cross section did not converge, accuracy value is very large

Hi Si,
obviously this integration is not working at all as shown. Note that Whizard per default does not apply any cuts, so in case the muons massless you must, in case their mass is kept, you better should apply to the outgoing muons. You can also apply a cut on the momentum transfer from the initial state into the t-channel of your VBF process. Is this the built-in 2HDM (called THDM) or the UFO version? For the built-in version you need to find a consistent set of parameters which is much easier for the UFO version as there you could input SLHA-like files with parameter sets from spectrum generators like SARAH, Pheno etc.
The term 'idles' that you were referring to amounts to my knowledge rather to threads in the integration and not to Feynman diagrams.
Cheers,
    JRR

Hi Juergen,

Currently I am using 2HDM UFO file.

The cuts I apply is:
cuts=all abs(Eta) <2.44 [Higgs]
   and all Pt>50 GeV [Higgs]
Could you list all the cuts I should apply?

Also I didn't do any thing to muon mass.
The whole process is:
alias Higgs="h2":"h3"
alias lep="mu+":"mu-"
process muta="mu+","mu-"=>("mu+","mu-","h2","h3")+("vm","vm~","h2","h3")
beams = "mu+","mu-" => isr,isr
isr_mass=0.1
isr_alpha=1/132.18417914
With changing sqrts.

Thanks!
Si

Hi Si,
thanks for the information. I separated your two processes, as they are integrated separately anyways. I first noted that without any further specifcation, the first part (the WW fusion) integrates without any problem, cf. (I used default parameters from the UFO 2HDM file and 10 TeV muon collider energy):
| Integrator: 34 chains, 220 channels, 10 dimensions
| Integrator: Using VAMP channel equivalences
| Integrator: 10000 initial calls, 20 bins, stratified = T
| Integrator: VAMP
|=============================================================================|
| It Calls Integral[fb] Error[fb] Err[%] Acc Eff[%] Chi2 N[It] |
|=============================================================================|
   1 9900 5.2526932E+01 1.25E+01 23.71 23.59* 3.25
   2 9776 2.9151854E+01 1.71E+00 5.87 5.80* 3.01
   3 9644 3.0914070E+01 1.70E+00 5.51 5.41* 3.04
   4 9503 3.3824578E+01 2.14E+00 6.33 6.17 2.95
   5 9386 3.3489552E+01 1.52E+00 4.55 4.41* 3.50
   6 9294 4.0944657E+01 4.87E+00 11.89 11.46 2.79
   7 9224 3.6724404E+01 1.21E+00 3.30 3.17* 5.32
   8 9153 3.5363989E+01 7.78E-01 2.20 2.10* 7.68
   9 9088 3.6765679E+01 1.41E+00 3.83 3.65 4.79
  10 9053 3.5114080E+01 7.61E-01 2.17 2.06* 7.50
|-----------------------------------------------------------------------------|
  10 94021 3.4816662E+01 4.10E-01 1.18 3.61 7.50 2.87 10
|-----------------------------------------------------------------------------|
  11 19966 3.5176165E+01 7.59E-01 2.16 3.05 4.92
  12 19966 3.5340588E+01 5.24E-01 1.48 2.09* 3.94
  13 19966 3.4487391E+01 5.07E-01 1.47 2.08* 3.44
  14 19966 3.4916295E+01 5.57E-01 1.60 2.25 2.98
  15 19966 3.5306737E+01 4.77E-01 1.35 1.91* 2.91
|-----------------------------------------------------------------------------|
  15 99830 3.5037508E+01 2.43E-01 0.69 2.19 2.91 0.48 5
|=============================================================================|

