Cross Section varying vastly despite same parameter, events not reaching the goal

Hi,

What is the (LO) physical value of the width?

From what I see the code is fluctuating between two answers.
So since we are using multi-channel, I would bet that the issue is that one channel of integration is sometimes returning zero cross-section and sometimes not.

The typical reason for such issue is that a cut is much too strong and makes extremelly hard for one channel to find phase-space point that are not zero and in that case and after a given amount of try if no event passed any of the cut, then we assume that this channel is simply zero.

But I would need to either have your full directy or the full instruction on how to reproduce this in order to be able to help you further.

Cheers,

Olivier

Hi Olivier,

Thanks for your quick reply. I have a few questions regarding your reply.

1. If I'm assuming correctly, you want to know the width that I have defined in the .fr file? If so, that is set to 1 for the dark pions.
2. I can send you the UFO file via email if you want to reproduce it, if that is okay.

Yes, please send it to <email address hidden> with a link to this webpage (or mention the number 705635)

For the width, I wanted to know what was the real value associated to the benchmark, so the value computed by the code if you write auto within the param_card but if have the model I can compute that myself obviously.

Cheers,

Olivier

I've sent the UFO file, as well as the process that I'm generating.

Thanks,

Shafakat

Yes I did receive it. But I guess that I'm missing some cuts or I do not use the correct benchmark point because the result of my run is:

The only customization of the cards that I did was
set width all auto

  === Results Summary for run: run_01 tag: tag_1 ===

     Cross-section : 9.767e+14 +- 2.528e+13 pb
     Nb of events : 10000

So it is super large.
Even with the default value set in the FR file,
  === Results Summary for run: run_02 tag: tag_1 ===

     Cross-section : 9.77e+14 +- 2.515e+13 pb
     Nb of events : 10000

Can you provide me more precise instructions?

Cheers,

Olivier

PS: The correct widths for the default mass spectrums are (at LO):

#
# PDG Width
DECAY 9000001 0.000000e+00
#
# PDG Width
DECAY 9000002 6.426180e+02
# BR NDA ID1 ID2 ...
   5.000416e-01 2 -9000004 9000004 # 321.3357208663297
   4.999584e-01 2 -9000006 9000006 # 321.28229971780974
#
# PDG Width
DECAY 9000003 3.909117e-09
# BR NDA ID1 ID2 ...
   9.882829e-01 2 9000001 9000001 # 3.863313685163986e-09
   1.168262e-02 2 22 9000001 # 4.566872912857281e-11
   3.452544e-05 2 22 22 # 1.349639791498827e-13
#
# PDG Width
DECAY 9000004 0.000000e+00
#
# PDG Width
DECAY 9000005 0.000000e+00
#
# PDG Width
DECAY 9000006 0.000000e+00
#
# PDG Width
DECAY 9000007 8.814020e-08
# BR NDA ID1 ID2 ...
   9.882846e-01 2 9000001 9000001 # 8.710759787634076e-08
   1.168093e-02 2 22 9000001 # 1.0295598980680865e-09
   3.451512e-05 2 22 22 # 3.042169321216173e-12

Hi Olivier,

I'm really sorry, I should have been more specific.

In the run_card, I used the following commands:

set fdecay = 1
set sde_strategy = 1

Also I also made sure to set zero width for t channels to be false (the t--channels will also have non-zero width)

Ah the widths are changing when set to auto, is that potentially the issue?

So what is this fdecay? If this is a width of a particle, then your model might not follow the UFO convention and you might be in trouble.

Looks like you do have some kind of singularity within the amplitude which cut did you have to prevent such divergence?

Cheers,

Olivier

Hi Olivier,

fdecay is the pion decay constant, it's a parameter and I was checking how the cross-section varies with increase in fdecay. I doubt this has anything to do with the width of the particle.

I tried doing this for the cuts:
set pt_min_pdg = {9000003:1}
set pt_min_pdg = {9000004:1}
set pt_min_pdg = {9000007:1}

and
set pt_min_pdg = {9000003:10}
set pt_min_pdg = {9000004:10}
set pt_min_pdg = {9000007:10}

9000003 being dark pi0, 9000004 being dark pi- and 9000007 being dark eta
But the cross-sections still vary by a lot.

1. Is this correct way to set a cut? If not, what is?
2. How can I decide what value of cut is needed to prevent a divergence?

Thanks,

Shafakat

---------------------------------
Edit: I tried checking "update psoptim" and now I'm trying different values of "set tmin_for_channel" from -0.9 to -0.1, not sure if that will help this problem or not.

Hi,

I would say that the correct way for such cut should be
set pt_min_pdg = {9000003:10, 9000004:10, 9000007:10}

But looks like such cut are not enough and that you need at least a rapidity cut as well.
You probably also need a deltaR separation cut between those particles and a invariant mass cut as well I guess.
I have the feeling that you are kind in the massless limit and therefore you have some soft/collinear limit.
But this is not clear to me since I have no clue what your theory is.

> 2. How can I decide what value of cut is needed to prevent a divergence?

Normally with soft and collinear divergency, those cuts are related to the scale to which you would start the resumation (for QED/QCD this is related to your parton-shower).

Additionally, it seems that sde_strategy=1 does not work well here, so i would just switc to sde_strategy=2 here which is designed for cases with large interference which is likely your case here.

Cheers,

Olivier

Hi Olivier,

I am in the massless limit, since the beam energy is 13 TeV and I am setting the masses of the dark pions to be much smaller (135 MeV). I am assuming I need to look into the pdf of the theory to set the cuts properly? If I set a high cut, the cross-section does not fluctuate, but if I lower the cut, it tends to do the same thing (fluctuates between two values).

Additionally, I checked for both sde_strategy = 1 and sde_strategy = 2. For sde_strategy = 1, with a very small cut (pt_min: 0.0001, eta_min: 0.00005, mxx_min = 0.0001), the cross-section jumps between three values:

2.555e+06 ± 1e+06
1.407e+06 ± 7.1e+05
2895 ± 4.3

meanwhile, for sde_strategy = 2, it jumps between two:

1.408e+06 ± 7.2e+05
 2.675e+06 ± 8.9e+05

Also if I do set width all auto, if the rapidity cut is equal to the pT cut, it fails. I do want to read further into cuts, so getting a reference for that would be great.

Cheers,
Shafakat

Olivier Mattelaer suggests this article as an answer to your question:
FAQ #3323: “How to implement new cuts”.

Hi Olivier,

Thanks for all the help, I have been trying to implement cuts and I have switched to luxqed PDF, since I have to use that. Sadly, even if I implement high enough cuts for the cross-section to be stable (10 GeV for pt_min and mxx_min, and 5 for eta_min), the cross-sections are still unstable. I noticed that most of the "unstableness" comes from the t-channel diagrams. I tested this with
photon fusion to 3 dark pions (which was stable in the interaction order of ChiPT <= 6), but including the t-channel diagrams (with interaction order of ChiPT == 8), the cross-sections choke and become unstable.

I think there's more to this problem than just implementing cuts.

Sincerely
Shafakat

Then the last hope is to play with the parameter:
tmin_for_channel
Here is the comment associated to it:
 limit the non-singular reach of --some-- channel of integration related to T-channel diagram (value between -1 and 0), -1 is no impact

This will allow you to limit the issue if you think that the issue is related to the phase-space integrator in that limit.
My experience is that this only helps for sde_strategy=1 but the correct strategy is sde_strategy=2. But maybe your process is different.

If nothing works, then I guess the only solution that remains for you is to create your own phase-space integrator tune for that specific channel.

Cheers,

Olivier