# Use of interference term while the width is large

Hello,
I am working with a BSM model having a heavy Z' particle decaying into heavy quarks and light leptons. For some of the parameter space, I noticed that the width of Z' can be as large as 40% of Z' mass. In that scenario, the narrow width approximation will not hold. I looked at a previously asked question:
where the suggestion was to include the interference term between diagrams for proper treatment of the large width.

I was wondering how we can force MadGraph to include such interference terms.

This is the generation command I am using in MadGraph for narrow width cases:

define p1 = g u d c s b u~ d~ c~ s~ b~ ## 5-flavour scheme
define j1 = g u d c s b u~ d~ c~ s~ b~ ## any jet
define j2 = b b~ ## only b's
# General case (inclusive)
generate p1 p1 > zp j2 j2 NP=2 QCD=2 QED=0, zp > mu+ mu-
add process p1 p1 > zp j2 NP=2 QCD=1 QED=0, zp > mu+ mu-

To include the interference term for large width, should I use this command instead
(Following this question:

:

define p1 = g u d c s b u~ d~ c~ s~ b~ ## 5-flavour scheme
define j1 = g u d c s b u~ d~ c~ s~ b~ ## any jet
define j2 = b b~ ## only b's
# General case (inclusive)
generate p1 p1 > zp j2 j2 > mu+ mu- j2 j2 NP=2 QCD=2 QED=0
add process p1 p1 > zp j2 > mu+ mu- j2 NP=2 QCD=1 QED=0

?

If this is not the right process to add interference terms, I like to know how I should do that.

Thank you very much,
Arka

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 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2022-04-25: #1

Hi,

I guess that you are looking for this syntax:

generate p1 p1 > mu+ mu- j2 j2 NP=2 QCD=2 QED=0
add process p1 p1 > mu+ mu- j2 NP=2 QCD=1 QED=0

(you do not want to force a zp propagator since it will remove the diagram with wich the interference can be relevant)

This being said, the combination of such two processes are quite weird on a QCD point of view.
Is this computation 4 or 5 flavor? It sounds like a mix of both.
The reason I asked is that I'm worried about the potential double counting between the two lines.

 Revision history for this message Arka Santra (santra-arka) said on 2022-04-26: #2

Hi Olivier,
Thank you very much for the prompt answer. We want a five flavor scheme. We checked the diagrams between line 1 and line 2 and we do not see a repetition of diagrams on a first glance. We will look at them more carefully.

I have two follow up questions.

First, we want only a zp propagator, we don't want to have interference from SM Z boson propagator. In that case, will this syntax work to include interference terms as well as only zp propagator:

define p1 = g u d c s b u~ d~ c~ s~ b~ ## 5-flavour scheme
define j1 = g u d c s b u~ d~ c~ s~ b~ ## any jet
define j2 = b b~ ## only b's
# General case (inclusive)
generate p1 p1 > zp j2 j2 > mu+ mu- j2 j2 NP=2 QCD=2 QED=0
add process p1 p1 > zp j2 > mu+ mu- j2 NP=2 QCD=1 QED=0

?

Second, this part is more related to MadWidth. I see that when I set zprime width to "Auto", then MadWidth works behind the curtain and computes zprime width and puts up a warning message:

1.
Please note that the automatic computation of the width is
only valid in narrow-width approximation and at tree-level.

For the extreme scenario in our parameter space, the automatic width calculated can be as large as 40% of the mass as stated earlier.

Now if I set the zprime width to a number (computed theoretically from the Lagrangian), I do not see the warning message 1 (even though the width is as large as 40% of the mass sometimes).
a. Does that mean MadGraph does not do narrow width approximation (NWA) in such cases where width is set manually?
Or b. Even then, NWA is done but MadWidth does not print out the warning message?
If b. above is correct, then
c. does that mean the only way to work with broad width in MadGraph is to include the interference terms?

I will be glad if you help me clarify my doubts and understand MadGraph better.

