tau polarization information and taking into account the tau spin when it is decayed

Asked by HH on 2020-12-19

Dear experts,

I generated events for the process
mu- mu+ > ta- ta+
while
polbeam1=-80 and polbeam2=+80.
Then I wanted to access tau leptons polarization information which I thought must be stored. But it seems while these info are stored in lhe file, they are not stored by pythia or delphes. So my first question is how can I store polarization info for final particles in my final root file?

My second question is related to the products of the tau decay. Distributions of some kinematic variables (like energy and angular distribution) of the tau decay products are strongly related to the polarization of the decaying tau. My second question is how can I generate events with tau leptons decayed taking into account their polarizations. To be more specific, the tau decay modes I need to study are the SM decay mode ta > e ve~ vt and a BSM 2 body tau decay.

Thanks in advance.

Question information

Language:
English Edit question
Status:
Solved
For:
MadGraph5_aMC@NLO Edit question
Assignee:
No assignee Edit question
Solved by:
HH
Solved:
2021-01-22
Last query:
2021-01-22
Last reply:
2020-12-31

Hi,

The last column of the lhe file contains polarization information.
Now this is not complete information and this is not allow full spin-corrrelation decay

But in the case that you describe you can just do

generate e+ e- > ta+ ta-, ta+ > e ve~ vt , ta- > e ve~ vt
add process e+ e- > ta+ ta-, ta+ > e ve~ vt , ta- > BSM BSM
add process e+ e- > ta+ ta-, ta+ > BSM BSM , ta- > BSM BSM

Obviously, you will need to have a massive tau and a non zero width.
Since the width will likely be too small for numerical computation, you will see a warning that we use a larger value for the width for the computation but use NWA to have the correct cross-section (but if you plot mtau --or related observables--, you will see that this is too large)

Cheers,

Olivier

HH (hh-madgrapher) said : #2

Thanks for your answer.

With the syntax you suggested the tau leptons are decayed in mad level. So 2 questions arise for me now.

1) In case taus are decayed in mad level, are all tau spin effects taken into account when MadGraph computes the kinematic variables of the decay products? for example the angular distribution (which is not isotropic in the presence of tau polarization) and energy distribution of the decay products.

2) Finally, I will need to include all decay modes of tau in my analysis and therefore I think I have to use PY8 to decay tau because PY8 has already a decay table for tau. What will happen to spin effects in that case? are such effects taken into account when PY8 decays taus?

Thanks.

Hi,

MadGraph use the fULL matrix-element (so 2>6 for the SM decay) so yes it contains the spin-correlation.

For Pythia8, I do not know.

Cheers,

Olivier

HH (hh-madgrapher) said : #4

Thanks for your answer.

Sorry I have another question. MadGraph doesn't show the information of some particles in the output .lhe file for some reasons (like being off-shell or ...). I wanted to know if it is possible to have info of such particles in the .lhe file?

HH (hh-madgrapher) said : #5

Sorry. Moreover I need to know if it is possible generate ta+ > e+ ve vt~ where ta+ is moving with a non-zero Pz ?

In a lot of cases this does not make any sense to add such information.
In your case if you have both
e+ e- > a > ta+ ta-
e+ e- > z > ta+ ta-
if Z is onshell then it decouples and we do write that information into the lhe events.
But in other region (especially above the Z peak) you do have sizeable interference between the two and any information about the propagator will not be accurate.

Additionally, the reason to include such information (or not) is related to some convention with the parton-shower program.
When we do write an intermediate particle this forces the parton-shower to shower in a different way the particle which originates from that particle in order to preserve the invariant mass of that particle. so changing the event record is not a good idea.

>Moreover I need to know if it is possible generate ta+ > e+ ve vt~ where ta+ is moving with a non-zero Pz ?

When you do "generate ta+ > e+ ve vt~ " the tau will be at rest. Now it is trivial to take the event and boost them in the frame that you want.

HH (hh-madgrapher) said : #7

Actually the information of tau leptons is important for me. I don't need the propagator info. Is it possible to have info of tau leptons in .lhe file?

