Combinatorics error with identical decays

[David Curtin]

I have a MG model where the higgs can decay to a "dark Z", called Zp, which has similar decays to the regular Z.

I can set parameters so that there is no h_Z_Zp vertex, just h_Zp_Zp. Furthermore, I set masses such that mZp < mh/2 (though that last part isn't important for the bug).

If I then calculate the partial width
h > zp ll, zp > ll
I get TWICE the partial width that I get from
h > zp zp, zp > ll

The latter is correct (verified by analytical calculation). The former is wrong by an extra factor of two.

This factor of two likely arises because MG does not realize that the 'first' MG decay (which happens in the 1->3 matrix element) is the same as the 'second' decay (of the 'on-shell Zp', though in this case both Zp are on-shell, and any way this shouldn't matter), so when it does the 'first' decay MG puts in an extra factor of two to account for the possibility that either of the two Zp could undergo that first decay.

[David Curtin (david-r-curtin)]

Note: if my interpretation is correct, this bug should also arise when calculating

h > z ll, z > ll
vs
h > 4l
(which is dominated by h>z*z > 4l)

[Olivier Mattelaer (olivier-mattelaer)]

Hi David,

Thanks a lot for this interesting fact. This is really useful that you report this to us.
However I’m not sure if this is a bug or just a case where the notion of Narrow-width-Approximation (and the factorization of the amplitude/restriction to a sub-set of diagram)
is valid. I think that this is the second option, but I would like to discuss this with some other developer before deciding what to do to either clarify/fix this situation.
Obviously, I’ll keep you in touch.

Thanks again,

Olivier

On Sep 9, 2014, at 5:54 PM, David Curtin <email address hidden> wrote:

> Note: if my interpretation is correct, this bug should also arise when
> calculating
>
> h > z ll, z > ll
> vs
> h > 4l
> (which is dominated by h>z*z > 4l)
>
> --
> You received this bug notification because you are subscribed to
> MadGraph5_aMC@NLO.
> https://bugs.launchpad.net/bugs/1367374
>
> Title:
> Combinatorics error with identical decays
>
> Status in MadGraph5_aMC@NLO Generator:
> New
>
> Bug description:
> I have a MG model where the higgs can decay to a "dark Z", called Zp,
> which has similar decays to the regular Z.
>
> I can set parameters so that there is no h_Z_Zp vertex, just h_Zp_Zp.
> Furthermore, I set masses such that mZp < mh/2 (though that last part
> isn't important for the bug).
>
> If I then calculate the partial width
> h > zp ll, zp > ll
> I get TWICE the partial width that I get from
> h > zp zp, zp > ll
>
> The latter is correct (verified by analytical calculation). The former
> is wrong by an extra factor of two.
>
> This factor of two likely arises because MG does not realize that the
> 'first' MG decay (which happens in the 1->3 matrix element) is the
> same as the 'second' decay (of the 'on-shell Zp', though in this case
> both Zp are on-shell, and any way this shouldn't matter), so when it
> does the 'first' decay MG puts in an extra factor of two to account
> for the possibility that either of the two Zp could undergo that first
> decay.
>
> To manage notifications about this bug go to:
> https://bugs.launchpad.net/mg5amcnlo/+bug/1367374/+subscriptions