# wired decay width with three- and four-body decay channels

Asked by Y Du on 2017-11-11

Hi experts,

I'm generating a process like " p p > A B, ( A > a b), ( B > c d, c > e f, d > g h)", where A and B are BSM particles and the decay width for them are calculated automatically by setting the appropriate parameters to be "Auto" in the parameter card.

The result for A is reasonable, but for B, the decay width result is incorrect (off by a factor of 10^4 compared with theoretical value). In the parameter card, I found the following (see below), which seems that when MadGraph calculates the decay width, three-body and four-body decay channels are also included. I checked my UFO file and am sure that no such decay channels are included in the decay.py file. So what's going on here? Any ideas?

Thanks a lot,
Yong

*************** problem described above can be found in detailed here ********************

MadGraph decay width calculation result in the param_card.dat

****************************************************************************************

# PDG Width
168 DECAY 9000002 9.517513e-05
169 # BR NDA ID1 ID2 ...
170 7.126862e-01 4 -3 4 22 22 # 6.78299965826e-05
171 2.467872e-01 4 -15 16 22 22 # 2.34879988927e-05
172 3.766320e-02 4 -1 4 22 22 # 3.58460019995e-06
173 2.002203e-03 4 -5 6 22 22 # 1.90559964632e-07
174 7.391216e-04 4 22 22 23 24 # 7.03459931693e-08
175 7.596190e-05 2 25 24 # 7.22968349562e-09
176 2.830779e-05 2 24 23 # 2.69419755389e-09
177 1.138631e-05 2 6 -5 # 1.08369372788e-09
178 4.554131e-06 3 24 25 25 # 4.33440020471e-10
179 8.045484e-07 3 -5 6 25 # 7.6573000263e-11
180 6.605717e-07 3 -24 24 24 # 6.28699950662e-11
181 3.344466e-07 3 -6 6 24 # 3.18309992274e-11
182 1.497030e-07 3 -5 6 23 # 1.42480005956e-11
183 9.358371e-10 2 16 -15 # 8.90684184697e-14
184 6.845388e-10 2 4 -3 # 6.51510725773e-14
185 3.653681e-11 2 4 -1 # 3.47739597902e-15
186 3.628565e-12 2 14 -13 # 3.45349104696e-16
187 3.210853e-13 2 12 -11 # 3.05593330057e-17
188 2.312273e-13 2 2 -3 # 2.20070912426e-17
189 1.345558e-14 2 2 -1 # 1.28063629378e-18
190 4.448544e-19 2 22 24 # 4.23390780423e-23

## Question information

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Olivier Mattelaer
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2017-11-11
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2017-11-11
2017-11-11
 Olivier Mattelaer (olivier-mattelaer) said on 2017-11-11: #1

Hi,

So far everything seems to work as expected.
Indeed the “Auto” keyword is suppose to include all relevant channel up to 4 body decay.
The decay.py should indeed only include the two-body decay but the “Auto” keyword do not (only) use that file.
All the algorithm is describe in arXiv:1402.1178.

Since you have a lot of photon for your 4 body decay, you need to check if those
contribution are genuine 4 body decay or if they should be consider as radiation of three body decay.
The code clearly consider that this is the first case (if this is not correct, this can indicate that the coupling order are not correctly set in the model, see the paper for more detail)

Cheers,

Olivier

> On Nov 11, 2017, at 19:27, Y Du <email address hidden> wrote:
>
> Question #660618 on MadGraph5_aMC@NLO changed:
>
> Description changed to:
> Hi experts,
>
> I'm generating a process like " p p > A B, ( A > a b), ( B > c d, c > e
> f, d > g h)", where A and B are BSM particles and the decay width for
> them are calculated automatically by setting the appropriate parameters
> to be "Auto" in the parameter card.
>
> The result for A is reasonable, but for B, the decay width result is
> incorrect (off by a factor of 10^4 compared with theoretical value). In
> the parameter card, I found the following (see below), which seems that
> when MadGraph calculates the decay width, three-body and four-body decay
> channels are also included. I checked my UFO file and am sure that no
> such decay channels are included in the decay.py file. So what's going
> on here? Any ideas?
>
> Thanks a lot,
> Yong
>
> *************** problem described above can be found in detailed here
> ********************
>
> MadGraph decay width calculation result in the param_card.dat
>
> ****************************************************************************************
>
> # PDG Width
> 168 DECAY 9000002 9.517513e-05
> 169 # BR NDA ID1 ID2 ...
> 170 7.126862e-01 4 -3 4 22 22 # 6.78299965826e-05
> 171 2.467872e-01 4 -15 16 22 22 # 2.34879988927e-05
> 172 3.766320e-02 4 -1 4 22 22 # 3.58460019995e-06
> 173 2.002203e-03 4 -5 6 22 22 # 1.90559964632e-07
> 174 7.391216e-04 4 22 22 23 24 # 7.03459931693e-08
> 175 7.596190e-05 2 25 24 # 7.22968349562e-09
> 176 2.830779e-05 2 24 23 # 2.69419755389e-09
> 177 1.138631e-05 2 6 -5 # 1.08369372788e-09
> 178 4.554131e-06 3 24 25 25 # 4.33440020471e-10
> 179 8.045484e-07 3 -5 6 25 # 7.6573000263e-11
> 180 6.605717e-07 3 -24 24 24 # 6.28699950662e-11
> 181 3.344466e-07 3 -6 6 24 # 3.18309992274e-11
> 182 1.497030e-07 3 -5 6 23 # 1.42480005956e-11
> 183 9.358371e-10 2 16 -15 # 8.90684184697e-14
> 184 6.845388e-10 2 4 -3 # 6.51510725773e-14
> 185 3.653681e-11 2 4 -1 # 3.47739597902e-15
> 186 3.628565e-12 2 14 -13 # 3.45349104696e-16
> 187 3.210853e-13 2 12 -11 # 3.05593330057e-17
> 188 2.312273e-13 2 2 -3 # 2.20070912426e-17
> 189 1.345558e-14 2 2 -1 # 1.28063629378e-18
> 190 4.448544e-19 2 22 24 # 4.23390780423e-23
>
> --