If you use the syntax:

generate e+ e- > ta+ ta-, ta+ > e ve~ vt , ta- > e ve~ vt
add process e+ e- > ta+ ta-, ta+ > e ve~ vt , ta- > BSM BSM
add process e+ e- > ta+ ta-, ta+ > BSM BSM , ta- > BSM BSM

You will always have the information about the tau written in the file.
so I'm not sure to understand the point of your question.

cheers,

Olivier

HH (hh-madgrapher) said : #9

Thanks. I generated lhe events and found tau info in lhe file. I cannot remember with what initial beam conditions I had lost tau info in .lhe file.

By the way, now I have tau info. But I see something unexpected in taus info. spin of tau leptons are 0 in all events in spite of the fact that they must be +1 or -1. the syntax I used for event generation is

import model sm-full
generate mu+ mu- > ta+ ta- weighted<=99, ta+ > e+ ve vt~, ta- > e- ve~ vt

Here I copy one complete lhe event:
<event>
 10 1 0.00093913 3.50000000e+02 7.54677100e-03 9.81689000e-02
      -13 -1 0 0 0 0 +0.0000000000e+00 +0.0000000000e+00 +1.7499996810e+02 1.7500000000e+02 1.0566000000e-01 0.0000e+00 -1.0000e+00
       13 -1 0 0 0 0 -0.0000000000e+00 -0.0000000000e+00 -1.7499996810e+02 1.7500000000e+02 1.0566000000e-01 0.0000e+00 1.0000e+00
      -15 2 1 2 0 0 -6.5995930164e+01 +1.0484103414e+02 +1.2359100711e+02 1.7500000002e+02 1.7770005075e+00 0.0000e+00 0.0000e+00
       15 2 1 2 0 0 +6.5995930164e+01 -1.0484103414e+02 -1.2359100711e+02 1.7499999998e+02 1.7769972018e+00 0.0000e+00 0.0000e+00
      -11 1 3 3 0 0 -2.1919179043e+01 +3.3398799169e+01 +4.0317778003e+01 5.6757848966e+01 5.1100000000e-04 0.0000e+00 1.0000e+00
       12 1 3 3 0 0 -1.6776975424e+01 +2.7180441563e+01 +3.1788238057e+01 4.5063681460e+01 0.0000000000e+00 0.0000e+00 -1.0000e+00
      -16 1 3 3 0 0 -2.7299775696e+01 +4.4261793403e+01 +5.1484991049e+01 7.3178469591e+01 0.0000000000e+00 0.0000e+00 1.0000e+00
       11 1 4 4 0 0 +5.7944227870e+00 -9.9047199234e+00 -1.1270706313e+01 1.6084390982e+01 5.1100000000e-04 0.0000e+00 -1.0000e+00
      -12 1 4 4 0 0 +4.9081484835e+01 -7.8020437814e+01 -9.1729319520e+01 1.3004018198e+02 0.0000000000e+00 0.0000e+00 1.0000e+00
       16 1 4 4 0 0 +1.1120022542e+01 -1.6915876398e+01 -2.0590981275e+01 2.8875427019e+01 0.0000000000e+00 0.0000e+00 -1.0000e+00
</event>

I generated events once again using the above syntax with subsequent decays ta+ > e+ ve vt~, ta- > e- ve~ vt removed. using the syntax

import model sm-full
generate mu+ mu- > ta+ ta- weighted<=99

now the spin of taus in .lhe file is -1 or +1 as expected. Below you can see one lhe event of this second generation:

<event>
 4 1 0.0309156 3.50000000e+02 7.54677100e-03 9.81689000e-02
      -13 -1 0 0 0 0 +0.0000000000e+00 +0.0000000000e+00 +1.7499996810e+02 1.7500000000e+02 1.0566000000e-01 0.0000e+00 -1.0000e+00
       13 -1 0 0 0 0 -0.0000000000e+00 -0.0000000000e+00 -1.7499996810e+02 1.7500000000e+02 1.0566000000e-01 0.0000e+00 1.0000e+00
      -15 1 1 2 0 0 -9.4678797851e+00 -1.3437311898e+02 +1.1169631336e+02 1.7500000000e+02 1.7770000000e+00 0.0000e+00 -1.0000e+00
       15 1 1 2 0 0 +9.4678797851e+00 +1.3437311898e+02 -1.1169631336e+02 1.7500000000e+02 1.7770000000e+00 0.0000e+00 1.0000e+00
</event>

Would you please let me know if there is something wrong with my generation? or there is a physical reason for the spin to be 0?

