 0.5000000E+03 -0.1074020E+03 -0.4307056E+03 0.1932163E+03 0.1250000E+03
 ---------------------------------
 Detailed result for each coupling orders combination.
 All Born contributions are of split orders (NP=0)
 ---------------------------------
 1L) Loop ME for orders (NP=2) :
  > accuracy = NA
  > finite = 4.6427737704485272E-002
  > 1eps = -2.0654569568568551E-002
  > 2eps = 0.0000000000000000
 2L) Loop ME for orders (NP=3) :
  > accuracy = NA
  > finite = -9.7965963944467369E-002
  > 1eps = 3.2208352390475939E-002
  > 2eps = 0.0000000000000000
 3L) Loop ME for orders (NP=4) :
  > accuracy = NA
  > finite = 5.8402985767897847E-002
  > 1eps = -1.8157098355789471E-002
  > 2eps = 0.0000000000000000
 ---------------------------------
 Unknown numerical stability because MadLoop is in the initialization stage.
 MadLoop return code = 130
 ---------------------------------
 ---------------------------------
 Matrix element born = 2.1191960886792802E-002 GeV^ 0
 Matrix element finite = 6.8647595279157508E-003 GeV^ 0
 Matrix element 1eps = -6.6033155338820829E-003 GeV^ 0
 Matrix element 2eps = 0.0000000000000000 GeV^ 0
 ---------------------------------
 finite / (born*ao2pi) = 17.190256255572525
 1eps / (born*ao2pi) = -16.535566279085661
 2eps / (born*ao2pi) = 0.0000000000000000
 ---------------------------------

Revision history for this message
Samuel Homiller (shomiller) said : 		#3

Hi,

Thanks for the feedback -- it sounds like that is indeed exactly what I should try. I have one immediate follow-up question: is there any way to select/filter which counterterm/R2 vertices are included in the calculation in a similar manner?

For instance, I can see in CT_vertices.py that each vertex includes a 'loop_particles=' field. Is this used anywhere? I'm wondering if there is any way to include only the relevant counterterms in any consistent manner, without having to add a new coupling with a different coupling order definition by hand.

Thanks for any help!

Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said : 		#4

Olivier Mattelaer suggests this article as an answer to your question:
FAQ #3328: “How to select of subset of the loop for the computation”.

Can you help with this problem?

Provide an answer of your own, or ask Samuel Homiller for more information if necessary.

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