NLO fixed-order calculation of p p > e+ e- with leptoquarks does not converge for high mll

Asked by Luc Schnell

Hello MadGraph team

I am trying to compute the cross section of p p > e+ e- at high invariant electron masses mll with contributions from leptoquarks and using fixed-order NLO. The computation works for small mll = 200. However, when I put mll = 1'250 or larger, the computation stalls after a few steps when setting up the grids. I increased req_acc_fo to 0.1, but this did not change anything. I also tried putting req_acc_fo = -1.0 and npoints_fo_grid = 5'000'000, npoints_fo = 5'000'000, but then the result I obtain is two orders of magnitude too large.

At LO I also got inconsistent results for the high-mll tail at first, which I could resolve by increasing max_events = 50'000'000 in Source/dsample.f. Is there a similar variable for fixed-order NLO calculations that might resolve my issues?

Or is there another way to simulate the high-mll tail of p p > e+ e- at NLO?

Thank you for your help!
Cheers,
Luc

Question information

Language:
English Edit question
Status:
Solved
For:
MadGraph5_aMC@NLO Edit question
Assignee:
marco zaro Edit question
Solved by:
marco zaro
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Last reply:
Revision history for this message
marco zaro (marco-zaro) said :
#1

Dear Luc,
could you please tell me where to find the model you use, the exact version of the code, the syntax and any parameter you change from the default?

Thanks!

cheers.

Marco

Revision history for this message
Luc Schnell (lucschnell) said :
#2

Hi Marco

Of course, sorry that I didn't provide this information in the first place. I took the NLO leptoquark model from:

https://www.uni-muenster.de/Physik.TP/~akule_01/nnllfast/lib/exe/fetch.php?media=lqnlo_v5.ufo.tar.gz

together with the following restrict card that only allows the couplings I am interested in (3rd generation couplings of the R2 leptoquark):

######################################################################
## PARAM_CARD AUTOMATICALY GENERATED BY THE UFO #####################
######################################################################

###################################
## INFORMATION FOR SMINPUTS
###################################
Block SMINPUTS
    1 1.279000e+02 # aEWM1
    2 1.166370e-05 # Gf
    3 1.184000e-01 # aS

###################################
## INFORMATION FOR MASS
###################################
Block MASS
    5 0.00000 # MB
    6 1.720000e+02 # MT
   15 1.777000e+00 # MTA
   23 9.118760e+01 # MZ
   25 1.250000e+02 # MH
  6000042 1.000000e+09 # MS1
  6001242 1.000000e+09 # MS3
  6100242 1.000000e+03 # MR2
## Not dependent paramater.
## Those values should be edited following analytical the
## analytical expression. Some generator could simply ignore
## those values and use the analytical expression
  22 0.000000 # a : 0.0
  24 79.824360 # W+ : cmath.sqrt(MZ**2/2. + cmath.sqrt(MZ**4/4. - (aEW*cmath.pi*MZ**2)/(Gf*cmath.sqrt(2))))
  21 0.000000 # g : 0.0
  9000001 0.000000 # ghA : 0.0
  9000003 79.824360 # ghWp : cmath.sqrt(MZ**2/2. + cmath.sqrt(MZ**4/4. - (aEW*cmath.pi*MZ**2)/(Gf*cmath.sqrt(2))))
  9000004 79.824360 # ghWm : cmath.sqrt(MZ**2/2. + cmath.sqrt(MZ**4/4. - (aEW*cmath.pi*MZ**2)/(Gf*cmath.sqrt(2))))
  82 0.000000 # ghG : 0.0
  12 0.000000 # ve : 0.0
  14 0.000000 # vm : 0.0
  16 0.000000 # vt : 0.0
  11 0.000000 # e- : 0.0
  13 0.000000 # mu- : 0.0
  2 0.000000 # u : 0.0
  4 0.000000 # c : 0.0
  1 0.000000 # d : 0.0
  3 0.000000 # s : 0.0
  251 79.824360 # G+ : cmath.sqrt(MZ**2/2. + cmath.sqrt(MZ**4/4. - (aEW*cmath.pi*MZ**2)/(Gf*cmath.sqrt(2))))
  9000002 91.187600 # ghZ : MZ
  250 91.187600 # G0 : MZ
  42 1.000000e+09 # LQ1d : MS1
  6000142 1.000000e+03 # LQ2uu : MR2
  6000242 1.000000e+03 # LQ2u : MR2
  6100142 1.000000e+09 # LQ2pu : MR2
  6001042 1.000000e+09 # LQ3u : MS3
  6001142 1.000000e+09 # LQ3d : MS3