HH (hh-madgrapher) said : #10

Please note that the initial beams are polarized. I use

set polbeam1 -100
set polbeam2 +100

to set pols in the card.

When the tau is decay we use the full spin-corrrelation for such decat and therefore include as well interference between the two polarization. Consequently the tau is not in +1 or -1 but in both (actually it also has contribution from two other polarization who vanishes onshell).
In that case, we simply write 0 but this should not be consider as a polarization information.

If you want to assign a polarization for the tau, you can evaluate for each event these four polarised matrix-element for
mu+ mu- > ta+{L} ta-{L} weighted<=99, ta+ > e+ ve vt~, ta- > e- ve~ vt
mu+ mu- > ta+{L} ta-{R} weighted<=99, ta+ > e+ ve vt~, ta- > e- ve~ vt
mu+ mu- > ta+{R} ta-{L} weighted<=99, ta+ > e+ ve vt~, ta- > e- ve~ vt
mu+ mu- > ta+{R} ta-{R} weighted<=99, ta+ > e+ ve vt~, ta- > e- ve~ vt
and then randomly assign the helicity proportionally to those four numbers.

Note that you then have to define the frame in which you evaluate the above matrix-element since those matrix-element are not lorentz invariant.

Cheers,

Olivier

HH (hh-madgrapher) said : #12

Thanks for your help. Now I see why the spin is 0 in lhe events.

My main problem for which I opened this question was that I came into this conclusion that the polarization of the Tau leptons is not taken into account when the Tau leptons in the process

mu+ mu- > ta+ ta- weighted<=99
polbeam1 = -100
polbeam2 = +100

are decayed. I found out that the problem was on PY8 side which seems to decay Taus regardless of their polarizations (although its authors say the polarization effects are taken into account).

To make sure that the problem is on PY8 side, I generated a new sample of events for the process

mu+ mu- > ta+ ta- weighted<=99, ta+ > e+ ve vt~, ta- > e- ve~ vt

where the Tau decay is, this time, performed by MadGraph5. I also turned on PY8 for FSR, ISR, ... . Again I plotted the kinematic variables of the final state electrons. The obtained distributions were completely consistent with the so-called Michel spectrum. According to the Michel spectrum the distribution of the energy of the final state electron depends on the polarization of the decayed Tau. So I came into this conclusion that the PY8 doesn't decay Tau leptons properly.

Then I asked Pythia8 authors for a way to correct this!

I am not sure if I can fix the problem with PY8. So I am thinking of a way to generate events independently of PY8. But I don't know if it is possible. Is it possible to define all decay modes of the Tau lepton in MG5 and perform all Tau decay processes fully in MG5? As far as I know the MG5 only knows the fundamental particles and composite particles like Pions which appear in Tau lepton decays have not been defined in MG5. I would highly appreciate it if you let me know if there is a way to perform Tau decays in MG5 independently of PY8.

Thanks

Hi,

You have that paper who is a bit old: 1212.6247 <https://arxiv.org/abs/1212.6247>
and who implemented what you need.

as far as I know, you can take "any" UFO model and do within MG5aMC
add model taudecay_UFO

and this will create a NEW UFO model which contains your original UFO model + all the particles (and interactions) for the tau-decay.

I suggest that you contact the author of the paper if you need more information about that.

Cheers,

Olivier

PS: Such functionallity is currently not working within the alpha version of 2.9.0.
I have put a note to see if I can fix it or not.