The ZZ fusion is not as good, but still ok with the default number of iterations:
|=============================================================================|
   1 9945 5.3669324E-01 4.76E-02 8.87 8.85* 2.66
   2 9892 8.3609967E-01 8.59E-02 10.27 10.22 2.13
   3 9831 7.3452832E-01 5.22E-02 7.10 7.04* 1.98
   4 9763 6.8586757E-01 3.26E-02 4.75 4.70* 2.33
   5 9694 1.0576465E+00 1.61E-01 15.19 14.96 0.94
   6 9634 8.6763945E-01 4.79E-02 5.52 5.42* 1.93
   7 9580 7.7375747E-01 3.13E-02 4.04 3.95* 2.70
   8 9513 8.1636684E-01 3.61E-02 4.42 4.31 2.92
   9 9453 7.9630097E-01 3.11E-02 3.91 3.80* 3.34
  10 9396 7.9528348E-01 2.95E-02 3.71 3.59* 3.30
|-----------------------------------------------------------------------------|
  10 96701 7.6421505E-01 1.26E-02 1.64 5.11 3.30 4.66 10
|-----------------------------------------------------------------------------|
  11 19950 8.3740914E-01 2.82E-02 3.37 4.76 1.86
  12 19950 9.8154323E-01 1.40E-01 14.26 20.14 0.66
  13 19950 8.2399087E-01 2.30E-02 2.79 3.94* 0.53
  14 19950 8.2849716E-01 2.09E-02 2.53 3.57* 0.53
  15 19950 8.0292058E-01 1.97E-02 2.46 3.47* 0.50
|-----------------------------------------------------------------------------|
  15 99750 8.2163041E-01 1.11E-02 1.36 4.29 0.50 0.66 5
|=============================================================================|
Ramping up the iterations to
iterations = 10:100000:"gw", 3:200000
|=============================================================================|
| It Calls Integral[fb] Error[fb] Err[%] Acc Eff[%] Chi2 N[It] |
|=============================================================================|
| VAMP: parameter mismatch, discarding grid file 'muta2.m1.vg'
   1 99918 7.9920320E-01 9.37E-02 11.72 37.05* 0.34
   2 99861 8.2500020E-01 3.16E-02 3.83 12.12* 0.43
   3 99821 8.7280539E-01 2.86E-02 3.27 10.34* 0.51
   4 99760 8.2612201E-01 8.78E-03 1.06 3.36* 1.49
   5 99681 8.3389030E-01 6.50E-03 0.78 2.46* 2.54
   6 99641 8.2519646E-01 5.44E-03 0.66 2.08* 3.41
   7 99584 8.4086800E-01 5.32E-03 0.63 2.00* 3.35
   8 99526 8.2938073E-01 4.63E-03 0.56 1.76* 4.68
   9 99474 8.2543893E-01 4.36E-03 0.53 1.67* 4.89
  10 99416 8.4076803E-01 4.41E-03 0.52 1.65* 4.99
|-----------------------------------------------------------------------------|
  10 996682 8.3229393E-01 1.97E-03 0.24 2.36 4.99 1.51 10
|-----------------------------------------------------------------------------|
  11 199941 8.3715085E-01 3.10E-03 0.37 1.65 4.19
  12 199941 8.2989613E-01 3.05E-03 0.37 1.65* 3.34
  13 199941 8.3197152E-01 3.01E-03 0.36 1.62* 3.11
|-----------------------------------------------------------------------------|
  13 599823 8.3295925E-01 1.76E-03 0.21 1.64 3.11 1.47 3
|=============================================================================|

This is also a very convergent integration. You had even more iterations and calls,. so I am a bit puzzled what is going on. It might either be a different model parameter (e.g. a width set to zero), or it is the error goal.
Cheers,
     JRR

Hi Juergen,

I found out if I change
integrate(muta){iterations=20:600000:"gw",5:200000}
into
integrate(muta)

it will work convergently.
What is the reason for that?
Why do more iterations and calls return a bad integration?

But when I add
mh2=1000
mh3=1000
mhc=1000
The integration is not convergent again. it shows:
|=============================================================================|
| It Calls Integral[fb] Error[fb] Err[%] Acc Eff[%] Chi2 N[It] |
|=============================================================================|
| VAMP: using grids and results from file 'muta.m1.vg'
   1 9956 1.1611969E-01 9.01E-02 77.60 77.43* 1.38
   2 9924 3.3591027E-02 8.96E-03 26.66 26.56* 0.13
   3 9890 1.2598076E-01 3.99E-02 31.69 31.51 0.09
   4 9850 1.3134627E+00 8.54E-01 65.00 64.51 0.04
   5 9810 2.1907991E-01 4.13E-02 18.86 18.68* 0.13
   6 9774 6.4055408E-01 1.21E-01 18.96 18.75 0.12
   7 9740 6.8405160E-01 7.16E-02 10.47 10.33* 0.28
   8 9706 1.1276106E+00 1.66E-01 14.69 14.47 0.19
   9 9672 3.0789859E+00 9.60E-01 31.18 30.66 0.08
  10 9642 5.0353421E+04 5.02E+04 99.63 97.83 0.02
|-----------------------------------------------------------------------------|
  10 97964 6.1225489E-02 8.42E-03 13.75 43.04 0.02 20.00 10
|-----------------------------------------------------------------------------|
| VAMP: using grids and results from file 'muta.m1.vg'
  11 19998 2.7420350E+03 2.30E+03 83.87 118.61 0.01
  12 19998 1.0383759E+02 4.41E+01 42.52 60.12* 0.00
  13 19998 3.6222740E+01 1.94E+01 53.49 75.64 0.00
  14 19998 9.2202530E+01 4.98E+01 54.04 76.43 0.00
  15 19998 1.6942917E+03 1.46E+03 85.95 121.54 0.01
|-----------------------------------------------------------------------------|
  15 99990 5.2570429E+01 1.67E+01 31.79 100.53 0.01 1.33 5
|=============================================================================|
How to solve this?