###################################
## INFORMATION FOR DECAY
###################################
DECAY 6 1.508336e+00
DECAY 23 2.495200e+00
DECAY 24 2.085000e+00
DECAY 25 4.070000e-03
DECAY 42 1.000000e+01
DECAY 6000042 1.010000e+01
DECAY 6000142 1.100000e+01
DECAY 6000242 1.110000e+01
DECAY 6001042 1.210000e+01
DECAY 6001142 1.220000e+01
DECAY 6001242 1.230000e+01
DECAY 6100142 1.120000e+01
DECAY 6100242 1.130000e+01
## Not dependent paramater.
## Those values should be edited following analytical the
## analytical expression. Some generator could simply ignore
## those values and use the analytical expression
DECAY 22 0.000000 # a : 0.0
DECAY 21 0.000000 # g : 0.0
DECAY 9000001 0.000000 # ghA : 0.0
DECAY 82 0.000000 # ghG : 0.0
DECAY 12 0.000000 # ve : 0.0
DECAY 14 0.000000 # vm : 0.0
DECAY 16 0.000000 # vt : 0.0
DECAY 11 0.000000 # e- : 0.0
DECAY 13 0.000000 # mu- : 0.0
DECAY 15 0.000000 # ta- : 0.0
DECAY 2 0.000000 # u : 0.0
DECAY 4 0.000000 # c : 0.0
DECAY 1 0.000000 # d : 0.0
DECAY 3 0.000000 # s : 0.0
DECAY 5 0.000000 # b : 0.0
DECAY 9000002 2.495200 # ghZ : WZ
DECAY 9000003 2.085000 # ghWp : WW
DECAY 9000004 2.085000 # ghWm : WW
DECAY 250 2.495200 # G0 : WZ
DECAY 251 2.085000 # G+ : WW

###################################
## INFORMATION FOR IMLQTY1RR
###################################
Block IMLQTY1RR
    1 1 0.0000e-02 # Ity1RR1x1
    1 2 0.0000e-02 # Ity1RR1x2
    1 3 0.0000e-02 # Ity1RR1x3
    2 1 0.0000e-02 # Ity1RR2x1
    2 2 0.0000e-02 # Ity1RR2x2
    2 3 0.0000e-02 # Ity1RR2x3
    3 1 0.0000e-02 # Ity1RR3x1
    3 2 0.0000e-02 # Ity1RR3x2
    3 3 0.0000e-02 # Ity1RR3x3

###################################
## INFORMATION FOR IMLQTY2RL
###################################
Block IMLQTY2RL
    1 1 0.0000e-02 # Ity2RL1x1
    1 2 0.0000e-02 # Ity2RL1x2
    1 3 0.0000e-02 # Ity2RL1x3
    2 1 0.0000e-02 # Ity2RL2x1
    2 2 0.0000e-02 # Ity2RL2x2
    2 3 0.0000e-02 # Ity2RL2x3
    3 1 0.0000e-02 # Ity2RL3x1
    3 2 0.0000e-02 # Ity2RL3x2
    3 3 0.0000e-02 # Ity2RL3x3

###################################
## INFORMATION FOR IMLQY1LL
###################################
Block IMLQY1LL
    1 1 0.0000e-02 # Iy1LL1x1
    1 2 0.0000e-02 # Iy1LL1x2
    1 3 0.0000e-02 # Iy1LL1x3
    2 1 0.0000e-02 # Iy1LL2x1
    2 2 0.0000e-02 # Iy1LL2x2
    2 3 0.0000e-02 # Iy1LL2x3
    3 1 0.0000e-02 # Iy1LL3x1
    3 2 0.0000e-02 # Iy1LL3x2
    3 3 0.0000e-02 # Iy1LL3x3