> On 28 Dec 2020, at 14:55, HH <email address hidden> wrote:
>
> Question #694581 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/694581
>
> Status: Answered => Open
>
> HH is still having a problem:
> Thanks for your help. Now I see why the spin is 0 in lhe events.
>
> My main problem for which I opened this question was that I came into
> this conclusion that the polarization of the Tau leptons is not taken
> into account when the Tau leptons in the process
>
> mu+ mu- > ta+ ta- weighted<=99
> polbeam1 = -100
> polbeam2 = +100
>
> are decayed. I found out that the problem was on PY8 side which seems to
> decay Taus regardless of their polarizations (although its authors say
> the polarization effects are taken into account).
>
> To make sure that the problem is on PY8 side, I generated a new sample
> of events for the process
>
> mu+ mu- > ta+ ta- weighted<=99, ta+ > e+ ve vt~, ta- > e- ve~ vt
>
> where the Tau decay is, this time, performed by MadGraph5. I also turned
> on PY8 for FSR, ISR, ... . Again I plotted the kinematic variables of
> the final state electrons. The obtained distributions were completely
> consistent with the so-called Michel spectrum. According to the Michel
> spectrum the distribution of the energy of the final state electron
> depends on the polarization of the decayed Tau. So I came into this
> conclusion that the PY8 doesn't decay Tau leptons properly.
>
> Then I asked Pythia8 authors for a way to correct this!
>
> I am not sure if I can fix the problem with PY8. So I am thinking of a
> way to generate events independently of PY8. But I don't know if it is
> possible. Is it possible to define all decay modes of the Tau lepton in
> MG5 and perform all Tau decay processes fully in MG5? As far as I know
> the MG5 only knows the fundamental particles and composite particles
> like Pions which appear in Tau lepton decays have not been defined in
> MG5. I would highly appreciate it if you let me know if there is a way
> to perform Tau decays in MG5 independently of PY8.
>
> Thanks
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

HH (hh-madgrapher) said : #14

Thanks a lot for your reply. I wanted to download the TauDecay package but the download link provided in their paper doesn't work. Do you know where I can download it from?

You do not need that tarball anymore, I have include it within mG5aMC.
You just have to do
add model taudecay_UFO

if you start from the SM, you will get the equivalent of their tarball (but the interest is that it should work for a large class of model)

Cheers,

Olivier

> On 29 Dec 2020, at 11:25, HH <email address hidden> wrote:
>
> Question #694581 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/694581
>
> Status: Answered => Open
>
> HH is still having a problem:
> Thanks a lot for your reply. I wanted to download the TauDecay package
> but the download link provided in their paper doesn't work. Do you know
> where I can download it from?
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

HH (hh-madgrapher) said : #16

Thanks a lot for your help. I managed to use this package. It works well and I could reconstruct the Michel spectrum. The only issue is that it is very time-consuming since to generate the process mu+ mu- > ta+ ta- weighted<=99 including all 6 decay modes of Tau implemented in this package I have to define 6*6=36 processes each of which for a specific combination of Tau decay modes. I'm using multi_run and I generate 100k events in each run.

I wanted to know if there is a way to speed up the generation? Does changing the number of subruns and the number events per subrun alter the computation time?

Thanks in advance

HH (hh-madgrapher) said : #17

I asked the pythia author for a solution to my problem. He said pythia doesn't support polarized beams and that's why spin correlation is not taken into account when Tau lepton is decayed by pythia. However he sent me a modified TauDecay.cc which make pythia take into account spin correlation when beams are polarized. The problem is that this file works with pythia8303 not with 8244 which is already installed in my MG5. I modified HEPToolsInstaller to change the version of the pythia MG5 installs but it didn't work for me. The installer files are updated each time I use "Install pythia8" command in MG5. Is there a way to install the newer version of pythia inside MG5?

Hi,

pythia8303 is not compatible with MG5aMC.
i'm waiting a patch from pythia author to fix such issue (more exactly in the interface code which is installed on top of pythia which is not under my control).

You can obviously run pythia8 outside of MG5aMC that is not an issue.
For the convenience question, did you use multi-particle flag?

Cheers,

Olivier

> On 31 Dec 2020, at 09:55, HH <email address hidden> wrote:
>
> Question #694581 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/694581
>
> HH gave more information on the question:
> I asked the pythia author for a solution to my problem. He said pythia
> doesn't support polarized beams and that's why spin correlation is not
> taken into account when Tau lepton is decayed by pythia. However he sent
> me a modified TauDecay.cc which make pythia take into account spin
> correlation when beams are polarized. The problem is that this file
> works with pythia8303 not with 8244 which is already installed in my
> MG5. I modified HEPToolsInstaller to change the version of the pythia
> MG5 installs but it didn't work for me. The installer files are updated
> each time I use "Install pythia8" command in MG5. Is there a way to
> install the newer version of pythia inside MG5?
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

HH (hh-madgrapher) said : #19

Hi,

Sorry for the delay and thanks for your help.

> For the convenience question, did you use multi-particle flag?
I didn't modify this flag. It has its default value.