# check whether phase space finds poles

Hi

is there a way to check whether the phase space integrator misses some narrow resonances in the decay chain ? I.e. if I have e.g. a 6 particle final state from pair-production and subsequent onshell resonant decays, with e.g. width/mass ~ permill for intermediate particles, is the phase space integrator supposed to correctly identify these resonances ? I am asking because the naive factorization result (production times decay) renders a result very different from the actual madgraph result. Things are OK if I e.g. force ma~ mb+mc for an intermediate a-> b c. ? Maybe its also a feature of the process, but I want to make sure it does not come from suboptimal phase space parametrization resulting in missed resonances, and if so, whether there is a way to improve this (other than artifically enhancing the width and rescaling the final result)

Thanks a lot in advance !!

Best Tania

## Question information

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- Status:
- Solved

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- Solved by:
- Tania Robens

- Solved:
- 2020-11-21

- Last query:
- 2020-11-21

- Last reply:
- 2020-11-20

## This question was reopened

Hi,

I would not worry about the phase-space integrator for onshell resonances.

The phase-space integrator knows where such resonances are and knows the width associated to such resonances.

If those resonances are too small to be integrated numerically, you will see a warning and the code will automatically increase the width to avoid the numerical issue (and will automatically re-scale the cross-section of the resonances channel). But the threshold for such security is much smaller than 1e-3.

Now the decay chain syntax assumes that particles are onshell so a process like this

generate p p > h j , (h > w+ w-, w+ > l+ vl, w- > l- vl~)

is not valid since both W will not be onshell at the same time.

This is enforce by MG5amC by having a cut off on the invariant mass of all decaying particle (so here on the Higgs and on both W).

This force each particle to be close to his pole mass (up to BWCUt times the width), BWcut is a parameter of the run_card

So the result of the above syntax will be quite weird due to those cuts (but mainly due to the fact that you use a syntax outside of his validity range since Narrow Width Approximation is not valid for such process).

Cheers,

Olivier

Tania Robens (tania-robens) said : | #2 |

Hi Olivier

thanks. In fact the first attempt was to identify final state particles only (in the above example, this would be p p > l+ vl l- vl~). The result here agrees with the one I have from using the sytnax above, but disagrees with factorization assumptions (all in between particles are onshell).

In fact in our example we also have Ws and Z's produced onshell. Then, the strange result comes about when I let them decay via the above syntax. I also recalculated all widths up to 4 body decays (I was wondering whether I was on some threshold and in fact a new channel for any involved particle would open up, once I go away from 2 particle final states), but they all agree, so no surprise there. So I have 2 different scenarios that give the same cross section prior to decay of W and Z, the same BRs for W and Z using autowidth (checked up to 4 body decays), and then a factor 2 difference once I allow the decays.

It can of course be that physics is such that W and Z are not onshell in "reality" in one of the scenarios, although this is certainly allowed by the mass spectrum. But I am still confused. Maybe setting the BR cutoff to higher values helps...

Cheers Tania

Tania Robens (tania-robens) said : | #3 |

Sorry I mean Breit Wigner cutoff...

Hi Tania,

For this process:

p p > l+ vl l- vl~

You have multiple type of contribution:

1) p p > h, h > l+ vl l- vl~

i.e. an onshell Higgs that decays to either W/Z (typically one of them is onshell) that decays

2) p p > z z, z> l+ l-, z >vl vl~

i.e. you have two Z onshell (and therefore considering the Higgs diagram, that higgs is far-offshell but you also have other diagram that can give you that)

3) p p > z z, w+ > l+ vl, w- > l- vl~

same as above but with two Z onshell.

The size of 1 and 3 are of the same order of magnitude (do not quote me on that, this is not a precise statement) and this fact is use to measure the width of the Higgs (since the cross-section of 1 does depend of the Higgs-width but cross-section 3 does.

So yes this is a perfect example where narrow-width approximation is not valid and that far off-shell effect (for the Higgs) are actually sizeable.

Cheers,

Olivier

Tania Robens (tania-robens) said : | #5 |

Hi Olivier

I am looking at a different process in fact, in a BSM model. I look at

pp > AB, A> C Z, B > C W, Z and W decay, and in all scenarios all particles can be onshell from a kinematic point of view.