###################################
## INFORMATION FOR IMLQY1RR
###################################
Block IMLQY1RR
    1 1 0.0000e-02 # Iy1RR1x1
    1 2 0.0000e-02 # Iy1RR1x2
    1 3 0.0000e-02 # Iy1RR1x3
    2 1 0.0000e-02 # Iy1RR2x1
    2 2 0.0000e-02 # Iy1RR2x2
    2 3 0.0000e-02 # Iy1RR2x3
    3 1 0.0000e-02 # Iy1RR3x1
    3 2 0.0000e-02 # Iy1RR3x2
    3 3 0.0000e-02 # Iy1RR3x3

###################################
## INFORMATION FOR IMLQY2LR
###################################
Block IMLQY2LR
    1 1 0.0000e-02 # Iy2LR1x1
    1 2 0.0000e-02 # Iy2LR1x2
    1 3 0.0000e-02 # Iy2LR1x3
    2 1 0.0000e-00 # Iy2LR2x1
    2 2 0.0000e-02 # Iy2LR2x2
    2 3 0.0000e-02 # Iy2LR2x3
    3 1 0.0000e-00 # Iy2LR3x1
    3 2 0.0000e-02 # Iy2LR3x2
    3 3 0.0000e-00 # Iy2LR3x3

###################################
## INFORMATION FOR IMLQY2RL
###################################
Block IMLQY2RL
    1 1 0.0000e-02 # Iy2RL1x1
    1 2 0.0000e-02 # Iy2RL1x2
    1 3 0.0000e-02 # Iy2RL1x3
    2 1 0.0000e-02 # Iy2RL2x1
    2 2 0.0000e-02 # Iy2RL2x2
    2 3 0.0000e-00 # Iy2RL2x3
    3 1 0.0000e-02 # Iy2RL3x1
    3 2 0.0000e-02 # Iy2RL3x2
    3 3 0.0000e-02 # Iy2RL3x3

###################################
## INFORMATION FOR IMLQY3LL
###################################
Block IMLQY3LL
    1 1 0.0000e-02 # Iy3LL1x1
    1 2 0.0000e-02 # Iy3LL1x2
    1 3 0.0000e-02 # Iy3LL1x3
    2 1 0.0000e-02 # Iy3LL2x1
    2 2 0.0000e-02 # Iy3LL2x2
    2 3 0.0000e-02 # Iy3LL2x3
    3 1 0.0000e-02 # Iy3LL3x1
    3 2 0.0000e-02 # Iy3LL3x2
    3 3 0.0000e-02 # Iy3LL3x3

###################################
## INFORMATION FOR LOOP
###################################
Block LOOP
    1 9.118800e+01 # MU_R

###################################
## INFORMATION FOR LQTY1RR
###################################
Block LQTY1RR
    1 1 0.0000e-01 # Rty1RR1x1
    1 2 0.0000e-01 # Rty1RR1x2
    1 3 0.0000e-01 # Rty1RR1x3
    2 1 0.0000e-01 # Rty1RR2x1
    2 2 0.0000e-01 # Rty1RR2x2
    2 3 0.0000e-01 # Rty1RR2x3
    3 1 0.0000e-01 # Rty1RR3x1
    3 2 0.0000e-01 # Rty1RR3x2
    3 3 0.0000e-01 # Rty1RR3x3

###################################
## INFORMATION FOR LQTY2RL
###################################
Block LQTY2RL
    1 1 0.0000e-01 # Rty2RL1x1
    1 2 0.0000e-01 # Rty2RL1x2
    1 3 0.0000e-01 # Rty2RL1x3
    2 1 0.0000e-01 # Rty2RL2x1
    2 2 0.0000e-01 # Rty2RL2x2
    2 3 0.0000e-00 # Ry2RL2x3
    3 1 0.0000e-01 # Rty2RL3x1
    3 2 0.0000e-01 # Rty2RL3x2
    3 3 0.0000e-01 # Rty2RL3x3

