Regarding Decay with computation of Heavy Neutrino

Hi,

Did you read 1402.1178 <https://arxiv.org/abs/1402.1178>?
It explains when/why the code stops at two body decay and gives information in order to force three/four body decay.

Cheers,

Olivier

> On 1 Mar 2022, at 07:05, ouseph cj <email address hidden> wrote:
>
> New question #700772 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/700772
>
> Dear Madgraph Experts,
>
> I am working on the 3 body decay of Heavy Neutrino N ( N > \nu l+ l-). In my model file, I also have an extra Zprime boson as a new mediator apart from the Z and W boson.
>
> I am considering the following mass range.
> Mn:[1 to 100]
> Mzp:[0.1,1,10]
>
> when Mn > Mw (mass of W boson) and Mn > Mz ( mass of Z boson), madgraph is not giving any 3 body decay of N, it completely decays into N > W l and N > Z \nu (2-body decay).
>
> Although if Mn > Mzp ( mass of Z prime), the two-body decay of Zp is started ( N > Zp \nu).
> when Mn > 80 GeV I can only see the two-body decay of Mn ( Mn > \nu Z, Mn > \nu Zp, Mn > l w).
>
> Could madgraph can able to produce 3 body decay in the above mass region. In my total decay width Vs Mn curve, I am getting a dip at Mn = 80 GeV, is reasonable?. Do the decay width at this mass region is reliable?
>
> Best
> ouseph
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Dear Oliver
Thanks for the replay, I have one more question regarding the same.

when Mn ( mass of Heavy Neutrino) > Mzp ( mass of Z prime), for example Mn > Mzp =1 GeV,
I have both the 2 body decay like N > Zp \nu and the 3-body decay N > \nu l+ l-, my Zp is coupled to leptons and quarks,
is there any double counting happening the partial decay width of the above two scenario.

Best
Ouseph

Hi,

The algorithm explained in 1402.1178 is careful to avoid double counting.
So in your case the process
N > \nu l+ l-
will NOT include the "zp" propagator since that contribution is already included in the two body decay.
Obviously such separation of the two/three body strongly relies on the narrow width approximation.

Now in presence of four point interaction this is sometimes quite difficult to know if the four point interaction should be seen as a radiative correction of a three point or as a new contribution. For that case, we need the paper to follow some additional convention
which are indicated in the paper.

Cheers,

Olivier

Dear Oliver,
Thanks for the clarification, How can I include this Zprime in the 3 body decay channel.

best
ouseph

You then need to give up with the auto-width mode. This can not be done.
But you can generate your BR table with other method.

Cheers,

Olivier

Dear Oliver,
Thanks for the reply. What did you mean by the other method? Could you please explain?

Best
Ouseph

You can compute partial width with madgraph with syntax like
generate N > nu l+ l-
add process N > ....
output
launch -i
calculate_decay_widths

and as output you will get a param_card where the width and BR are included according to the process that you defined.
So in that case you are in control on the separation in 2/3 body decay and are obviously responsible of not having double counting/channel missing/...

Cheers,

Olivier

Dear Oliver,

Thank you very much for your reply.

In order to check The algorithm explained in 1402.1178 ( the double counting), I tried the following,
I only consider the Zp mediated process.

generate n1 > vm l+ l- / z w+ w-

Mn=5 GeV
Mzp=0.1 GeV

and put the width of n1 and Zp to auto in the para.card, But I am getting the following results.

( 9000005 is the zp, 9990012 is n1)

# PDG Width
DECAY 9990012 1.503533e-08
# BR NDA ID1 ID2 ...
   9.845877e-01 2 9000005 14 # 1.48036048416e-08
   1.523677e-02 3 -13 13 14 # 2.29089997468e-10
   1.755664e-04 3 -15 14 15 # 2.63970021431e-12

here I have both the 3- body and 2-body decay. According to 1402.1178 , we should only get either 2-body or 3-body to avoid double counting.

But the above results are not against the 1402.1178. How I am getting this 3-body and 2-body decay even if i stopes the decay through z and w.

Best
Ouseph

> here I have both the 3- body and 2-body decay. According to 1402.1178 ,
> we should only get either 2-body or 3-body to avoid double counting.

This is not what is stated in 1402.1178.
The main point of that paper is to have an algorithm that include in an automatic way three body decay into the computation
in a fully automatic way and without double counting.

You can see in your result that you (likely) do not have double counting since
the two body decay is much larger than the three-body decay.
If the three body decay was including the "zp" diagram, I would expect that the the three body decay to be much larger) and you would have double counting.

So from what you show i do not spot any issue (maybe I miss your issue here)

> But the above results are not against the 1402.1178. How I am getting
> this 3-body and 2-body decay even if i stopes the decay through z and w.

The auto-width is another code, which does NOT depend of the syntax of your process.
So your restriction of "/z w+ w-" is not passed to the auto-width code.
I do not think that the madwidth code has such type of option (would make only little sense) and certainly not via the "auto" shortcut.

Cheers,

Olivier

> On 2 Mar 2022, at 12:15, ouseph cj <email address hidden> wrote:
>
> Question #700772 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/700772
>
> Status: Answered => Open
>
> ouseph cj is still having a problem:
> Dear Oliver,
>
> Thank you very much for your reply.
>
> In order to check The algorithm explained in 1402.1178 ( the double counting), I tried the following,
> I only consider the Zp mediated process.
>
> generate n1 > vm l+ l- / z w+ w-
>
> Mn=5 GeV
> Mzp=0.1 GeV
>
> and put the width of n1 and Zp to auto in the para.card, But I am
> getting the following results.
>
> ( 9000005 is the zp, 9990012 is n1)
>
> # PDG Width
> DECAY 9990012 1.503533e-08
> # BR NDA ID1 ID2 ...
> 9.845877e-01 2 9000005 14 # 1.48036048416e-08
> 1.523677e-02 3 -13 13 14 # 2.29089997468e-10
> 1.755664e-04 3 -15 14 15 # 2.63970021431e-12
>
> here I have both the 3- body and 2-body decay. According to 1402.1178 ,
> we should only get either 2-body or 3-body to avoid double counting.
>
> But the above results are not against the 1402.1178. How I am getting
> this 3-body and 2-body decay even if i stopes the decay through z and w.
>
> Best
> Ouseph
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Dear Oliver,

> The auto-width is another code, which does NOT depend of the syntax of your process.
So your restriction of "/z w+ w-" is not passed to the auto-width code.

This statement makes it clear.

Thank you very much

Best
Ouseph