(the initial generation was p p > C C l+ nul nul nul~, but the above process is dominant)

I look at two different scenarios. In both cases everything can be onshell from a kinematic viewpoint, ie mA> mC+mZ, mB> mW+mZ, etc, although in one case mA ~ mC+mZ.

If I generate

pp > CC ZW I get the same result for both cases

If I generate

pp > CC ZW, W> nul l+, Z > nl nl~

I have a factor 2, although the Brs agree.

So the question is whether the intermediate particles and/ or W/Z are not onshell although they can be in the second case, and whether this is a correct description of the physics or not........

Cheers Tania

Hi tania.

If you are not specific, I'm afraid that my answer can not be specific either.

Did you check the FAQ:

https:/

Independently of the above points, this is not enough for mA> mC+mZ to have the narrow width approximation to be valid.

In particular in the area mA ~ mC+mZ it is "easy" for NWA to not be a correct approximation, but this highly depends of the definition of "~" in this context and of the value of the width for the three particles obviously. Now I have no clue if this is possible or not in your case since i do not have the model/benchmark.

Cheers,

Olivier

Tania Robens (tania-robens) said : | #7 |

Hi Olivier

in fact in the mA ~ mC+mZ case things work as expected... If you are willing to check I would be happy to send you the model/ param_cards. I just did not want to upload everything here.

It could very well be a physics effect, but then I want to understand it (better)

Thanks :-) Cheers Tania

Tania Robens (tania-robens) said : | #8 |

Hi Olivier

the solution is hidden elsewhere...

So for the case mA~ mZ+ mC, in fact the total width you obtain using autowidth is a factor 3 too small... this also does not get remedied if you force 3 or 4 body decay, as MG always says "but look I have a nice 2 body decay A-> Z C, this is the dominant one"

But if you do it yourself, ie you do

define alldec = l+ l- v v~ j j b b~ (with appropriate definition of the vs etc)

and then do

generate A > C alldec alldec

you obtain the correct width for A... which is a factor 3 larger than the one you obtain for A > C Z.

So now I know what happened; the question is whether there is a way to force autowidth to do the full 3 body calculation for the width and disregard the 2 body one in such cases.

Maybe this answer is already hidden somewhere in another launchpad question.

Thanks Tania

hi,

if you use "auto" in the param_card you can not choose any parameter.

But you can force the compuation of three body decay via

the compute_width XXX [OPTIONS]

But I do not think that this will work since if the decay mode is open it will not allow that 3 body contribution since it will be seen as a double counting of a two body. This make sense since the first hyppothesis of the auto-width is that narrow width approximation is valid.

Cheers,

Olivier

> On 20 Nov 2020, at 21:35, Tania Robens <email address hidden> wrote:

>

> Question #694098 on MadGraph5_aMC@NLO changed:

> https:/

>

> Tania Robens gave more information on the question:

> Hi Olivier

>

> the solution is hidden elsewhere...

>

> So for the case mA~ mZ+ mC, in fact the total width you obtain using

> autowidth is a factor 3 too small... this also does not get remedied if

> you force 3 or 4 body decay, as MG always says "but look I have a nice 2

> body decay A-> Z C, this is the dominant one"

>

> But if you do it yourself, ie you do

>

> define alldec = l+ l- v v~ j j b b~ (with appropriate definition of the

> vs etc)

>

> and then do

>

> generate A > C alldec alldec

>

> you obtain the correct width for A... which is a factor 3 larger than

> the one you obtain for A > C Z.

>

> So now I know what happened; the question is whether there is a way to

> force autowidth to do the full 3 body calculation for the width and

> disregard the 2 body one in such cases.

>

> Maybe this answer is already hidden somewhere in another launchpad

> question.

>

> Thanks Tania

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

Tania Robens (tania-robens) said : | #10 |

Hi Olivier

OK thanks. I did some more checks and things now work as expected... so I understand whats going on. Care must be taken for nearly mass-degenerate scenarios (with the above mA ~ mB + mC) with respect to autowidth, better to cross check using the above recipe.

I think this closes this thread then.

Stay healthy ! Tania