###################################
## INFORMATION FOR LQY1LL
###################################
Block LQY1LL
    1 1 0.0000e-01 # Ry1LL1x1
    1 2 0.0000e-01 # Ry1LL1x2
    1 3 0.0000e-01 # Ry1LL1x3
    2 1 0.0000e-01 # Ry1LL2x1
    2 2 0.0000e-01 # Ry1LL2x2
    2 3 0.0000e-01 # Ry1LL2x3
    3 1 0.0000e-01 # Ry1LL3x1
    3 2 0.0000e-01 # Ry1LL3x2
    3 3 0.0000e-01 # Ry1LL3x3

###################################
## INFORMATION FOR LQY1RR
###################################
Block LQY1RR
    1 1 0.0000e-01 # Ry1RR1x1
    1 2 0.0000e-01 # Ry1RR1x2
    1 3 0.0000e-01 # Ry1RR1x3
    2 1 0.0000e-01 # Ry1RR2x1
    2 2 0.0000e-01 # Ry1RR2x2
    2 3 0.0000e-01 # Ry1RR2x3
    3 1 0.0000e-01 # Ry1RR3x1
    3 2 0.0000e-01 # Ry1RR3x2
    3 3 0.0000e-01 # Ry1RR3x3

###################################
## INFORMATION FOR LQY2LR
###################################
Block LQY2LR
    1 1 0.0000e-01 # Ry2LR1x1
    1 2 0.0000e-01 # Ry2LR1x2
    1 3 0.0000e-01 # Ry2LR1x3
    2 1 0.0000e-00 # Ry2LR2x1
    2 2 0.0000e-01 # Ry2LR2x2
    2 3 0.0000e-01 # Ry2LR2x3
    3 1 0.0000e-01 # Ry2LR3x1
    3 2 2.0000e+00 # Ry2LR3x2
    3 3 0.0000e-01 # Ry2LR3x3

###################################
## INFORMATION FOR LQY2RL
###################################
Block LQY2RL
    1 1 0.0000e+00 # Ry2RL1x1
    1 2 0.0000e-01 # Ry2RL1x2
    1 3 0.0000e-01 # Ry2RL1x3
    2 1 0.0000e-01 # Ry2RL2x1
    2 2 0.0000e-01 # Ry2RL2x2
    2 3 0.0000e-01 # Ry2RL2x3
    3 1 0.0000e-01 # Ry2RL3x1
    3 2 0.0000e+00 # Ry2RL3x2
    3 3 0.0000e-01 # Ry2RL3x3

###################################
## INFORMATION FOR LQY3LL
###################################
Block LQY3LL
    1 1 0.0000e-01 # Ry3LL1x1
    1 2 0.0000e-01 # Ry3LL1x2
    1 3 0.0000e-01 # Ry3LL1x3
    2 1 0.0000e-01 # Ry3LL2x1
    2 2 0.0000e-01 # Ry3LL2x2
    2 3 0.0000e-01 # Ry3LL2x3
    3 1 0.0000e-01 # Ry3LL3x1
    3 2 0.0000e-01 # Ry3LL3x2
    3 3 0.0000e-01 # Ry3LL3x3

###################################
## INFORMATION FOR YUKAWA
###################################
Block YUKAWA
    6 1.720000e+02 # ymt
   15 1.777000e+00 # ymtau
#===========================================================
# QUANTUM NUMBERS OF NEW STATE(S) (NON SM PDG CODE)
#===========================================================

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)
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)
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)
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)
Block QNUMBERS 82 # 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)
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)
Block QNUMBERS 42 # LQ1d
        1 -1 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6000042 # LQ1dd
        1 -4 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6000142 # LQ2uu
        1 5 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6000242 # LQ2u
        1 2 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6100142 # LQ2pu
        1 2 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6100242 # LQ2d
        1 -1 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6001042 # LQ3u
        1 2 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6001142 # LQ3d
        1 -1 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)
Block QNUMBERS 6001242 # LQ3dd
        1 -4 # 3 times electric charge
        2 1 # number of spin states (2S+1)
        3 3 # colour rep (1: singlet, 3: triplet, 8: octet)
        4 1 # Particle/Antiparticle distinction (0=own anti)