Cheers,
Si

Thanks for solveing the problem!

Hi Juergen,
The width of Higgs are Independent parameters,
I guess whether changing the mass of the Higgs will need also to change the Higgs width.
Thanks!
Si

Hi Juergen,

I did not change the Higgs mass, and run the process with default interations.
But the result is strange, there are two part of cross section, the final result is quite different from the first part.
See below:
|=============================================================================|
| It Calls Integral[fb] Error[fb] Err[%] Acc Eff[%] Chi2 N[It] |
|=============================================================================|
| VAMP: parameter mismatch, discarding grid file 'muta.m2.vg'
   1 9945 5.9751680E-01 1.88E-01 31.47 31.38* 1.66
   2 9883 4.1504889E-01 8.42E-02 20.30 20.18* 1.37
   3 9826 3.9321425E-01 5.27E-02 13.40 13.28* 2.50
   4 9754 7.6103815E-01 2.30E-01 30.16 29.78 1.66
   5 9705 5.1211514E-01 5.99E-02 11.70 11.53* 1.24
   6 9639 4.2225177E-01 3.14E-02 7.45 7.31* 1.80
   7 9591 4.3903737E-01 2.61E-02 5.94 5.82* 1.99
   8 9554 5.0831363E-01 3.33E-02 6.55 6.40 1.61
   9 9505 1.3145230E+00 6.44E-01 49.03 47.80 0.48
  10 9435 5.1259020E-01 3.07E-02 5.98 5.81* 1.53
|-----------------------------------------------------------------------------|
  10 96837 4.6498860E-01 1.38E-02 2.96 9.22 1.53 1.52 10
|-----------------------------------------------------------------------------|
  11 19943 5.6201750E-01 3.01E-02 5.36 7.57 0.84
  12 19943 5.6129236E-01 3.35E-02 5.96 8.42 0.66
  13 19943 5.5883756E-01 2.58E-02 4.61 6.51* 0.54
  14 19943 5.2777855E-01 2.26E-02 4.28 6.04* 0.49
  15 19943 5.3899828E-01 2.91E-02 5.40 7.63 0.49
|-----------------------------------------------------------------------------|
  15 99715 5.4699218E-01 1.23E-02 2.24 7.08 0.49 0.36 5
|=============================================================================|
| Time estimate for generating 10000 events: 0d:00h:04m:15s
| Integrate: sum of all components
|=============================================================================|
| It Calls Integral[fb] Error[fb] Err[%] Acc Eff[%] Chi2 N[It] |
|=============================================================================|
   1 0 1.8705113E+01 1.89E-01 1.01 0.00* 1.32
|=============================================================================|
What happens here? Why there are two parts of cross section? Where did the second one come from?

And with changing sqrts, the cross section is decreasing with increasing sqrts(3 TeV to 15 TeV):
# Plot: foo
# x y yerr xerr
   3.000000000000E+03 2.162021186374E+02 1.301675242448E+00 0.000000000000E+00
   4.000000000000E+03 1.476444575786E+02 8.778208129106E-01 0.000000000000E+00
   5.000000000000E+03 1.080268408097E+02 6.861430458171E-01 0.000000000000E+00
   6.000000000000E+03 8.273973608979E+01 6.280801117398E-01 0.000000000000E+00
   7.000000000000E+03 6.460622603521E+01 4.258139657326E-01 0.000000000000E+00
   8.000000000000E+03 5.320648095128E+01 5.337731835555E-01 0.000000000000E+00
   9.000000000000E+03 4.373955310956E+01 3.708540254158E-01 0.000000000000E+00
   1.000000000000E+04 3.689998995625E+01 3.801548054458E-01 0.000000000000E+00
   1.100000000000E+04 3.221357625910E+01 3.762749774688E-01 0.000000000000E+00
   1.200000000000E+04 2.758885102820E+01 2.706912187747E-01 0.000000000000E+00
   1.300000000000E+04 2.453248901089E+01 2.361935114893E-01 0.000000000000E+00
   1.400000000000E+04 2.136163430798E+01 2.059105060602E-01 0.000000000000E+00
   1.500000000000E+04 1.870511343609E+01 1.890229297332E-01 0.000000000000E+00