 Y Du (fallive) said on 2017-11-11: #2

Hi Olivier,

Thanks for your quick update. I will have a look at the ref soon.

I have been debugging in the afternoon, and the 4-body decay is actually genuine. But as said in the post, A and B are both BSM particles, both of which have the di-photon decay channel, but only B has the 4-body decay, so I don't understand why the preference.

I tried removing the di-photon decay channel for B by setting the corresponding coupling to be zero, then all those four-body decay channels went away, but the three-body decay channels were still there (the three-body decay channels with three W bosons in the final state are also genuine). I guess this info might help.

On the other hand, I'm trying to use MadSpin to deal with the long decay chains, do you think this might help?

Thanks,
Yong

 Y Du (fallive) said on 2017-11-11: #3

I understand that there is nothing wrong with the code, but I want to figure out why the decay width calculation for A and B are different.

I had a discussion with my colleagues and they said they never saw three- or four-body decay channels being included before when did the same thing as me. So the general question is: when will MadGraph consider three- and even four-body decay channels in the calculation?

 Olivier Mattelaer (olivier-mattelaer) said on 2017-11-11: #4

Hi,

We always consider three body decay but we do not always write their contribution in the param_card (and we do not always compute those precisely)

The algorithm (described in the above paper) is based on the following
1) evalutation of the 2-body decay
2) compute an estimator of the 3-body decay (fast but not very precise)
3) if the estimator shows that the 3-body decay is negligeable stop
4) create the Feynman diagram for the 3-body decay
5) compute an estimator of the 3-body decay based on the Feynman diagram (quite precise)
6) if the estimator shows that the 3-body decay is negligeable stop
7) Run a monte-carlo integrator to get the exact 3 body contribution

8) compute an estimator of the 4-body decay (fast but not very precise)
9) if the estimator shows that the 4-body decay is negligeable stop
10) create the Feynman diagram for the 4-body decay
11) compute an estimator of the 4-body decay based on the Feynman diagram (quite precise)
12) if the estimator shows that the 4-body decay is negligeable stop
13) Run a monte-carlo integrator to get the exact 4 body contribution

In most cases, the code stops at the third step (lilely what happen for A)

Cheers,

Olivier

 Y Du (fallive) said on 2017-11-11: #5

Hi Oliver,

Thank you a lot for your quick reply and a detailed explanation on the process of decay width calculation. It is clear now for me where I should investigate to solve my problem.

I have one last question, if the calculated three- or four-body decay width is negligible, then it's contribution to the total decay width will not appear in the param_card.dat, is this correct?

Thanks a lot,
Yong

 Olivier Mattelaer (olivier-mattelaer) said on 2017-11-11: #6

Hi,

Yes that’s correct. In the paper, you will see how to compute the width without the “Auto” keyword, which allow you to possibility to force the computation of the 3/4 body decay (or to forbid them).
If you want to see their importance for your A particle.

Cheers,

Olivier
> On Nov 11, 2017, at 21:53, Y Du <email address hidden> wrote:
>
> Question #660618 on MadGraph5_aMC@NLO changed:
>
>
> Y Du is still having a problem:
> Hi Oliver,
>
> Thank you a lot for your quick reply and a detailed explanation on the
> process of decay width calculation. It is clear now for me where I
> should investigate to solve my problem.
>
> I have one last question, if the calculated three- or four-body decay
> width is negligible, then it's contribution to the total decay width
> will not appear in the param_card.dat, is this correct?
>
> Thanks a lot,
> Yong
>
> --

 Y Du (fallive) said on 2017-11-11: #7

Hi Olivier,

Thank your for your confirmation and for pointing out that point to me. I'm now reading the paper. Thank you for solving my headache and I appreciate it a lot.

Wish you a great day!
Yong

 Y Du (fallive) said on 2017-11-11: #8

Thanks Olivier Mattelaer, that solved my question.