I would like to model the leptoquark effects in the high-mll tail of the Drell-Yan process. I managed to model the SM^2 and the LQ-SM interference term, but so far not the NP^2 term. The latter is much larger than the interference term, that's why I don't just omit it. For this I generated

p p > mu+ mu- / lq1d lq1dd lq3u lq3d lq3dd lq2d lq2pu lq2d~ lq2pu~ QED^2=0 QCD^2=0 NEW^2==4 [QCD] (for QCD corrections)

and put

(NLO, fixed-order)
req_acc_FO = 0.1
mll_sf = 3500

I let it run over night on a Desktop computer, but the simulation did not go beyond the initialization phase. I suspect that this is due to the strict mll_sf cut, since the cross section at large mll is much smaller than the one at small mll, so that this cut basically discards most of the events. But it is exactly the high-energy tail I am interested in, so I would like to know the cross-section for mll_sf > 3500.

Thank you for your help and cheers,
Luc

Revision history for this message
Luc Schnell (lucschnell) said :
#3

Oh, and I'm using the MadGraph5_aMC@NLO version 3.2.0.

Revision history for this message
marco zaro (marco-zaro) said :
#4

Dear Luc,
the reason why it does not converge at NLO (even without increasing the mll cut) is that in some real emission diagrams you have a leptoquark decaying to b mu (see eg diagrams 1 and 3 in matrix2.ps inside P0_bbx_mummup...)
You need to remove these contributions, and in order to do so you can use MadSTR, which however works only with v2 (possibly only with v2.8)

Cheers,

Marco

Revision history for this message
Luc Schnell (lucschnell) said :
#5

Dear Marco

Thank you for your answer! :) I have downloaded v2.8.3.2 and generated the same process as above

p p > mu+ mu- / lq1d lq1dd lq3u lq3d lq3dd lq2d lq2pu lq2d~ lq2pu~ QED^2=0 QCD^2=2 NEW^2==4 [QCD]

using ./mg5_aMC --mode=MadSTR.

Then I set

(NLO, fixed-order)
req_acc_FO = 0.1
istr = 1

in the run_card to exclude the diagrams with the LQ-resonance. Now I do get results for mll_sf = 30, but as soon as I set a larger cut (e.g. mll_sf = 1000 or 3500), the execution stalls again in the initialization phase:

INFO: Compiling directories...
INFO: Compiling on 16 cores
INFO: Compiling P0_bbx_mupmum_no_lq1dlq1ddlq3ulq3dlq3ddlq2dlq2pulq2dlq2pu...
INFO: Compiling P0_bxb_mupmum_no_lq1dlq1ddlq3ulq3dlq3ddlq2dlq2pulq2dlq2pu...
INFO: P0_bxb_mupmum_no_lq1dlq1ddlq3ulq3dlq3ddlq2dlq2pulq2dlq2pu done.
...

Do you know a way to model the high-mll tail in this situation?

Thank you once again and cheers,
Luc

Revision history for this message
Best marco zaro (marco-zaro) said :
#6

Dear Luc,
thanks for reporting.
Indeed it looks like the piece of code that checks the soft/collinear behaviour of the matrix-element hangs because of some floating point exception in phase-space functions. (for reference, this is "Error#2 in lambda" inside genps_fks, which is called by yminmax in the same file). However the problem seems specific to that piece of code, while the main integrator runs smoothly with the very large mll cut once i disable these tests.
In order to disable the tests (you'd better do a run with a low mll cut in order to check that these tests pass) just change line
5024 tests = ['test_ME']
of bin/internal/amcatnlo_run_interface.pu
to
5024 tests = []

Cheers,

Marco

Revision history for this message
Luc Schnell (lucschnell) said :
#7

Dear Marco

That solves my problem, thank you so much for your help!

Cheers,
Luc

Revision history for this message
Luc Schnell (lucschnell) said :
#8

Thanks marco zaro, that solved my question.