# Summary:
n_entries = 13

Here is my full sin file:
model=F2HDM_UFO(ufo("/home/si/Dropbox/Linux/Whizard/UFO"))
show(model)
!mh2=1000
!mh3=1000
!mhc=1000
alias Higgs="h2":"h3"
alias lep="mu+":"mu-"
process muta="mu+","mu-"=>("mu+","mu-","h2","h3")+("vm","vm~","h2","h3")
beams = "mu+","mu-" => isr,isr
isr_mass=0.1
isr_alpha=1/132.18417914
openmp_num_threads=16
plot foo
scan sqrts = ((3 TeV => 15 TeV /+ 1 TeV)){
cuts=all abs(Eta) <2.44 [Higgs]
   and all Pt>50 GeV [Higgs]
relative_error_goal=1e-2
integrate(muta)
!integrate(muta){iterations=20:600000:"gw",5:200000}
record foo(sqrts, integral (muta), error (muta))
}
write_analysis { $out_file = "sig_isr.dat"}

Thank you!
Si

Hi Si,
in your last example, you defined the process as consisting of two components, WW and ZZ fusion, so the final line shows the sum of WW and ZZ fusion. The cross section falls off with 1/s as it should , right?
To your post before: the mass and widths of particles are normally independent input parameters in UFO models, if you change the mass, you need to calculate and set the widths correspondingly.
Also for the Higgs masses of
mh2 = 1000
mh3 = 1000
mhc = 1000
I get perfectly convergent results.
Cheers,
     JRR

Hi Juergen,

The VBF process has effective W/Z /photon approximation, and the splitting function has log(s) terms.
We would expect with increasing sqrts, should the cross section increase?
Is 1/s behavior only for s-channel diagram?

Cheers,
Si

You applied cuts on the Higgs bosons, if I omit those cuts the xsec rises as you expected it:
###############################################################################
# Plot: foo
# x y yerr xerr
   3.000000000000E+03 4.252312189798E+00 1.611215504833E-01 0.000000000000E+00
   4.000000000000E+03 7.210224063083E+00 1.371960156182E-01 0.000000000000E+00
   5.000000000000E+03 1.536254749617E+01 8.043504724267E-02 0.000000000000E+00
   6.000000000000E+03 2.768296360355E+01 1.630478405040E-01 0.000000000000E+00
   7.000000000000E+03 3.767365277206E+01 1.353801988577E-01 0.000000000000E+00
   8.000000000000E+03 4.688854661976E+01 1.313748117173E-01 0.000000000000E+00
   9.000000000000E+03 5.354670490565E+01 1.357304412907E-01 0.000000000000E+00
   1.000000000000E+04 5.851478117712E+01 1.736862380540E-01 0.000000000000E+00
   1.100000000000E+04 6.247265617240E+01 1.992949377840E-01 0.000000000000E+00
   1.200000000000E+04 6.496946427151E+01 1.542138131288E-01 0.000000000000E+00
   1.300000000000E+04 6.669337362377E+01 1.879949479470E-01 0.000000000000E+00
   1.400000000000E+04 6.737220119779E+01 1.618234205053E-01 0.000000000000E+00
   1.500000000000E+04 6.766774337931E+01 2.003215669420E-01 0.000000000000E+00

Hi Juergen,

Your answer seems not for this question? Is that belong to other questions?

And, I still do not get the increasing cross section.
Could you share your whole sin file?

Thank you!
Si

Yes, this answer was from a different question. I simply erased the cuts statement from the SINDARIN.

Hi Juergen,

I did erase the cuts. But the cross section is still decreasing.
Maybe you can share your whole sin file, I can repeat it.
To see whether it works or not.
Or you can use my whole sin file, to see the result.

Thanks!
Si

Hi Juergen,

Thank you! That solved my problem.

The situation is if not set
mh2 = 1000
mh3 = 1000
mhc = 1000
The cross section will decrease.
Also the cuts will have some influence.

I noticed you do not change the Higgs width. Is that ok?
I want to know one more thing: If the Higgs mass width is correct, what will it influence in Whizard? How?

Cheers,
Si

The correct width gives the correct normalization of cross section if on-shell residua of propoagators are then correctly normalized.

Thanks Juergen Reuter, that solved my question.