Thank you very much,
Arka

 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2022-04-27: #3

Hi,

> Thank you very much for the prompt answer. We want a five flavor scheme. We checked the diagrams between line 1 and line 2 and we do not see a repetition of diagrams on a first glance. We will look at them more carefully.

Note that , not having the same diagram twice is not enough to avoid double counting since we use renormalized PDF and renormalization of the strong coupling.

In Five flavour, "b" should normally be consider at the matrix-element level completly indistinguishable as the other flavour.
So the presence of "j2" in your process definition is apriori problematic (with the running of alpha_s and therefore the double counting between the two process). I know that this is not your question, but it is not trivial to me how you can have meaningfull result with such type of syntax (even with MLM or CKKW-L mechanism)

>First, we want only a zp propagator, we don't want to have interference from SM Z boson propagator. In that case, will this syntax work to include interference terms as well as only zp propagator:

Here two questions:
1) why you do not want them? By why it can be a physics reason (like they are suppressed due to symmetry and therefore a waste of time) or a technical reason (those are considered within the background or will be generated in a dedicated sample, ...)
The typical reason used to only consider one particle is the narrow width approximation which obviously does not hold in your case.

2) You ask me the syntax to add interference, but you do not want the interference with the Z boson, in that case, which interference do you want?

Now those syntax does not make any sense:
generate p1 p1 > zp j2 j2 > mu+ mu- j2 j2 NP=2 QCD=2 QED=0
add process p1 p1 > zp j2 > mu+ mu- j2 NP=2 QCD=1 QED=0

First because I do not understand why you ask to have at least one "j2" to be present as a S-channel.
Second the syntax "> zp j2 j2 >" is the same as ">zp j2 >" asking twice for "at least one j2 to be present in S-channel" is the same as asking once.

>Now if I set the zprime width to a number (computed theoretically from the Lagrangian), I do not see the warning message 1 (even though the width is as large as 40% of the mass sometimes).

That warning is raised as soon as you use the auto-width. If you are not using it that warning will not be printed
The phase-space integration itself does not rely on the narrow-width approximation so here they are no issue.
Now the syntax that you use can rely on the narrow width approximation for your computation to make sense.
the use of the following syntax
generate p1 p1 > zp j2 j2 NP=2 QCD=2 QED=0, zp > mu+ mu-
is based on narrow-width approximation and the phase-space integrator will be optimized accordingly.
and you will have a cut on the invariant mass of zp to try to enforce that approximation.

If you use
generate p1 p1 > zp > mu+ mu- j2 j2 NP=2 QCD=2 QED=0
here the phase-space integrator will not be optimised for the narrow-width and you will not have cut on the invariant mass.
Now you are performing a diagram filtering that need to be justified (as asked above) and the typical justification will not be working.

> c. does that mean the only way to work with broad width in MadGraph is to include the interference terms?

Here the question of MadGraph capabilities is secondary. The first question is what is the physics that I need to simulate in a broad width regime.
In that regime, I do claim that keeping interference term is a must-have.
After that we do support multiple strategy of computation (like one sample with only the interference, or one sample with BSM+interference (but not the SM contribution), or the full computation)

Cheers,

Olivier

 Revision history for this message Roy Brener (rbrener) said on 2022-05-01: #4

Dear Olivier,
I am a colleague of Arka, working jointly to simulate this signal.
Let me firstly thank you kindly again for all your help and elaborate replies. These are immensely helpful!

I'll try to address the points you've raised.

So the presence of "j2" in your process definition is apriori problematic (with the running of alpha_s and therefore the double counting between the two process). I know that this is not your question, but it is not trivial to me how you can have meaningfull result with such type of syntax (even with MLM or CKKW-L mechanism)

---> This just means we want the zp to couple to b-quarks only and generate the leading process matching that. Our j2 is a b-quark/antiquark. How could avoid double counting in that respect? Why isn't it OK to have one of the process object definitions as a b-quark?

1) why you do not want them? By why it can be a physics reason (like they are suppressed due to symmetry and therefore a waste of time) or a technical reason (those are considered within the background or will be generated in a dedicated sample, ...)
The typical reason used to only consider one particle is the narrow width approximation which obviously does not hold in your case.

---> We are conducting a search for new heavy resonances, far above the W/Z mass (our lowest zp mass is 500 GeV). Also, we are simulating (separately) the DY background stemming from Z->mumu+jb/jbjb processes (amongst other backgrounds e.g. ttbar). Moreover, if the signal we are simulating under some configurations turns out to be as wide as to the extent interference terms must be included, we would consider neglecting those configuration (as they may belong more relevantly to a tail-enhancement/non-resonant search e.g. contact interactions analysis).

First because I do not understand why you ask to have at least one "j2" to be present as a S-channel.
Second the syntax "> zp j2 j2 >" is the same as ">zp j2 >" asking twice for "at least one j2 to be present in S-channel" is the same as asking once.

---> I've just verified this to be sure about our statements. When running generate p1 p1 > zp j2 NP=2 QCD=1 QED=0, zp > mu+ mu- as the only process simulated, diagrams with only one b-jet in the final state emerge i.e. not at least one. Conversely, when running generate p1 p1 > zp j2 j2 NP=2 QCD=2 QED=0, zp > mu+ mu- as the only process simulated, diagrams with only two b-jets in the final-state emerge. So by this, it seems simulating them both together would not constitute double counting (of diagrams at least). Why would this be wrong then? I should say the reason for requiring these is because they have been found as the leading processes of our signal model. The process including two b-jets in the final state accounts for about 20% of the inclusive cross-section i.e. must be considered.
If there exists a strategy to simulate this physics more correctly, we would certainly be open to adapting our run syntax accordingly with your advice.

I think the above touches upon all the salient points, more or less.

Your thoughts would be deeply appreciated.

Cheers,

Roy

 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2022-05-01: #5

> ---> This just means we want the zp to couple to b-quarks only and
> generate the leading process matching that.

Do you mean by that that if you had put "j" and not "j2" you would have get the same diagram?
For the first process, this can make sense to me but for the second this sounds difficult.

> How could avoid double counting in that respect?

The easiest is likely to do a four flavour computation and not a five flavor computation.
In five flavor, your computation will be tricky and you need to be very careful with QCD.
Obviously for very large Zp mass, going to four flavor will introduce large log related to the b mass and I can understand that
this is not ideal either. But actually, forcing some b in the final state will anyway re-introduce such type of log.

The other solution is to replace "j2" by "j" in your computation then the 5 flavor scheme should be consistent.

> ---> We are conducting a search for new heavy resonances, far above the
> W/Z mass (our lowest zp mass is 500 GeV). Also, we are simulating
> (separately) the DY background stemming from Z->mumu+jb/jbjb processes
> (amongst other backgrounds e.g. ttbar). Moreover, if the signal we are
> simulating under some configurations turns out to be as wide as to the
> extent interference terms must be included, we would consider neglecting
> those configuration (as they may belong more relevantly to a tail-
> enhancement/non-resonant search e.g. contact interactions analysis).

So I guess that the original question does not really make sense.

> ---> I've just verified this to be sure about our statements.

I guess we are not speaking about the same part here.
generate p1 p1 > zp j2 j2 > mu+ mu- j2 j2 NP=2 QCD=2 QED=0

where the "> zp j2 j2 >" is weird since that j2 requires at least one j2 in S-channel

You are discussing the decay chain syntax which behaves differently.

> Conversely, when running generate p1 p1 > zp j2 j2 NP=2 QCD=2 QED=0, zp > mu+ mu- as the only process simulated, diagrams with only two b-jets in the final-state emerge. So by this, it seems simulating them both together would not constitute double counting (of diagrams at least). Why would this be wrong then?

Remember that computation are inclusive (we use renormalized pdf and alphas).
And the parton (which is unitary) when starting from the first process will generate more b-jet
(since this is a five flavor computation) and those b-jet will double count with the process where you ask for two b jet at the hard matrix-element level.

> If there exists a strategy to simulate this physics more correctly, we would certainly be open to adapting our run syntax accordingly with your advice.

Remember that double counting is worse than using an approximation of the computation.
If you are not worry about the precision, the first step is to only include the process with one "j2"
and let the parton-shower to generate configuration with more b.

If this is problematic (too many of those b jet are not QCD related and then not included by the parton-shower) then you need to remove the QCD double counting which means using the MLM method.
This is likely the default with your syntax, but to be consistent you need to use the method above (QCD need to be handle with care)

Cheers,

Olivier

> On 1 May 2022, at 15:05, Roy Brener <email address hidden> wrote:
>
> Question #701520 on MadGraph5_aMC@NLO changed:
>
> Roy Brener posted a new comment:
> Dear Olivier,
> I am a colleague of Arka, working jointly to simulate this signal.
> Let me firstly thank you kindly again for all your help and elaborate replies. These are immensely helpful!
>
> I'll try to address the points you've raised.
>
> So the presence of "j2" in your process definition is apriori
> problematic (with the running of alpha_s and therefore the double
> counting between the two process). I know that this is not your
> question, but it is not trivial to me how you can have meaningfull
> result with such type of syntax (even with MLM or CKKW-L mechanism)
>
> ---> This just means we want the zp to couple to b-quarks only and
> generate the leading process matching that. Our j2 is a
> b-quark/antiquark. How could avoid double counting in that respect? Why
> isn't it OK to have one of the process object definitions as a b-quark?
>
> 1) why you do not want them? By why it can be a physics reason (like they are suppressed due to symmetry and therefore a waste of time) or a technical reason (those are considered within the background or will be generated in a dedicated sample, ...)
> The typical reason used to only consider one particle is the narrow width approximation which obviously does not hold in your case.
>
> ---> We are conducting a search for new heavy resonances, far above the
> W/Z mass (our lowest zp mass is 500 GeV). Also, we are simulating
> (separately) the DY background stemming from Z->mumu+jb/jbjb processes
> (amongst other backgrounds e.g. ttbar). Moreover, if the signal we are
> simulating under some configurations turns out to be as wide as to the
> extent interference terms must be included, we would consider neglecting
> those configuration (as they may belong more relevantly to a tail-
> enhancement/non-resonant search e.g. contact interactions analysis).
>
> First because I do not understand why you ask to have at least one "j2" to be present as a S-channel.
> Second the syntax "> zp j2 j2 >" is the same as ">zp j2 >" asking twice for "at least one j2 to be present in S-channel" is the same as asking once.
>
> ---> I've just verified this to be sure about our statements. When running generate p1 p1 > zp j2 NP=2 QCD=1 QED=0, zp > mu+ mu- as the only process simulated, diagrams with only one b-jet in the final state emerge i.e. not at least one. Conversely, when running generate p1 p1 > zp j2 j2 NP=2 QCD=2 QED=0, zp > mu+ mu- as the only process simulated, diagrams with only two b-jets in the final-state emerge. So by this, it seems simulating them both together would not constitute double counting (of diagrams at least). Why would this be wrong then? I should say the reason for requiring these is because they have been found as the leading processes of our signal model. The process including two b-jets in the final state accounts for about 20% of the inclusive cross-section i.e. must be considered.
> If there exists a strategy to simulate this physics more correctly, we would certainly be open to adapting our run syntax accordingly with your advice.
>
>
> I think the above touches upon all the salient points, more or less.
>
> Your thoughts would be deeply appreciated.
>
> Cheers,
>
> Roy
>
> --

 Revision history for this message Roy Brener (rbrener) said on 2022-05-02: #6

Hi Olivier,

Thanks again for your very detailed reply. Trying to narrow things down to the essentials.

1. By double counting did you mean that b-jets from the di-b-jet process process i.e.
p1 p1 > zp j2 j2 NP=2 QCD=2 QED=0, zp > mu+ mu-
would be double-counted with b-jets from PS initiated by the single-b-jet process i.e.
p1 p1 > zp j2 NP=2 QCD=1 QED=0, zp > mu+ mu-?
However, this is only relevant when going beyond MadGraph, e.g. when simulating PS with Pythia. Is this what you meant? If it is indeed, the only fix seems to be keeping just the single-b-jet process. However, demonstrably, this ignores ~20% of the signal at MadGraph level which worries us.

2. The four-flavour scheme doesn't work for us since we are trying to simulate a signal based on a specific model which must include b-jets, where the zp only couples to b-quarks (and also slightly to s-quarks with negligible difference). This model related to violations of LFU through b->sll processes (benchmark: arXiv 1910.00014). When trying implementing the four-flavour scheme the leading subprocesses included gluons in the final state rather than b-jets, which is not what we want. This is why we are using the five-flavour scheme protons and b-quark/antiquark j2. Do you think there is a fundamental flaw in the manner in which we've implemented this here relating to QCD considerations or otherwise?

Your thoughts are always deeply appreciated.

Cheers,

Roy

 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2022-05-03: #7

Hi,

1.
let simplify
p1 p1 > zp j2 j2 NP=2 QCD=2 QED=0
To this:
b b~ > zp b b~

Some of the Feynman diagram can be split into an initial state radiation:
b > b g
followed by an "hard process"
"g b > zp b"
Since in the soft/collinear limit the gluon is onshell, you can actually use the renormalization and absorb that contribution with a renormalized pdf.

So in other word (since we use renormalized pdf), the contribution b b~ > zp b b~ is already included within g b > zp b and you do have --at least some-- double counting.

> However, this is only relevant when going beyond MadGraph, e.g. when simulating PS with Pythia.

This is NOT True, the issue is at the madgraph level since your cross-section will be (approximatively) two times too big.
In CKKW-L the parton-shower algorithm is actually modified to remove correctly the double counting, in MLM approach, the parton-shower algorith is not modified but the inclusion of the sudakov form-factor is not perfect.

> However, demonstrably, this ignores ~20% of the signal at MadGraph level which worries us.

Where this 20% is comming from?

The motivation for going to MLM/CKKW-L type of computation is the fact that the SHAPE of hard jet is not reliable from the parton-shower. (actually this is typically problematic for the second radiation described by the parton-shower, the first one being quite reliable even when hard due to special matrix-element correction)

One of the "validation" of the MLM/CKKW-L approach is that the total crosss-section after merging the sample and removing the double counting is actually back to the one when starting from the lowest multiplicity sample.

2. The four-flavour scheme doesn't work for us since we are trying to simulate a signal based on a specific model which must include b-jets, where the zp only couples to b-quarks (and also slightly to s-quarks with negligible difference).

In theory, all computation that can be done in 4 flavour can be done in 5 (and the opposite).
So your statement is too strong to my point of view.
Now I do agree that they are technical limitation (cpu limitation) and theory limitation (limitation to LO/NLO) which leads to large dependence into the log. and those can forbid to go to 4 flavour.

> When trying implementing the four-flavour scheme the leading subprocesses included gluons in the final state rather than b-jets, which is not what we want.

In four flavor your leading process will have one b quark and one light parton (gluon or quark)
the process should be (I guess)
p p > zp j2 j NP=2 QCD=1 QED=0, zp > mu+ mu-

> Do you think there is a fundamental flaw in the manner in which we've implemented this here relating to QCD considerations or otherwise?

I do not know the details of what you are doing, so I can not be specific (I have not done a review of your work/...).
But it is an understatement, that the way you answer my questions on this makes me worry about the proper treatment of QCD.